Properties

Label 880.2.bo.j.641.2
Level $880$
Weight $2$
Character 880.641
Analytic conductor $7.027$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(81,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bo (of order \(5\), degree \(4\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 641.2
Root \(0.421568 + 1.29745i\) of defining polynomial
Character \(\chi\) \(=\) 880.641
Dual form 880.2.bo.j.81.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.260543 - 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.46997 + 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +O(q^{10})\) \(q+(-0.260543 - 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.46997 + 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +(-0.231864 + 3.30851i) q^{11} +(-3.06058 + 2.22364i) q^{13} +(0.260543 - 0.801870i) q^{15} +(-4.03055 - 2.92836i) q^{17} +(-0.964489 - 2.96839i) q^{19} +4.01074 q^{21} -9.39001 q^{23} +(0.309017 + 0.951057i) q^{25} +(-3.60777 - 2.62120i) q^{27} +(-0.805585 + 2.47934i) q^{29} +(-2.98421 + 2.16816i) q^{31} +(2.71341 - 0.676086i) q^{33} +(-3.84844 + 2.79605i) q^{35} +(-1.06536 + 3.27883i) q^{37} +(2.58048 + 1.87483i) q^{39} +(2.88263 + 8.87181i) q^{41} +11.7051 q^{43} +2.28912 q^{45} +(0.513451 + 1.58024i) q^{47} +(-12.6436 - 9.18613i) q^{49} +(-1.29804 + 3.99494i) q^{51} +(1.56945 - 1.14027i) q^{53} +(-2.13228 + 2.54035i) q^{55} +(-2.12897 + 1.54679i) q^{57} +(-0.0321114 + 0.0988288i) q^{59} +(8.21258 + 5.96679i) q^{61} +(3.36494 + 10.3562i) q^{63} -3.78308 q^{65} +4.99277 q^{67} +(2.44651 + 7.52957i) q^{69} +(-5.03960 - 3.66149i) q^{71} +(-2.25783 + 6.94889i) q^{73} +(0.682112 - 0.495583i) q^{75} +(-14.6272 - 5.91239i) q^{77} +(8.53069 - 6.19791i) q^{79} +(0.960251 - 2.95535i) q^{81} +(4.60338 + 3.34455i) q^{83} +(-1.53953 - 4.73819i) q^{85} +2.19800 q^{87} +13.6371 q^{89} +(-5.56102 - 17.1151i) q^{91} +(2.51610 + 1.82805i) q^{93} +(0.964489 - 2.96839i) q^{95} +(-11.0809 + 8.05072i) q^{97} +(4.02224 + 6.43913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9} + 4 q^{11} - 7 q^{13} - q^{15} + 7 q^{17} - 3 q^{19} + 4 q^{21} - 36 q^{23} - 3 q^{25} - 8 q^{27} + 13 q^{29} - 2 q^{31} - 19 q^{33} + 2 q^{35} - 22 q^{37} + q^{39} + 7 q^{41} - 6 q^{43} - 20 q^{45} + 2 q^{47} - 19 q^{49} + 33 q^{51} + 3 q^{53} - 4 q^{55} - 25 q^{57} - 19 q^{59} + 22 q^{61} + 2 q^{63} + 12 q^{65} - 22 q^{67} + 21 q^{69} - 44 q^{71} + 17 q^{73} + q^{75} - 38 q^{77} + 43 q^{79} - 85 q^{81} + 15 q^{83} + 18 q^{85} - 50 q^{87} + 2 q^{89} - 59 q^{91} + 5 q^{93} + 3 q^{95} - 20 q^{97} + 79 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

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
\(3\) −0.260543 0.801870i −0.150425 0.462960i 0.847244 0.531204i \(-0.178260\pi\)
−0.997669 + 0.0682442i \(0.978260\pi\)
\(4\) 0 0
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) 0 0
\(7\) −1.46997 + 4.52411i −0.555597 + 1.70995i 0.138764 + 0.990325i \(0.455687\pi\)
−0.694361 + 0.719627i \(0.744313\pi\)
\(8\) 0 0
\(9\) 1.85194 1.34551i 0.617313 0.448504i
\(10\) 0 0
\(11\) −0.231864 + 3.30851i −0.0699096 + 0.997553i
\(12\) 0 0
\(13\) −3.06058 + 2.22364i −0.848851 + 0.616726i −0.924829 0.380383i \(-0.875792\pi\)
0.0759779 + 0.997109i \(0.475792\pi\)
\(14\) 0 0
\(15\) 0.260543 0.801870i 0.0672720 0.207042i
\(16\) 0 0
\(17\) −4.03055 2.92836i −0.977551 0.710233i −0.0203914 0.999792i \(-0.506491\pi\)
−0.957160 + 0.289559i \(0.906491\pi\)
\(18\) 0 0
\(19\) −0.964489 2.96839i −0.221269 0.680996i −0.998649 0.0519645i \(-0.983452\pi\)
0.777380 0.629031i \(-0.216548\pi\)
\(20\) 0 0
\(21\) 4.01074 0.875215
\(22\) 0 0
\(23\) −9.39001 −1.95795 −0.978976 0.203975i \(-0.934614\pi\)
−0.978976 + 0.203975i \(0.934614\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 0 0
\(27\) −3.60777 2.62120i −0.694316 0.504450i
\(28\) 0 0
\(29\) −0.805585 + 2.47934i −0.149593 + 0.460401i −0.997573 0.0696276i \(-0.977819\pi\)
0.847980 + 0.530029i \(0.177819\pi\)
\(30\) 0 0
\(31\) −2.98421 + 2.16816i −0.535980 + 0.389413i −0.822590 0.568635i \(-0.807472\pi\)
0.286610 + 0.958047i \(0.407472\pi\)
\(32\) 0 0
\(33\) 2.71341 0.676086i 0.472343 0.117691i
\(34\) 0 0
\(35\) −3.84844 + 2.79605i −0.650504 + 0.472619i
\(36\) 0 0
\(37\) −1.06536 + 3.27883i −0.175143 + 0.539036i −0.999640 0.0268308i \(-0.991458\pi\)
0.824497 + 0.565867i \(0.191458\pi\)
\(38\) 0 0
\(39\) 2.58048 + 1.87483i 0.413208 + 0.300213i
\(40\) 0 0
\(41\) 2.88263 + 8.87181i 0.450190 + 1.38554i 0.876690 + 0.481056i \(0.159747\pi\)
−0.426499 + 0.904488i \(0.640253\pi\)
\(42\) 0 0
\(43\) 11.7051 1.78500 0.892502 0.451043i \(-0.148948\pi\)
0.892502 + 0.451043i \(0.148948\pi\)
\(44\) 0 0
\(45\) 2.28912 0.341242
\(46\) 0 0
\(47\) 0.513451 + 1.58024i 0.0748945 + 0.230502i 0.981495 0.191489i \(-0.0613316\pi\)
−0.906600 + 0.421990i \(0.861332\pi\)
\(48\) 0 0
\(49\) −12.6436 9.18613i −1.80623 1.31230i
\(50\) 0 0
\(51\) −1.29804 + 3.99494i −0.181761 + 0.559404i
\(52\) 0 0
\(53\) 1.56945 1.14027i 0.215580 0.156628i −0.474755 0.880118i \(-0.657463\pi\)
0.690335 + 0.723490i \(0.257463\pi\)
\(54\) 0 0
\(55\) −2.13228 + 2.54035i −0.287516 + 0.342541i
\(56\) 0 0
\(57\) −2.12897 + 1.54679i −0.281990 + 0.204877i
\(58\) 0 0
\(59\) −0.0321114 + 0.0988288i −0.00418055 + 0.0128664i −0.953125 0.302577i \(-0.902153\pi\)
0.948944 + 0.315443i \(0.102153\pi\)
\(60\) 0 0
\(61\) 8.21258 + 5.96679i 1.05151 + 0.763969i 0.972499 0.232905i \(-0.0748231\pi\)
0.0790130 + 0.996874i \(0.474823\pi\)
\(62\) 0 0
\(63\) 3.36494 + 10.3562i 0.423943 + 1.30476i
\(64\) 0 0
\(65\) −3.78308 −0.469233
\(66\) 0 0
\(67\) 4.99277 0.609964 0.304982 0.952358i \(-0.401350\pi\)
0.304982 + 0.952358i \(0.401350\pi\)
\(68\) 0 0
\(69\) 2.44651 + 7.52957i 0.294525 + 0.906454i
\(70\) 0 0
\(71\) −5.03960 3.66149i −0.598091 0.434538i 0.247110 0.968987i \(-0.420519\pi\)
−0.845201 + 0.534449i \(0.820519\pi\)
\(72\) 0 0
\(73\) −2.25783 + 6.94889i −0.264259 + 0.813306i 0.727604 + 0.685998i \(0.240634\pi\)
−0.991863 + 0.127309i \(0.959366\pi\)
\(74\) 0 0
\(75\) 0.682112 0.495583i 0.0787635 0.0572250i
\(76\) 0 0
\(77\) −14.6272 5.91239i −1.66693 0.673780i
\(78\) 0 0
\(79\) 8.53069 6.19791i 0.959778 0.697319i 0.00667849 0.999978i \(-0.497874\pi\)
0.953099 + 0.302658i \(0.0978742\pi\)
\(80\) 0 0
\(81\) 0.960251 2.95535i 0.106695 0.328372i
\(82\) 0 0
\(83\) 4.60338 + 3.34455i 0.505287 + 0.367113i 0.811033 0.585001i \(-0.198906\pi\)
−0.305746 + 0.952113i \(0.598906\pi\)
\(84\) 0 0
\(85\) −1.53953 4.73819i −0.166986 0.513929i
\(86\) 0 0
\(87\) 2.19800 0.235650
\(88\) 0 0
\(89\) 13.6371 1.44553 0.722767 0.691091i \(-0.242870\pi\)
0.722767 + 0.691091i \(0.242870\pi\)
\(90\) 0 0
\(91\) −5.56102 17.1151i −0.582953 1.79415i
\(92\) 0 0
\(93\) 2.51610 + 1.82805i 0.260907 + 0.189560i
\(94\) 0 0
\(95\) 0.964489 2.96839i 0.0989545 0.304551i
\(96\) 0 0
\(97\) −11.0809 + 8.05072i −1.12509 + 0.817427i −0.984973 0.172708i \(-0.944748\pi\)
−0.140118 + 0.990135i \(0.544748\pi\)
\(98\) 0 0
\(99\) 4.02224 + 6.43913i 0.404250 + 0.647157i
\(100\) 0 0
\(101\) −3.91797 + 2.84657i −0.389852 + 0.283244i −0.765395 0.643561i \(-0.777456\pi\)
0.375543 + 0.926805i \(0.377456\pi\)
\(102\) 0 0
\(103\) −0.279529 + 0.860303i −0.0275428 + 0.0847682i −0.963883 0.266326i \(-0.914190\pi\)
0.936340 + 0.351094i \(0.114190\pi\)
\(104\) 0 0
\(105\) 3.24476 + 2.35745i 0.316656 + 0.230064i
\(106\) 0 0
\(107\) 4.57082 + 14.0675i 0.441878 + 1.35996i 0.885872 + 0.463931i \(0.153561\pi\)
−0.443994 + 0.896030i \(0.646439\pi\)
\(108\) 0 0
\(109\) 3.39429 0.325114 0.162557 0.986699i \(-0.448026\pi\)
0.162557 + 0.986699i \(0.448026\pi\)
\(110\) 0 0
\(111\) 2.90677 0.275898
\(112\) 0 0
\(113\) −3.14440 9.67748i −0.295801 0.910381i −0.982951 0.183866i \(-0.941139\pi\)
0.687151 0.726515i \(-0.258861\pi\)
\(114\) 0 0
\(115\) −7.59668 5.51931i −0.708394 0.514678i
\(116\) 0 0
\(117\) −2.67607 + 8.23608i −0.247402 + 0.761426i
\(118\) 0 0
\(119\) 19.1730 13.9300i 1.75759 1.27696i
\(120\) 0 0
\(121\) −10.8925 1.53425i −0.990225 0.139477i
\(122\) 0 0
\(123\) 6.36299 4.62298i 0.573732 0.416840i
\(124\) 0 0
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) −8.86580 6.44138i −0.786712 0.571580i 0.120274 0.992741i \(-0.461623\pi\)
−0.906986 + 0.421161i \(0.861623\pi\)
\(128\) 0 0
\(129\) −3.04968 9.38594i −0.268509 0.826386i
\(130\) 0 0
\(131\) −12.9021 −1.12726 −0.563631 0.826027i \(-0.690596\pi\)
−0.563631 + 0.826027i \(0.690596\pi\)
\(132\) 0 0
\(133\) 14.8471 1.28741
\(134\) 0 0
\(135\) −1.37805 4.24119i −0.118603 0.365023i
\(136\) 0 0
\(137\) −15.2762 11.0988i −1.30514 0.948236i −0.305144 0.952306i \(-0.598705\pi\)
−0.999992 + 0.00406991i \(0.998705\pi\)
\(138\) 0 0
\(139\) −3.36495 + 10.3563i −0.285412 + 0.878406i 0.700863 + 0.713295i \(0.252798\pi\)
−0.986275 + 0.165111i \(0.947202\pi\)
\(140\) 0 0
\(141\) 1.13337 0.823442i 0.0954471 0.0693463i
\(142\) 0 0
\(143\) −6.64729 10.6415i −0.555875 0.889889i
\(144\) 0 0
\(145\) −2.10905 + 1.53231i −0.175147 + 0.127252i
\(146\) 0 0
\(147\) −4.07187 + 12.5319i −0.335842 + 1.03362i
\(148\) 0 0
\(149\) −1.37058 0.995782i −0.112282 0.0815776i 0.530227 0.847856i \(-0.322107\pi\)
−0.642509 + 0.766278i \(0.722107\pi\)
\(150\) 0 0
\(151\) 1.07842 + 3.31904i 0.0877606 + 0.270099i 0.985299 0.170836i \(-0.0546468\pi\)
−0.897539 + 0.440935i \(0.854647\pi\)
\(152\) 0 0
\(153\) −11.4045 −0.921997
\(154\) 0 0
\(155\) −3.68869 −0.296283
\(156\) 0 0
\(157\) 6.39675 + 19.6872i 0.510517 + 1.57121i 0.791294 + 0.611435i \(0.209408\pi\)
−0.280778 + 0.959773i \(0.590592\pi\)
\(158\) 0 0
\(159\) −1.32326 0.961403i −0.104941 0.0762442i
\(160\) 0 0
\(161\) 13.8030 42.4814i 1.08783 3.34800i
\(162\) 0 0
\(163\) 13.2542 9.62977i 1.03815 0.754262i 0.0682284 0.997670i \(-0.478265\pi\)
0.969924 + 0.243408i \(0.0782653\pi\)
\(164\) 0 0
\(165\) 2.59259 + 1.04794i 0.201833 + 0.0815817i
\(166\) 0 0
\(167\) 11.6508 8.46481i 0.901567 0.655027i −0.0373009 0.999304i \(-0.511876\pi\)
0.938868 + 0.344277i \(0.111876\pi\)
\(168\) 0 0
\(169\) 0.405336 1.24750i 0.0311797 0.0959612i
\(170\) 0 0
\(171\) −5.78018 4.19955i −0.442021 0.321147i
\(172\) 0 0
\(173\) −2.51031 7.72595i −0.190855 0.587393i 0.809144 0.587610i \(-0.199931\pi\)
−1.00000 0.000216923i \(0.999931\pi\)
\(174\) 0 0
\(175\) −4.75693 −0.359590
\(176\) 0 0
\(177\) 0.0876143 0.00658549
\(178\) 0 0
\(179\) −0.925011 2.84689i −0.0691386 0.212787i 0.910517 0.413471i \(-0.135684\pi\)
−0.979656 + 0.200684i \(0.935684\pi\)
\(180\) 0 0
\(181\) 11.7521 + 8.53841i 0.873527 + 0.634655i 0.931531 0.363662i \(-0.118474\pi\)
−0.0580038 + 0.998316i \(0.518474\pi\)
\(182\) 0 0
\(183\) 2.64486 8.14003i 0.195513 0.601728i
\(184\) 0 0
\(185\) −2.78914 + 2.02643i −0.205062 + 0.148986i
\(186\) 0 0
\(187\) 10.6231 12.6561i 0.776835 0.925508i
\(188\) 0 0
\(189\) 17.1619 12.4689i 1.24835 0.906976i
\(190\) 0 0
\(191\) 2.46207 7.57746i 0.178149 0.548286i −0.821614 0.570044i \(-0.806926\pi\)
0.999763 + 0.0217578i \(0.00692628\pi\)
\(192\) 0 0
\(193\) 15.7728 + 11.4596i 1.13535 + 0.824879i 0.986464 0.163976i \(-0.0524320\pi\)
0.148884 + 0.988855i \(0.452432\pi\)
\(194\) 0 0
\(195\) 0.985657 + 3.03354i 0.0705843 + 0.217236i
\(196\) 0 0
\(197\) 17.9751 1.28067 0.640336 0.768095i \(-0.278795\pi\)
0.640336 + 0.768095i \(0.278795\pi\)
\(198\) 0 0
\(199\) 7.17717 0.508776 0.254388 0.967102i \(-0.418126\pi\)
0.254388 + 0.967102i \(0.418126\pi\)
\(200\) 0 0
\(201\) −1.30083 4.00355i −0.0917537 0.282389i
\(202\) 0 0
\(203\) −10.0326 7.28911i −0.704150 0.511595i
\(204\) 0 0
\(205\) −2.88263 + 8.87181i −0.201331 + 0.619634i
\(206\) 0 0
\(207\) −17.3897 + 12.6344i −1.20867 + 0.878149i
\(208\) 0 0
\(209\) 10.0446 2.50276i 0.694798 0.173119i
\(210\) 0 0
\(211\) −3.58625 + 2.60556i −0.246888 + 0.179374i −0.704346 0.709857i \(-0.748760\pi\)
0.457459 + 0.889231i \(0.348760\pi\)
\(212\) 0 0
\(213\) −1.62300 + 4.99508i −0.111206 + 0.342257i
\(214\) 0 0
\(215\) 9.46959 + 6.88006i 0.645821 + 0.469216i
\(216\) 0 0
\(217\) −5.42227 16.6880i −0.368088 1.13286i
\(218\) 0 0
\(219\) 6.16037 0.416280
\(220\) 0 0
\(221\) 18.8474 1.26781
\(222\) 0 0
\(223\) 4.70031 + 14.4661i 0.314756 + 0.968720i 0.975855 + 0.218421i \(0.0700906\pi\)
−0.661098 + 0.750299i \(0.729909\pi\)
\(224\) 0 0
\(225\) 1.85194 + 1.34551i 0.123463 + 0.0897008i
\(226\) 0 0
\(227\) −1.32382 + 4.07431i −0.0878652 + 0.270421i −0.985329 0.170667i \(-0.945408\pi\)
0.897463 + 0.441089i \(0.145408\pi\)
\(228\) 0 0
\(229\) 3.31418 2.40789i 0.219007 0.159118i −0.472872 0.881131i \(-0.656783\pi\)
0.691880 + 0.722013i \(0.256783\pi\)
\(230\) 0 0
\(231\) −0.929945 + 13.2696i −0.0611859 + 0.873074i
\(232\) 0 0
\(233\) 13.9580 10.1411i 0.914421 0.664365i −0.0277085 0.999616i \(-0.508821\pi\)
0.942129 + 0.335251i \(0.108821\pi\)
\(234\) 0 0
\(235\) −0.513451 + 1.58024i −0.0334938 + 0.103083i
\(236\) 0 0
\(237\) −7.19253 5.22568i −0.467205 0.339445i
\(238\) 0 0
\(239\) 1.05259 + 3.23954i 0.0680865 + 0.209549i 0.979311 0.202362i \(-0.0648617\pi\)
−0.911224 + 0.411910i \(0.864862\pi\)
\(240\) 0 0
\(241\) −20.1839 −1.30016 −0.650080 0.759866i \(-0.725265\pi\)
−0.650080 + 0.759866i \(0.725265\pi\)
\(242\) 0 0
\(243\) −15.9983 −1.02629
\(244\) 0 0
\(245\) −4.82943 14.8635i −0.308541 0.949592i
\(246\) 0 0
\(247\) 9.55252 + 6.94031i 0.607813 + 0.441602i
\(248\) 0 0
\(249\) 1.48252 4.56272i 0.0939507 0.289151i
\(250\) 0 0
\(251\) 15.9353 11.5777i 1.00583 0.730776i 0.0424968 0.999097i \(-0.486469\pi\)
0.963330 + 0.268321i \(0.0864688\pi\)
\(252\) 0 0
\(253\) 2.17720 31.0669i 0.136880 1.95316i
\(254\) 0 0
\(255\) −3.39830 + 2.46901i −0.212810 + 0.154615i
\(256\) 0 0
\(257\) −3.31063 + 10.1891i −0.206512 + 0.635577i 0.793136 + 0.609044i \(0.208447\pi\)
−0.999648 + 0.0265331i \(0.991553\pi\)
\(258\) 0 0
\(259\) −13.2677 9.63957i −0.824417 0.598974i
\(260\) 0 0
\(261\) 1.84408 + 5.67550i 0.114146 + 0.351305i
\(262\) 0 0
\(263\) −8.86317 −0.546527 −0.273263 0.961939i \(-0.588103\pi\)
−0.273263 + 0.961939i \(0.588103\pi\)
\(264\) 0 0
\(265\) 1.93994 0.119170
\(266\) 0 0
\(267\) −3.55307 10.9352i −0.217444 0.669225i
\(268\) 0 0
\(269\) 1.74328 + 1.26656i 0.106289 + 0.0772238i 0.639660 0.768658i \(-0.279075\pi\)
−0.533371 + 0.845881i \(0.679075\pi\)
\(270\) 0 0
\(271\) −3.16904 + 9.75331i −0.192506 + 0.592472i 0.807491 + 0.589880i \(0.200825\pi\)
−0.999997 + 0.00259160i \(0.999175\pi\)
\(272\) 0 0
\(273\) −12.2752 + 8.91844i −0.742927 + 0.539768i
\(274\) 0 0
\(275\) −3.21823 + 0.801870i −0.194067 + 0.0483546i
\(276\) 0 0
\(277\) −11.9939 + 8.71410i −0.720645 + 0.523579i −0.886590 0.462556i \(-0.846933\pi\)
0.165945 + 0.986135i \(0.446933\pi\)
\(278\) 0 0
\(279\) −2.60930 + 8.03059i −0.156214 + 0.480779i
\(280\) 0 0
\(281\) 13.6295 + 9.90242i 0.813069 + 0.590729i 0.914719 0.404091i \(-0.132412\pi\)
−0.101650 + 0.994820i \(0.532412\pi\)
\(282\) 0 0
\(283\) 1.51240 + 4.65468i 0.0899028 + 0.276692i 0.985892 0.167384i \(-0.0535320\pi\)
−0.895989 + 0.444076i \(0.853532\pi\)
\(284\) 0 0
\(285\) −2.63156 −0.155880
\(286\) 0 0
\(287\) −44.3744 −2.61934
\(288\) 0 0
\(289\) 2.41671 + 7.43787i 0.142159 + 0.437522i
\(290\) 0 0
\(291\) 9.34268 + 6.78786i 0.547678 + 0.397911i
\(292\) 0 0
\(293\) 3.69507 11.3723i 0.215869 0.664375i −0.783222 0.621742i \(-0.786425\pi\)
0.999091 0.0426332i \(-0.0135747\pi\)
\(294\) 0 0
\(295\) −0.0840688 + 0.0610796i −0.00489467 + 0.00355619i
\(296\) 0 0
\(297\) 9.50878 11.3286i 0.551755 0.657351i
\(298\) 0 0
\(299\) 28.7388 20.8800i 1.66201 1.20752i
\(300\) 0 0
\(301\) −17.2061 + 52.9549i −0.991743 + 3.05227i
\(302\) 0 0
\(303\) 3.30338 + 2.40005i 0.189774 + 0.137879i
\(304\) 0 0
\(305\) 3.13692 + 9.65446i 0.179620 + 0.552813i
\(306\) 0 0
\(307\) −16.8325 −0.960680 −0.480340 0.877082i \(-0.659487\pi\)
−0.480340 + 0.877082i \(0.659487\pi\)
\(308\) 0 0
\(309\) 0.762681 0.0433874
\(310\) 0 0
\(311\) −7.60024 23.3911i −0.430970 1.32639i −0.897160 0.441705i \(-0.854374\pi\)
0.466190 0.884684i \(-0.345626\pi\)
\(312\) 0 0
\(313\) −5.83297 4.23790i −0.329699 0.239540i 0.410604 0.911814i \(-0.365318\pi\)
−0.740303 + 0.672274i \(0.765318\pi\)
\(314\) 0 0
\(315\) −3.36494 + 10.3562i −0.189593 + 0.583508i
\(316\) 0 0
\(317\) 6.92439 5.03086i 0.388912 0.282561i −0.376097 0.926580i \(-0.622734\pi\)
0.765010 + 0.644019i \(0.222734\pi\)
\(318\) 0 0
\(319\) −8.01612 3.24016i −0.448817 0.181414i
\(320\) 0 0
\(321\) 10.0894 7.33041i 0.563138 0.409144i
\(322\) 0 0
\(323\) −4.80511 + 14.7886i −0.267364 + 0.822861i
\(324\) 0 0
\(325\) −3.06058 2.22364i −0.169770 0.123345i
\(326\) 0 0
\(327\) −0.884359 2.72178i −0.0489052 0.150515i
\(328\) 0 0
\(329\) −7.90393 −0.435758
\(330\) 0 0
\(331\) 25.4094 1.39662 0.698312 0.715793i \(-0.253935\pi\)
0.698312 + 0.715793i \(0.253935\pi\)
\(332\) 0 0
\(333\) 2.43873 + 7.50564i 0.133642 + 0.411306i
\(334\) 0 0
\(335\) 4.03924 + 2.93468i 0.220687 + 0.160339i
\(336\) 0 0
\(337\) −5.85288 + 18.0133i −0.318827 + 0.981248i 0.655324 + 0.755348i \(0.272532\pi\)
−0.974150 + 0.225900i \(0.927468\pi\)
\(338\) 0 0
\(339\) −6.94083 + 5.04281i −0.376974 + 0.273888i
\(340\) 0 0
\(341\) −6.48144 10.3760i −0.350990 0.561893i
\(342\) 0 0
\(343\) 33.2057 24.1254i 1.79294 1.30265i
\(344\) 0 0
\(345\) −2.44651 + 7.52957i −0.131715 + 0.405378i
\(346\) 0 0
\(347\) −6.38484 4.63885i −0.342756 0.249027i 0.403068 0.915170i \(-0.367944\pi\)
−0.745824 + 0.666143i \(0.767944\pi\)
\(348\) 0 0
\(349\) 2.30483 + 7.09353i 0.123375 + 0.379708i 0.993601 0.112943i \(-0.0360278\pi\)
−0.870227 + 0.492651i \(0.836028\pi\)
\(350\) 0 0
\(351\) 16.8705 0.900478
\(352\) 0 0
\(353\) −2.03405 −0.108262 −0.0541308 0.998534i \(-0.517239\pi\)
−0.0541308 + 0.998534i \(0.517239\pi\)
\(354\) 0 0
\(355\) −1.92496 5.92441i −0.102166 0.314435i
\(356\) 0 0
\(357\) −16.1655 11.7449i −0.855568 0.621606i
\(358\) 0 0
\(359\) −5.03775 + 15.5046i −0.265882 + 0.818301i 0.725607 + 0.688110i \(0.241559\pi\)
−0.991489 + 0.130191i \(0.958441\pi\)
\(360\) 0 0
\(361\) 7.49021 5.44196i 0.394222 0.286419i
\(362\) 0 0
\(363\) 1.60770 + 9.13409i 0.0843822 + 0.479416i
\(364\) 0 0
\(365\) −5.91108 + 4.29465i −0.309400 + 0.224792i
\(366\) 0 0
\(367\) 0.238220 0.733165i 0.0124350 0.0382709i −0.944647 0.328090i \(-0.893595\pi\)
0.957081 + 0.289819i \(0.0935951\pi\)
\(368\) 0 0
\(369\) 17.2756 + 12.5514i 0.899330 + 0.653402i
\(370\) 0 0
\(371\) 2.85166 + 8.77652i 0.148051 + 0.455654i
\(372\) 0 0
\(373\) −5.01958 −0.259904 −0.129952 0.991520i \(-0.541482\pi\)
−0.129952 + 0.991520i \(0.541482\pi\)
\(374\) 0 0
\(375\) 0.843136 0.0435394
\(376\) 0 0
\(377\) −3.04759 9.37953i −0.156959 0.483070i
\(378\) 0 0
\(379\) 2.95681 + 2.14825i 0.151881 + 0.110348i 0.661130 0.750271i \(-0.270077\pi\)
−0.509250 + 0.860619i \(0.670077\pi\)
\(380\) 0 0
\(381\) −2.85522 + 8.78748i −0.146278 + 0.450196i
\(382\) 0 0
\(383\) 4.43460 3.22192i 0.226597 0.164633i −0.468694 0.883361i \(-0.655275\pi\)
0.695291 + 0.718728i \(0.255275\pi\)
\(384\) 0 0
\(385\) −8.35846 13.3809i −0.425986 0.681953i
\(386\) 0 0
\(387\) 21.6770 15.7493i 1.10191 0.800581i
\(388\) 0 0
\(389\) 0.259746 0.799417i 0.0131697 0.0405321i −0.944256 0.329213i \(-0.893217\pi\)
0.957425 + 0.288681i \(0.0932166\pi\)
\(390\) 0 0
\(391\) 37.8469 + 27.4974i 1.91400 + 1.39060i
\(392\) 0 0
\(393\) 3.36156 + 10.3458i 0.169568 + 0.521877i
\(394\) 0 0
\(395\) 10.5445 0.530552
\(396\) 0 0
\(397\) 3.61935 0.181650 0.0908249 0.995867i \(-0.471050\pi\)
0.0908249 + 0.995867i \(0.471050\pi\)
\(398\) 0 0
\(399\) −3.86831 11.9054i −0.193658 0.596018i
\(400\) 0 0
\(401\) −8.16132 5.92954i −0.407557 0.296107i 0.365055 0.930986i \(-0.381050\pi\)
−0.772612 + 0.634879i \(0.781050\pi\)
\(402\) 0 0
\(403\) 4.31221 13.2716i 0.214807 0.661107i
\(404\) 0 0
\(405\) 2.51397 1.82651i 0.124920 0.0907598i
\(406\) 0 0
\(407\) −10.6010 4.28498i −0.525473 0.212399i
\(408\) 0 0
\(409\) −10.0189 + 7.27916i −0.495403 + 0.359931i −0.807258 0.590198i \(-0.799050\pi\)
0.311855 + 0.950130i \(0.399050\pi\)
\(410\) 0 0
\(411\) −4.91970 + 15.1413i −0.242671 + 0.746864i
\(412\) 0 0
\(413\) −0.399909 0.290551i −0.0196783 0.0142971i
\(414\) 0 0
\(415\) 1.75834 + 5.41160i 0.0863133 + 0.265645i
\(416\) 0 0
\(417\) 9.18109 0.449600
\(418\) 0 0
\(419\) 0.612942 0.0299442 0.0149721 0.999888i \(-0.495234\pi\)
0.0149721 + 0.999888i \(0.495234\pi\)
\(420\) 0 0
\(421\) −10.3660 31.9031i −0.505206 1.55486i −0.800424 0.599434i \(-0.795392\pi\)
0.295218 0.955430i \(-0.404608\pi\)
\(422\) 0 0
\(423\) 3.07711 + 2.23565i 0.149614 + 0.108701i
\(424\) 0 0
\(425\) 1.53953 4.73819i 0.0746783 0.229836i
\(426\) 0 0
\(427\) −39.0666 + 28.3836i −1.89057 + 1.37358i
\(428\) 0 0
\(429\) −6.80122 + 8.10285i −0.328366 + 0.391209i
\(430\) 0 0
\(431\) 7.05473 5.12556i 0.339814 0.246890i −0.404769 0.914419i \(-0.632648\pi\)
0.744583 + 0.667529i \(0.232648\pi\)
\(432\) 0 0
\(433\) −3.51360 + 10.8138i −0.168853 + 0.519676i −0.999300 0.0374224i \(-0.988085\pi\)
0.830447 + 0.557098i \(0.188085\pi\)
\(434\) 0 0
\(435\) 1.77822 + 1.29195i 0.0852589 + 0.0619443i
\(436\) 0 0
\(437\) 9.05656 + 27.8732i 0.433234 + 1.33336i
\(438\) 0 0
\(439\) −24.3176 −1.16061 −0.580307 0.814398i \(-0.697067\pi\)
−0.580307 + 0.814398i \(0.697067\pi\)
\(440\) 0 0
\(441\) −35.7752 −1.70358
\(442\) 0 0
\(443\) 0.0704295 + 0.216760i 0.00334620 + 0.0102986i 0.952716 0.303863i \(-0.0982766\pi\)
−0.949369 + 0.314162i \(0.898277\pi\)
\(444\) 0 0
\(445\) 11.0327 + 8.01571i 0.522999 + 0.379981i
\(446\) 0 0
\(447\) −0.441393 + 1.35847i −0.0208772 + 0.0642534i
\(448\) 0 0
\(449\) −32.6872 + 23.7486i −1.54260 + 1.12077i −0.593928 + 0.804518i \(0.702424\pi\)
−0.948676 + 0.316249i \(0.897576\pi\)
\(450\) 0 0
\(451\) −30.0208 + 7.48014i −1.41363 + 0.352226i
\(452\) 0 0
\(453\) 2.38046 1.72951i 0.111844 0.0812593i
\(454\) 0 0
\(455\) 5.56102 17.1151i 0.260705 0.802367i
\(456\) 0 0
\(457\) −3.67858 2.67265i −0.172077 0.125021i 0.498413 0.866939i \(-0.333916\pi\)
−0.670490 + 0.741918i \(0.733916\pi\)
\(458\) 0 0
\(459\) 6.86547 + 21.1297i 0.320453 + 0.986252i
\(460\) 0 0
\(461\) −36.5792 −1.70366 −0.851832 0.523815i \(-0.824508\pi\)
−0.851832 + 0.523815i \(0.824508\pi\)
\(462\) 0 0
\(463\) 5.18502 0.240968 0.120484 0.992715i \(-0.461555\pi\)
0.120484 + 0.992715i \(0.461555\pi\)
\(464\) 0 0
\(465\) 0.961064 + 2.95785i 0.0445683 + 0.137167i
\(466\) 0 0
\(467\) −8.15502 5.92497i −0.377369 0.274175i 0.382891 0.923794i \(-0.374929\pi\)
−0.760260 + 0.649619i \(0.774929\pi\)
\(468\) 0 0
\(469\) −7.33923 + 22.5878i −0.338894 + 1.04301i
\(470\) 0 0
\(471\) 14.1199 10.2587i 0.650612 0.472697i
\(472\) 0 0
\(473\) −2.71398 + 38.7263i −0.124789 + 1.78064i
\(474\) 0 0
\(475\) 2.52507 1.83457i 0.115858 0.0841757i
\(476\) 0 0
\(477\) 1.37227 4.22342i 0.0628320 0.193377i
\(478\) 0 0
\(479\) 2.07381 + 1.50671i 0.0947548 + 0.0688434i 0.634154 0.773207i \(-0.281349\pi\)
−0.539399 + 0.842050i \(0.681349\pi\)
\(480\) 0 0
\(481\) −4.03033 12.4041i −0.183767 0.565577i
\(482\) 0 0
\(483\) −37.6609 −1.71363
\(484\) 0 0
\(485\) −13.6967 −0.621935
\(486\) 0 0
\(487\) −0.745567 2.29462i −0.0337849 0.103979i 0.932742 0.360545i \(-0.117409\pi\)
−0.966527 + 0.256565i \(0.917409\pi\)
\(488\) 0 0
\(489\) −11.1751 8.11921i −0.505357 0.367163i
\(490\) 0 0
\(491\) −4.64533 + 14.2969i −0.209641 + 0.645208i 0.789850 + 0.613300i \(0.210158\pi\)
−0.999491 + 0.0319079i \(0.989842\pi\)
\(492\) 0 0
\(493\) 10.5074 7.63404i 0.473227 0.343820i
\(494\) 0 0
\(495\) −0.530764 + 7.57358i −0.0238561 + 0.340407i
\(496\) 0 0
\(497\) 23.9730 17.4174i 1.07534 0.781278i
\(498\) 0 0
\(499\) −2.29614 + 7.06680i −0.102789 + 0.316353i −0.989205 0.146536i \(-0.953187\pi\)
0.886416 + 0.462890i \(0.153187\pi\)
\(500\) 0 0
\(501\) −9.82323 7.13699i −0.438869 0.318857i
\(502\) 0 0
\(503\) −4.69638 14.4540i −0.209401 0.644471i −0.999504 0.0314963i \(-0.989973\pi\)
0.790103 0.612975i \(-0.210027\pi\)
\(504\) 0 0
\(505\) −4.84287 −0.215505
\(506\) 0 0
\(507\) −1.10594 −0.0491164
\(508\) 0 0
\(509\) −7.11646 21.9022i −0.315431 0.970798i −0.975576 0.219660i \(-0.929505\pi\)
0.660145 0.751138i \(-0.270495\pi\)
\(510\) 0 0
\(511\) −28.1186 20.4294i −1.24389 0.903741i
\(512\) 0 0
\(513\) −4.30109 + 13.2374i −0.189898 + 0.584445i
\(514\) 0 0
\(515\) −0.731817 + 0.531696i −0.0322477 + 0.0234293i
\(516\) 0 0
\(517\) −5.34729 + 1.33236i −0.235174 + 0.0585970i
\(518\) 0 0
\(519\) −5.54116 + 4.02589i −0.243230 + 0.176717i
\(520\) 0 0
\(521\) 0.341879 1.05220i 0.0149780 0.0460975i −0.943288 0.331975i \(-0.892285\pi\)
0.958266 + 0.285877i \(0.0922850\pi\)
\(522\) 0 0
\(523\) −0.945974 0.687290i −0.0413645 0.0300531i 0.566911 0.823779i \(-0.308138\pi\)
−0.608275 + 0.793726i \(0.708138\pi\)
\(524\) 0 0
\(525\) 1.23939 + 3.81444i 0.0540913 + 0.166476i
\(526\) 0 0
\(527\) 18.3772 0.800522
\(528\) 0 0
\(529\) 65.1723 2.83358
\(530\) 0 0
\(531\) 0.0735069 + 0.226231i 0.00318993 + 0.00981759i
\(532\) 0 0
\(533\) −28.5502 20.7429i −1.23665 0.898476i
\(534\) 0 0
\(535\) −4.57082 + 14.0675i −0.197614 + 0.608193i
\(536\) 0 0
\(537\) −2.04183 + 1.48348i −0.0881115 + 0.0640168i
\(538\) 0 0
\(539\) 33.3240 39.7016i 1.43537 1.71007i
\(540\) 0 0
\(541\) 2.77596 2.01685i 0.119348 0.0867112i −0.526510 0.850169i \(-0.676500\pi\)
0.645858 + 0.763458i \(0.276500\pi\)
\(542\) 0 0
\(543\) 3.78476 11.6483i 0.162420 0.499876i
\(544\) 0 0
\(545\) 2.74604 + 1.99511i 0.117627 + 0.0854612i
\(546\) 0 0
\(547\) 12.9614 + 39.8911i 0.554190 + 1.70562i 0.698072 + 0.716027i \(0.254041\pi\)
−0.143882 + 0.989595i \(0.545959\pi\)
\(548\) 0 0
\(549\) 23.2376 0.991755
\(550\) 0 0
\(551\) 8.13662 0.346632
\(552\) 0 0
\(553\) 15.5001 + 47.7045i 0.659133 + 2.02860i
\(554\) 0 0
\(555\) 2.35162 + 1.70856i 0.0998209 + 0.0725241i
\(556\) 0 0
\(557\) −10.0451 + 30.9156i −0.425624 + 1.30994i 0.476771 + 0.879028i \(0.341807\pi\)
−0.902395 + 0.430910i \(0.858193\pi\)
\(558\) 0 0
\(559\) −35.8242 + 26.0278i −1.51520 + 1.10086i
\(560\) 0 0
\(561\) −12.9163 5.22085i −0.545328 0.220424i
\(562\) 0 0
\(563\) −30.1426 + 21.8999i −1.27036 + 0.922969i −0.999217 0.0395706i \(-0.987401\pi\)
−0.271141 + 0.962540i \(0.587401\pi\)
\(564\) 0 0
\(565\) 3.14440 9.67748i 0.132286 0.407135i
\(566\) 0 0
\(567\) 11.9588 + 8.68856i 0.502222 + 0.364885i
\(568\) 0 0
\(569\) −11.5993 35.6989i −0.486267 1.49658i −0.830138 0.557559i \(-0.811738\pi\)
0.343871 0.939017i \(-0.388262\pi\)
\(570\) 0 0
\(571\) 21.6905 0.907718 0.453859 0.891073i \(-0.350047\pi\)
0.453859 + 0.891073i \(0.350047\pi\)
\(572\) 0 0
\(573\) −6.71762 −0.280632
\(574\) 0 0
\(575\) −2.90167 8.93043i −0.121008 0.372425i
\(576\) 0 0
\(577\) 21.7873 + 15.8294i 0.907019 + 0.658988i 0.940259 0.340460i \(-0.110583\pi\)
−0.0332403 + 0.999447i \(0.510583\pi\)
\(578\) 0 0
\(579\) 5.07961 15.6334i 0.211101 0.649703i
\(580\) 0 0
\(581\) −21.8980 + 15.9098i −0.908481 + 0.660050i
\(582\) 0 0
\(583\) 3.40870 + 5.45692i 0.141174 + 0.226003i
\(584\) 0 0
\(585\) −7.00603 + 5.09018i −0.289664 + 0.210453i
\(586\) 0 0
\(587\) 4.78226 14.7183i 0.197385 0.607488i −0.802556 0.596577i \(-0.796527\pi\)
0.999940 0.0109109i \(-0.00347313\pi\)
\(588\) 0 0
\(589\) 9.31418 + 6.76715i 0.383784 + 0.278836i
\(590\) 0 0
\(591\) −4.68329 14.4137i −0.192645 0.592900i
\(592\) 0 0
\(593\) 24.7646 1.01696 0.508481 0.861073i \(-0.330207\pi\)
0.508481 + 0.861073i \(0.330207\pi\)
\(594\) 0 0
\(595\) 23.6992 0.971571
\(596\) 0 0
\(597\) −1.86996 5.75516i −0.0765326 0.235543i
\(598\) 0 0
\(599\) 10.4687 + 7.60597i 0.427740 + 0.310772i 0.780745 0.624850i \(-0.214840\pi\)
−0.353004 + 0.935622i \(0.614840\pi\)
\(600\) 0 0
\(601\) −5.80697 + 17.8720i −0.236871 + 0.729015i 0.759996 + 0.649927i \(0.225201\pi\)
−0.996868 + 0.0790874i \(0.974799\pi\)
\(602\) 0 0
\(603\) 9.24630 6.71783i 0.376539 0.273571i
\(604\) 0 0
\(605\) −7.91039 7.64367i −0.321603 0.310759i
\(606\) 0 0
\(607\) −11.6066 + 8.43268i −0.471097 + 0.342272i −0.797869 0.602831i \(-0.794039\pi\)
0.326772 + 0.945103i \(0.394039\pi\)
\(608\) 0 0
\(609\) −3.23099 + 9.94397i −0.130926 + 0.402950i
\(610\) 0 0
\(611\) −5.08534 3.69471i −0.205731 0.149472i
\(612\) 0 0
\(613\) −12.1838 37.4979i −0.492099 1.51453i −0.821429 0.570310i \(-0.806823\pi\)
0.329330 0.944215i \(-0.393177\pi\)
\(614\) 0 0
\(615\) 7.86509 0.317151
\(616\) 0 0
\(617\) 32.9316 1.32578 0.662888 0.748718i \(-0.269330\pi\)
0.662888 + 0.748718i \(0.269330\pi\)
\(618\) 0 0
\(619\) 12.7342 + 39.1919i 0.511832 + 1.57526i 0.788973 + 0.614428i \(0.210613\pi\)
−0.277141 + 0.960829i \(0.589387\pi\)
\(620\) 0 0
\(621\) 33.8770 + 24.6131i 1.35944 + 0.987689i
\(622\) 0 0
\(623\) −20.0462 + 61.6959i −0.803135 + 2.47180i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) 0 0
\(627\) −4.62394 7.40238i −0.184662 0.295622i
\(628\) 0 0
\(629\) 13.8956 10.0957i 0.554053 0.402543i
\(630\) 0 0
\(631\) −2.40842 + 7.41235i −0.0958776 + 0.295081i −0.987481 0.157735i \(-0.949581\pi\)
0.891604 + 0.452816i \(0.149581\pi\)
\(632\) 0 0
\(633\) 3.02370 + 2.19684i 0.120181 + 0.0873167i
\(634\) 0 0
\(635\) −3.38643 10.4224i −0.134386 0.413599i
\(636\) 0 0
\(637\) 59.1234 2.34255
\(638\) 0 0
\(639\) −14.2596 −0.564101
\(640\) 0 0
\(641\) −5.24398 16.1393i −0.207125 0.637464i −0.999619 0.0275853i \(-0.991218\pi\)
0.792495 0.609879i \(-0.208782\pi\)
\(642\) 0 0
\(643\) 0.280367 + 0.203699i 0.0110566 + 0.00803310i 0.593300 0.804982i \(-0.297825\pi\)
−0.582243 + 0.813015i \(0.697825\pi\)
\(644\) 0 0
\(645\) 3.04968 9.38594i 0.120081 0.369571i
\(646\) 0 0
\(647\) 6.65994 4.83873i 0.261829 0.190230i −0.449124 0.893469i \(-0.648264\pi\)
0.710953 + 0.703239i \(0.248264\pi\)
\(648\) 0 0
\(649\) −0.319531 0.129156i −0.0125427 0.00506981i
\(650\) 0 0
\(651\) −11.9689 + 8.69592i −0.469098 + 0.340820i
\(652\) 0 0
\(653\) 10.1807 31.3330i 0.398403 1.22616i −0.527877 0.849321i \(-0.677012\pi\)
0.926280 0.376836i \(-0.122988\pi\)
\(654\) 0 0
\(655\) −10.4380 7.58366i −0.407847 0.296318i
\(656\) 0 0
\(657\) 5.16845 + 15.9069i 0.201640 + 0.620586i
\(658\) 0 0
\(659\) −18.7687 −0.731127 −0.365563 0.930786i \(-0.619124\pi\)
−0.365563 + 0.930786i \(0.619124\pi\)
\(660\) 0 0
\(661\) 8.66066 0.336860 0.168430 0.985714i \(-0.446130\pi\)
0.168430 + 0.985714i \(0.446130\pi\)
\(662\) 0 0
\(663\) −4.91057 15.1132i −0.190711 0.586948i
\(664\) 0 0
\(665\) 12.0116 + 8.72691i 0.465788 + 0.338415i
\(666\) 0 0
\(667\) 7.56445 23.2810i 0.292897 0.901444i
\(668\) 0 0
\(669\) 10.3753 7.53808i 0.401132 0.291439i
\(670\) 0 0
\(671\) −21.6454 + 25.7879i −0.835610 + 0.995531i
\(672\) 0 0
\(673\) 9.47261 6.88225i 0.365142 0.265291i −0.390052 0.920793i \(-0.627543\pi\)
0.755194 + 0.655502i \(0.227543\pi\)
\(674\) 0 0
\(675\) 1.37805 4.24119i 0.0530410 0.163243i
\(676\) 0 0
\(677\) 25.1379 + 18.2637i 0.966127 + 0.701932i 0.954566 0.298001i \(-0.0963198\pi\)
0.0115613 + 0.999933i \(0.496320\pi\)
\(678\) 0 0
\(679\) −20.1338 61.9654i −0.772663 2.37801i
\(680\) 0 0
\(681\) 3.61198 0.138411
\(682\) 0 0
\(683\) 31.0210 1.18698 0.593492 0.804840i \(-0.297749\pi\)
0.593492 + 0.804840i \(0.297749\pi\)
\(684\) 0 0
\(685\) −5.83500 17.9583i −0.222944 0.686150i
\(686\) 0 0
\(687\) −2.79431 2.03018i −0.106609 0.0774563i
\(688\) 0 0
\(689\) −2.26786 + 6.97977i −0.0863987 + 0.265908i
\(690\) 0 0
\(691\) 33.9401 24.6589i 1.29114 0.938069i 0.291314 0.956628i \(-0.405908\pi\)
0.999828 + 0.0185582i \(0.00590761\pi\)
\(692\) 0 0
\(693\) −35.0439 + 8.73172i −1.33121 + 0.331690i
\(694\) 0 0
\(695\) −8.80956 + 6.40052i −0.334166 + 0.242786i
\(696\) 0 0
\(697\) 14.3613 44.1996i 0.543974 1.67418i
\(698\) 0 0
\(699\) −11.7685 8.55033i −0.445126 0.323403i
\(700\) 0 0
\(701\) −3.02060 9.29646i −0.114087 0.351122i 0.877669 0.479268i \(-0.159098\pi\)
−0.991755 + 0.128145i \(0.959098\pi\)
\(702\) 0 0
\(703\) 10.7604 0.405835
\(704\) 0 0
\(705\) 1.40092 0.0527618
\(706\) 0 0
\(707\) −7.11889 21.9097i −0.267733 0.823999i
\(708\) 0 0
\(709\) −14.2652 10.3643i −0.535742 0.389240i 0.286759 0.958003i \(-0.407422\pi\)
−0.822501 + 0.568763i \(0.807422\pi\)
\(710\) 0 0
\(711\) 7.45895 22.9563i 0.279732 0.860928i
\(712\) 0 0
\(713\) 28.0218 20.3590i 1.04942 0.762451i
\(714\) 0 0
\(715\) 0.877159 12.5164i 0.0328039 0.468085i
\(716\) 0 0
\(717\) 2.32345 1.68808i 0.0867707 0.0630426i
\(718\) 0 0
\(719\) −15.8862 + 48.8927i −0.592455 + 1.82339i −0.0254492 + 0.999676i \(0.508102\pi\)
−0.567006 + 0.823714i \(0.691898\pi\)
\(720\) 0 0
\(721\) −3.48120 2.52924i −0.129647 0.0941939i
\(722\) 0 0
\(723\) 5.25879 + 16.1849i 0.195576 + 0.601922i
\(724\) 0 0
\(725\) −2.60693 −0.0968189
\(726\) 0 0
\(727\) 17.3527 0.643577 0.321788 0.946812i \(-0.395716\pi\)
0.321788 + 0.946812i \(0.395716\pi\)
\(728\) 0 0
\(729\) 1.28751 + 3.96255i 0.0476856 + 0.146761i
\(730\) 0 0
\(731\) −47.1778 34.2767i −1.74493 1.26777i
\(732\) 0 0
\(733\) 13.2425 40.7562i 0.489123 1.50537i −0.336796 0.941578i \(-0.609343\pi\)
0.825919 0.563788i \(-0.190657\pi\)
\(734\) 0 0
\(735\) −10.6603 + 7.74516i −0.393211 + 0.285684i
\(736\) 0 0
\(737\) −1.15764 + 16.5186i −0.0426423 + 0.608472i
\(738\) 0 0
\(739\) −19.8915 + 14.4520i −0.731722 + 0.531627i −0.890108 0.455750i \(-0.849371\pi\)
0.158386 + 0.987377i \(0.449371\pi\)
\(740\) 0 0
\(741\) 3.07638 9.46814i 0.113014 0.347821i
\(742\) 0 0
\(743\) −3.79451 2.75687i −0.139207 0.101140i 0.516002 0.856587i \(-0.327420\pi\)
−0.655209 + 0.755447i \(0.727420\pi\)
\(744\) 0 0
\(745\) −0.523513 1.61121i −0.0191800 0.0590301i
\(746\) 0 0
\(747\) 13.0253 0.476571
\(748\) 0 0
\(749\) −70.3621 −2.57097
\(750\) 0 0
\(751\) 14.9231 + 45.9286i 0.544552 + 1.67596i 0.722053 + 0.691838i \(0.243199\pi\)
−0.177501 + 0.984121i \(0.556801\pi\)
\(752\) 0 0
\(753\) −13.4356 9.76155i −0.489621 0.355731i
\(754\) 0 0
\(755\) −1.07842 + 3.31904i −0.0392478 + 0.120792i
\(756\) 0 0
\(757\) −31.4094 + 22.8203i −1.14159 + 0.829417i −0.987341 0.158614i \(-0.949297\pi\)
−0.154254 + 0.988031i \(0.549297\pi\)
\(758\) 0 0
\(759\) −25.4789 + 6.34845i −0.924826 + 0.230434i
\(760\) 0 0
\(761\) 22.5616 16.3919i 0.817857 0.594208i −0.0982411 0.995163i \(-0.531322\pi\)
0.916098 + 0.400955i \(0.131322\pi\)
\(762\) 0 0
\(763\) −4.98951 + 15.3561i −0.180632 + 0.555929i
\(764\) 0 0
\(765\) −9.22641 6.70338i −0.333582 0.242361i
\(766\) 0 0
\(767\) −0.121480 0.373877i −0.00438639 0.0134999i
\(768\) 0 0
\(769\) −38.2240 −1.37839 −0.689197 0.724574i \(-0.742036\pi\)
−0.689197 + 0.724574i \(0.742036\pi\)
\(770\) 0 0
\(771\) 9.03288 0.325311
\(772\) 0 0
\(773\) 2.59445 + 7.98490i 0.0933159 + 0.287197i 0.986811 0.161876i \(-0.0517544\pi\)
−0.893495 + 0.449073i \(0.851754\pi\)
\(774\) 0 0
\(775\) −2.98421 2.16816i −0.107196 0.0778825i
\(776\) 0 0
\(777\) −4.27287 + 13.1505i −0.153288 + 0.471773i
\(778\) 0 0
\(779\) 23.5547 17.1135i 0.843936 0.613156i
\(780\) 0 0
\(781\) 13.2826 15.8246i 0.475287 0.566249i
\(782\) 0 0
\(783\) 9.40520 6.83328i 0.336114 0.244201i
\(784\) 0 0
\(785\) −6.39675 + 19.6872i −0.228310 + 0.702666i
\(786\) 0 0
\(787\) 28.6593 + 20.8222i 1.02159 + 0.742231i 0.966609 0.256256i \(-0.0824892\pi\)
0.0549842 + 0.998487i \(0.482489\pi\)
\(788\) 0 0
\(789\) 2.30924 + 7.10712i 0.0822112 + 0.253020i
\(790\) 0 0
\(791\) 48.4042 1.72105
\(792\) 0 0
\(793\) −38.4032 −1.36374
\(794\) 0 0
\(795\) −0.505440 1.55558i −0.0179261 0.0551709i
\(796\) 0 0
\(797\) −43.1931 31.3816i −1.52998 1.11159i −0.956250 0.292550i \(-0.905496\pi\)
−0.573729 0.819045i \(-0.694504\pi\)
\(798\) 0 0
\(799\) 2.55803 7.87280i 0.0904966 0.278520i
\(800\) 0 0
\(801\) 25.2551 18.3489i 0.892347 0.648328i
\(802\) 0 0
\(803\) −22.4670 9.08126i −0.792842 0.320471i
\(804\) 0 0
\(805\) 36.1369 26.2550i 1.27366 0.925366i
\(806\) 0 0
\(807\) 0.561421 1.72788i 0.0197630 0.0608241i
\(808\) 0 0
\(809\) 3.10733 + 2.25760i 0.109248 + 0.0793731i 0.641068 0.767484i \(-0.278492\pi\)
−0.531820 + 0.846857i \(0.678492\pi\)
\(810\) 0 0
\(811\) −7.33142 22.5638i −0.257441 0.792322i −0.993339 0.115229i \(-0.963240\pi\)
0.735898 0.677093i \(-0.236760\pi\)
\(812\) 0 0
\(813\) 8.64657 0.303248
\(814\) 0 0
\(815\) 16.3831 0.573877
\(816\) 0 0
\(817\) −11.2894 34.7452i −0.394966 1.21558i
\(818\) 0 0
\(819\) −33.3272 24.2136i −1.16455 0.846092i
\(820\) 0 0
\(821\) 0.0470633 0.144846i 0.00164252 0.00505516i −0.950232 0.311543i \(-0.899154\pi\)
0.951874 + 0.306488i \(0.0991540\pi\)
\(822\) 0 0
\(823\) −40.5913 + 29.4913i −1.41492 + 1.02800i −0.422341 + 0.906437i \(0.638792\pi\)
−0.992583 + 0.121566i \(0.961208\pi\)
\(824\) 0 0
\(825\) 1.48148 + 2.37168i 0.0515787 + 0.0825713i
\(826\) 0 0
\(827\) 17.9610 13.0494i 0.624566 0.453773i −0.229948 0.973203i \(-0.573856\pi\)
0.854513 + 0.519430i \(0.173856\pi\)
\(828\) 0 0
\(829\) 2.52957 7.78523i 0.0878558 0.270392i −0.897470 0.441075i \(-0.854597\pi\)
0.985326 + 0.170683i \(0.0545973\pi\)
\(830\) 0 0
\(831\) 10.1125 + 7.34717i 0.350799 + 0.254871i
\(832\) 0 0
\(833\) 24.0604 + 74.0502i 0.833643 + 2.56569i
\(834\) 0 0
\(835\) 14.4012 0.498374
\(836\) 0 0
\(837\) 16.4495 0.568579
\(838\) 0 0
\(839\) −2.45790 7.56463i −0.0848561 0.261160i 0.899622 0.436670i \(-0.143842\pi\)
−0.984478 + 0.175510i \(0.943842\pi\)
\(840\) 0 0
\(841\) 17.9634 + 13.0511i 0.619426 + 0.450039i
\(842\) 0 0
\(843\) 4.38938 13.5091i 0.151178 0.465279i
\(844\) 0 0
\(845\) 1.06118 0.770995i 0.0365058 0.0265230i
\(846\) 0 0
\(847\) 22.9527 47.0235i 0.788665 1.61574i
\(848\) 0 0
\(849\) 3.33841 2.42549i 0.114574 0.0832428i
\(850\) 0 0
\(851\) 10.0037 30.7882i 0.342923 1.05541i
\(852\) 0 0
\(853\) 4.75049 + 3.45143i 0.162654 + 0.118175i 0.666135 0.745832i \(-0.267948\pi\)
−0.503481 + 0.864006i \(0.667948\pi\)
\(854\) 0 0
\(855\) −2.20783 6.79501i −0.0755063 0.232384i
\(856\) 0 0
\(857\) 30.9089 1.05583 0.527914 0.849298i \(-0.322974\pi\)
0.527914 + 0.849298i \(0.322974\pi\)
\(858\) 0 0
\(859\) 10.9133 0.372358 0.186179 0.982516i \(-0.440390\pi\)
0.186179 + 0.982516i \(0.440390\pi\)
\(860\) 0 0
\(861\) 11.5615 + 35.5825i 0.394014 + 1.21265i
\(862\) 0 0
\(863\) −9.97830 7.24966i −0.339665 0.246781i 0.404855 0.914381i \(-0.367322\pi\)
−0.744521 + 0.667599i \(0.767322\pi\)
\(864\) 0 0
\(865\) 2.51031 7.72595i 0.0853532 0.262690i
\(866\) 0 0
\(867\) 5.33455 3.87577i 0.181171 0.131628i
\(868\) 0 0
\(869\) 18.5279 + 29.6609i 0.628515 + 1.00618i
\(870\) 0 0
\(871\) −15.2808 + 11.1021i −0.517769 + 0.376181i
\(872\) 0 0
\(873\) −9.68874 + 29.8189i −0.327914 + 1.00922i
\(874\) 0 0
\(875\) −3.84844 2.79605i −0.130101 0.0945238i
\(876\) 0 0
\(877\) −14.0157 43.1359i −0.473276 1.45659i −0.848269 0.529566i \(-0.822355\pi\)
0.374992 0.927028i \(-0.377645\pi\)
\(878\) 0 0
\(879\) −10.0818 −0.340051
\(880\) 0 0
\(881\) −24.4098 −0.822388 −0.411194 0.911548i \(-0.634888\pi\)
−0.411194 + 0.911548i \(0.634888\pi\)
\(882\) 0 0
\(883\) −10.8135 33.2805i −0.363903 1.11998i −0.950665 0.310218i \(-0.899598\pi\)
0.586763 0.809759i \(-0.300402\pi\)
\(884\) 0 0
\(885\) 0.0708815 + 0.0514984i 0.00238265 + 0.00173110i
\(886\) 0 0
\(887\) 13.8444 42.6087i 0.464849 1.43066i −0.394322 0.918972i \(-0.629021\pi\)
0.859172 0.511687i \(-0.170979\pi\)
\(888\) 0 0
\(889\) 42.1740 30.6412i 1.41447 1.02767i
\(890\) 0 0
\(891\) 9.55516 + 3.86224i 0.320110 + 0.129390i
\(892\) 0 0
\(893\) 4.19555 3.04825i 0.140399 0.102006i
\(894\) 0 0
\(895\) 0.925011 2.84689i 0.0309197 0.0951611i
\(896\) 0 0
\(897\) −24.2308 17.6047i −0.809041 0.587803i
\(898\) 0 0
\(899\) −2.97155 9.14550i −0.0991069 0.305020i
\(900\) 0 0
\(901\) −9.66486 −0.321983
\(902\) 0 0
\(903\) 46.9459 1.56226
\(904\) 0 0
\(905\) 4.48891 + 13.8154i 0.149216 + 0.459240i
\(906\) 0 0
\(907\) 5.61236 + 4.07762i 0.186355 + 0.135395i 0.677051 0.735936i \(-0.263257\pi\)
−0.490696 + 0.871331i \(0.663257\pi\)
\(908\) 0 0
\(909\) −3.42574 + 10.5433i −0.113625 + 0.349701i
\(910\) 0 0
\(911\) −21.6373 + 15.7204i −0.716875 + 0.520840i −0.885384 0.464860i \(-0.846105\pi\)
0.168510 + 0.985700i \(0.446105\pi\)
\(912\) 0 0
\(913\) −12.1328 + 14.4549i −0.401539 + 0.478386i
\(914\) 0 0
\(915\) 6.92432 5.03081i 0.228911 0.166314i
\(916\) 0 0
\(917\) 18.9657 58.3705i 0.626303 1.92756i
\(918\) 0 0
\(919\) 44.5982 + 32.4025i 1.47116 + 1.06886i 0.980276 + 0.197632i \(0.0633250\pi\)
0.490881 + 0.871227i \(0.336675\pi\)
\(920\) 0 0
\(921\) 4.38559 + 13.4975i 0.144510 + 0.444757i
\(922\) 0 0
\(923\) 23.5659 0.775681
\(924\) 0 0
\(925\) −3.44757 −0.113355
\(926\) 0 0
\(927\) 0.639877 + 1.96934i 0.0210163 + 0.0646815i
\(928\) 0 0
\(929\) −11.0730 8.04499i −0.363293 0.263948i 0.391131 0.920335i \(-0.372084\pi\)
−0.754424 + 0.656387i \(0.772084\pi\)
\(930\) 0 0
\(931\) −15.0734 + 46.3911i −0.494011 + 1.52041i
\(932\) 0 0
\(933\) −16.7765 + 12.1888i −0.549237 + 0.399044i
\(934\) 0 0
\(935\) 16.0333 3.99494i 0.524346 0.130649i
\(936\) 0 0
\(937\) −15.2988 + 11.1152i −0.499790 + 0.363119i −0.808937 0.587896i \(-0.799957\pi\)
0.309147 + 0.951014i \(0.399957\pi\)
\(938\) 0 0
\(939\) −1.87850 + 5.78144i −0.0613027 + 0.188670i
\(940\) 0 0
\(941\) 8.89866 + 6.46526i 0.290088 + 0.210761i 0.723306 0.690528i \(-0.242622\pi\)
−0.433218 + 0.901289i \(0.642622\pi\)
\(942\) 0 0
\(943\) −27.0679 83.3064i −0.881451 2.71283i
\(944\) 0 0
\(945\) 21.2133 0.690068
\(946\) 0 0
\(947\) 11.9776 0.389219 0.194610 0.980881i \(-0.437656\pi\)
0.194610 + 0.980881i \(0.437656\pi\)
\(948\) 0 0
\(949\) −8.54156 26.2882i −0.277271 0.853352i
\(950\) 0 0
\(951\) −5.83820 4.24170i −0.189317 0.137547i
\(952\) 0 0
\(953\) −8.11980 + 24.9902i −0.263026 + 0.809511i 0.729115 + 0.684391i \(0.239932\pi\)
−0.992142 + 0.125120i \(0.960068\pi\)
\(954\) 0 0
\(955\) 6.44577 4.68313i 0.208580 0.151542i
\(956\) 0 0
\(957\) −0.509636 + 7.27209i −0.0164742 + 0.235073i
\(958\) 0 0
\(959\) 72.6679 52.7963i 2.34657 1.70488i
\(960\) 0 0
\(961\) −5.37491 + 16.5423i −0.173384 + 0.533621i
\(962\) 0 0
\(963\) 27.3929 + 19.9021i 0.882724 + 0.641337i
\(964\) 0 0
\(965\) 6.02466 + 18.5420i 0.193941 + 0.596888i
\(966\) 0 0
\(967\) 11.2656 0.362277 0.181138 0.983458i \(-0.442022\pi\)
0.181138 + 0.983458i \(0.442022\pi\)
\(968\) 0 0
\(969\) 13.1105 0.421170
\(970\) 0 0
\(971\) 17.6151 + 54.2138i 0.565296 + 1.73980i 0.667069 + 0.744996i \(0.267548\pi\)
−0.101773 + 0.994808i \(0.532452\pi\)
\(972\) 0 0
\(973\) −41.9065 30.4468i −1.34346 0.976080i
\(974\) 0 0
\(975\) −0.985657 + 3.03354i −0.0315663 + 0.0971510i
\(976\) 0 0
\(977\) 28.3013 20.5621i 0.905437 0.657839i −0.0344195 0.999407i \(-0.510958\pi\)
0.939857 + 0.341569i \(0.110958\pi\)
\(978\) 0 0
\(979\) −3.16196 + 45.1186i −0.101057 + 1.44200i
\(980\) 0 0
\(981\) 6.28601 4.56705i 0.200697 0.145815i
\(982\) 0 0
\(983\) −5.55084 + 17.0837i −0.177044 + 0.544886i −0.999721 0.0236234i \(-0.992480\pi\)
0.822677 + 0.568509i \(0.192480\pi\)
\(984\) 0 0
\(985\) 14.5421 + 10.5655i 0.463351 + 0.336644i
\(986\) 0 0
\(987\) 2.05932 + 6.33793i 0.0655488 + 0.201739i
\(988\) 0 0
\(989\) −109.911 −3.49495
\(990\) 0 0
\(991\) −47.2159 −1.49986 −0.749931 0.661516i \(-0.769913\pi\)
−0.749931 + 0.661516i \(0.769913\pi\)
\(992\) 0 0
\(993\) −6.62024 20.3750i −0.210087 0.646581i
\(994\) 0 0
\(995\) 5.80645 + 4.21863i 0.184077 + 0.133740i
\(996\) 0 0
\(997\) −6.23192 + 19.1799i −0.197367 + 0.607433i 0.802574 + 0.596553i \(0.203463\pi\)
−0.999941 + 0.0108803i \(0.996537\pi\)
\(998\) 0 0
\(999\) 12.4380 9.03675i 0.393522 0.285910i
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 880.2.bo.j.641.2 12
4.3 odd 2 440.2.y.b.201.2 yes 12
11.2 odd 10 9680.2.a.cy.1.3 6
11.4 even 5 inner 880.2.bo.j.81.2 12
11.9 even 5 9680.2.a.cx.1.3 6
44.15 odd 10 440.2.y.b.81.2 12
44.31 odd 10 4840.2.a.bf.1.4 6
44.35 even 10 4840.2.a.be.1.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.y.b.81.2 12 44.15 odd 10
440.2.y.b.201.2 yes 12 4.3 odd 2
880.2.bo.j.81.2 12 11.4 even 5 inner
880.2.bo.j.641.2 12 1.1 even 1 trivial
4840.2.a.be.1.4 6 44.35 even 10
4840.2.a.bf.1.4 6 44.31 odd 10
9680.2.a.cx.1.3 6 11.9 even 5
9680.2.a.cy.1.3 6 11.2 odd 10