Properties

Label 966.2.f.c.461.15
Level $966$
Weight $2$
Character 966.461
Analytic conductor $7.714$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(461,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.461");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.f (of order \(2\), degree \(1\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.15
Character \(\chi\) \(=\) 966.461
Dual form 966.2.f.c.461.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.64221 + 0.550576i) q^{3} -1.00000 q^{4} -1.99217 q^{5} +(-0.550576 - 1.64221i) q^{6} +(2.64482 + 0.0703415i) q^{7} -1.00000i q^{8} +(2.39373 - 1.80833i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.64221 + 0.550576i) q^{3} -1.00000 q^{4} -1.99217 q^{5} +(-0.550576 - 1.64221i) q^{6} +(2.64482 + 0.0703415i) q^{7} -1.00000i q^{8} +(2.39373 - 1.80833i) q^{9} -1.99217i q^{10} +1.51113i q^{11} +(1.64221 - 0.550576i) q^{12} +5.17124i q^{13} +(-0.0703415 + 2.64482i) q^{14} +(3.27157 - 1.09684i) q^{15} +1.00000 q^{16} +1.10115 q^{17} +(1.80833 + 2.39373i) q^{18} +0.372080i q^{19} +1.99217 q^{20} +(-4.38208 + 1.34066i) q^{21} -1.51113 q^{22} +1.00000i q^{23} +(0.550576 + 1.64221i) q^{24} -1.03127 q^{25} -5.17124 q^{26} +(-2.93540 + 4.28759i) q^{27} +(-2.64482 - 0.0703415i) q^{28} +1.32252i q^{29} +(1.09684 + 3.27157i) q^{30} -2.16237i q^{31} +1.00000i q^{32} +(-0.831993 - 2.48160i) q^{33} +1.10115i q^{34} +(-5.26892 - 0.140132i) q^{35} +(-2.39373 + 1.80833i) q^{36} -10.7679 q^{37} -0.372080 q^{38} +(-2.84716 - 8.49227i) q^{39} +1.99217i q^{40} +5.04520 q^{41} +(-1.34066 - 4.38208i) q^{42} -1.65782 q^{43} -1.51113i q^{44} +(-4.76872 + 3.60249i) q^{45} -1.00000 q^{46} -6.00567 q^{47} +(-1.64221 + 0.550576i) q^{48} +(6.99010 + 0.372080i) q^{49} -1.03127i q^{50} +(-1.80833 + 0.606269i) q^{51} -5.17124i q^{52} +3.58482i q^{53} +(-4.28759 - 2.93540i) q^{54} -3.01042i q^{55} +(0.0703415 - 2.64482i) q^{56} +(-0.204859 - 0.611036i) q^{57} -1.32252 q^{58} -11.6790 q^{59} +(-3.27157 + 1.09684i) q^{60} -5.71197i q^{61} +2.16237 q^{62} +(6.45818 - 4.61432i) q^{63} -1.00000 q^{64} -10.3020i q^{65} +(2.48160 - 0.831993i) q^{66} -6.62562 q^{67} -1.10115 q^{68} +(-0.550576 - 1.64221i) q^{69} +(0.140132 - 5.26892i) q^{70} +13.6887i q^{71} +(-1.80833 - 2.39373i) q^{72} -9.75254i q^{73} -10.7679i q^{74} +(1.69356 - 0.567791i) q^{75} -0.372080i q^{76} +(-0.106295 + 3.99666i) q^{77} +(8.49227 - 2.84716i) q^{78} -3.85596 q^{79} -1.99217 q^{80} +(2.45990 - 8.65730i) q^{81} +5.04520i q^{82} +0.708838 q^{83} +(4.38208 - 1.34066i) q^{84} -2.19368 q^{85} -1.65782i q^{86} +(-0.728150 - 2.17187i) q^{87} +1.51113 q^{88} -9.89948 q^{89} +(-3.60249 - 4.76872i) q^{90} +(-0.363752 + 13.6770i) q^{91} -1.00000i q^{92} +(1.19055 + 3.55107i) q^{93} -6.00567i q^{94} -0.741247i q^{95} +(-0.550576 - 1.64221i) q^{96} -1.06712i q^{97} +(-0.372080 + 6.99010i) q^{98} +(2.73262 + 3.61724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.64221 + 0.550576i −0.948132 + 0.317875i
\(4\) −1.00000 −0.500000
\(5\) −1.99217 −0.890925 −0.445462 0.895301i \(-0.646961\pi\)
−0.445462 + 0.895301i \(0.646961\pi\)
\(6\) −0.550576 1.64221i −0.224772 0.670431i
\(7\) 2.64482 + 0.0703415i 0.999647 + 0.0265866i
\(8\) 1.00000i 0.353553i
\(9\) 2.39373 1.80833i 0.797910 0.602776i
\(10\) 1.99217i 0.629979i
\(11\) 1.51113i 0.455623i 0.973705 + 0.227811i \(0.0731570\pi\)
−0.973705 + 0.227811i \(0.926843\pi\)
\(12\) 1.64221 0.550576i 0.474066 0.158938i
\(13\) 5.17124i 1.43424i 0.696948 + 0.717121i \(0.254541\pi\)
−0.696948 + 0.717121i \(0.745459\pi\)
\(14\) −0.0703415 + 2.64482i −0.0187995 + 0.706857i
\(15\) 3.27157 1.09684i 0.844715 0.283203i
\(16\) 1.00000 0.250000
\(17\) 1.10115 0.267069 0.133534 0.991044i \(-0.457367\pi\)
0.133534 + 0.991044i \(0.457367\pi\)
\(18\) 1.80833 + 2.39373i 0.426227 + 0.564208i
\(19\) 0.372080i 0.0853611i 0.999089 + 0.0426806i \(0.0135898\pi\)
−0.999089 + 0.0426806i \(0.986410\pi\)
\(20\) 1.99217 0.445462
\(21\) −4.38208 + 1.34066i −0.956249 + 0.292555i
\(22\) −1.51113 −0.322174
\(23\) 1.00000i 0.208514i
\(24\) 0.550576 + 1.64221i 0.112386 + 0.335215i
\(25\) −1.03127 −0.206253
\(26\) −5.17124 −1.01416
\(27\) −2.93540 + 4.28759i −0.564917 + 0.825148i
\(28\) −2.64482 0.0703415i −0.499823 0.0132933i
\(29\) 1.32252i 0.245586i 0.992432 + 0.122793i \(0.0391852\pi\)
−0.992432 + 0.122793i \(0.960815\pi\)
\(30\) 1.09684 + 3.27157i 0.200255 + 0.597303i
\(31\) 2.16237i 0.388373i −0.980965 0.194186i \(-0.937793\pi\)
0.980965 0.194186i \(-0.0622067\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.831993 2.48160i −0.144831 0.431991i
\(34\) 1.10115i 0.188846i
\(35\) −5.26892 0.140132i −0.890610 0.0236866i
\(36\) −2.39373 + 1.80833i −0.398955 + 0.301388i
\(37\) −10.7679 −1.77023 −0.885114 0.465375i \(-0.845919\pi\)
−0.885114 + 0.465375i \(0.845919\pi\)
\(38\) −0.372080 −0.0603594
\(39\) −2.84716 8.49227i −0.455911 1.35985i
\(40\) 1.99217i 0.314989i
\(41\) 5.04520 0.787928 0.393964 0.919126i \(-0.371104\pi\)
0.393964 + 0.919126i \(0.371104\pi\)
\(42\) −1.34066 4.38208i −0.206868 0.676170i
\(43\) −1.65782 −0.252815 −0.126407 0.991978i \(-0.540345\pi\)
−0.126407 + 0.991978i \(0.540345\pi\)
\(44\) 1.51113i 0.227811i
\(45\) −4.76872 + 3.60249i −0.710878 + 0.537028i
\(46\) −1.00000 −0.147442
\(47\) −6.00567 −0.876017 −0.438008 0.898971i \(-0.644316\pi\)
−0.438008 + 0.898971i \(0.644316\pi\)
\(48\) −1.64221 + 0.550576i −0.237033 + 0.0794689i
\(49\) 6.99010 + 0.372080i 0.998586 + 0.0531544i
\(50\) 1.03127i 0.145843i
\(51\) −1.80833 + 0.606269i −0.253217 + 0.0848946i
\(52\) 5.17124i 0.717121i
\(53\) 3.58482i 0.492413i 0.969217 + 0.246206i \(0.0791841\pi\)
−0.969217 + 0.246206i \(0.920816\pi\)
\(54\) −4.28759 2.93540i −0.583468 0.399457i
\(55\) 3.01042i 0.405926i
\(56\) 0.0703415 2.64482i 0.00939977 0.353428i
\(57\) −0.204859 0.611036i −0.0271342 0.0809336i
\(58\) −1.32252 −0.173656
\(59\) −11.6790 −1.52048 −0.760238 0.649645i \(-0.774918\pi\)
−0.760238 + 0.649645i \(0.774918\pi\)
\(60\) −3.27157 + 1.09684i −0.422357 + 0.141602i
\(61\) 5.71197i 0.731343i −0.930744 0.365671i \(-0.880839\pi\)
0.930744 0.365671i \(-0.119161\pi\)
\(62\) 2.16237 0.274621
\(63\) 6.45818 4.61432i 0.813654 0.581349i
\(64\) −1.00000 −0.125000
\(65\) 10.3020i 1.27780i
\(66\) 2.48160 0.831993i 0.305464 0.102411i
\(67\) −6.62562 −0.809448 −0.404724 0.914439i \(-0.632632\pi\)
−0.404724 + 0.914439i \(0.632632\pi\)
\(68\) −1.10115 −0.133534
\(69\) −0.550576 1.64221i −0.0662816 0.197699i
\(70\) 0.140132 5.26892i 0.0167490 0.629756i
\(71\) 13.6887i 1.62455i 0.583273 + 0.812276i \(0.301772\pi\)
−0.583273 + 0.812276i \(0.698228\pi\)
\(72\) −1.80833 2.39373i −0.213114 0.282104i
\(73\) 9.75254i 1.14145i −0.821142 0.570724i \(-0.806663\pi\)
0.821142 0.570724i \(-0.193337\pi\)
\(74\) 10.7679i 1.25174i
\(75\) 1.69356 0.567791i 0.195555 0.0655628i
\(76\) 0.372080i 0.0426806i
\(77\) −0.106295 + 3.99666i −0.0121135 + 0.455462i
\(78\) 8.49227 2.84716i 0.961561 0.322377i
\(79\) −3.85596 −0.433829 −0.216915 0.976191i \(-0.569599\pi\)
−0.216915 + 0.976191i \(0.569599\pi\)
\(80\) −1.99217 −0.222731
\(81\) 2.45990 8.65730i 0.273322 0.961923i
\(82\) 5.04520i 0.557149i
\(83\) 0.708838 0.0778050 0.0389025 0.999243i \(-0.487614\pi\)
0.0389025 + 0.999243i \(0.487614\pi\)
\(84\) 4.38208 1.34066i 0.478124 0.146278i
\(85\) −2.19368 −0.237938
\(86\) 1.65782i 0.178767i
\(87\) −0.728150 2.17187i −0.0780659 0.232848i
\(88\) 1.51113 0.161087
\(89\) −9.89948 −1.04934 −0.524671 0.851305i \(-0.675812\pi\)
−0.524671 + 0.851305i \(0.675812\pi\)
\(90\) −3.60249 4.76872i −0.379736 0.502667i
\(91\) −0.363752 + 13.6770i −0.0381316 + 1.43374i
\(92\) 1.00000i 0.104257i
\(93\) 1.19055 + 3.55107i 0.123454 + 0.368229i
\(94\) 6.00567i 0.619437i
\(95\) 0.741247i 0.0760503i
\(96\) −0.550576 1.64221i −0.0561930 0.167608i
\(97\) 1.06712i 0.108350i −0.998531 0.0541749i \(-0.982747\pi\)
0.998531 0.0541749i \(-0.0172529\pi\)
\(98\) −0.372080 + 6.99010i −0.0375858 + 0.706107i
\(99\) 2.73262 + 3.61724i 0.274639 + 0.363546i
\(100\) 1.03127 0.103127
\(101\) −4.85686 −0.483276 −0.241638 0.970367i \(-0.577685\pi\)
−0.241638 + 0.970367i \(0.577685\pi\)
\(102\) −0.606269 1.80833i −0.0600296 0.179051i
\(103\) 16.7641i 1.65182i 0.563803 + 0.825909i \(0.309338\pi\)
−0.563803 + 0.825909i \(0.690662\pi\)
\(104\) 5.17124 0.507081
\(105\) 8.72984 2.67082i 0.851945 0.260645i
\(106\) −3.58482 −0.348189
\(107\) 6.16806i 0.596289i 0.954521 + 0.298144i \(0.0963677\pi\)
−0.954521 + 0.298144i \(0.903632\pi\)
\(108\) 2.93540 4.28759i 0.282459 0.412574i
\(109\) −5.38632 −0.515916 −0.257958 0.966156i \(-0.583050\pi\)
−0.257958 + 0.966156i \(0.583050\pi\)
\(110\) 3.01042 0.287033
\(111\) 17.6831 5.92854i 1.67841 0.562712i
\(112\) 2.64482 + 0.0703415i 0.249912 + 0.00664664i
\(113\) 16.8518i 1.58529i 0.609686 + 0.792643i \(0.291296\pi\)
−0.609686 + 0.792643i \(0.708704\pi\)
\(114\) 0.611036 0.204859i 0.0572287 0.0191868i
\(115\) 1.99217i 0.185771i
\(116\) 1.32252i 0.122793i
\(117\) 9.35129 + 12.3785i 0.864527 + 1.14440i
\(118\) 11.6790i 1.07514i
\(119\) 2.91235 + 0.0774567i 0.266974 + 0.00710044i
\(120\) −1.09684 3.27157i −0.100127 0.298652i
\(121\) 8.71649 0.792408
\(122\) 5.71197 0.517138
\(123\) −8.28529 + 2.77777i −0.747060 + 0.250463i
\(124\) 2.16237i 0.194186i
\(125\) 12.0153 1.07468
\(126\) 4.61432 + 6.45818i 0.411076 + 0.575340i
\(127\) −13.2753 −1.17799 −0.588995 0.808137i \(-0.700476\pi\)
−0.588995 + 0.808137i \(0.700476\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.72249 0.912756i 0.239702 0.0803637i
\(130\) 10.3020 0.903543
\(131\) 13.7049 1.19741 0.598703 0.800971i \(-0.295683\pi\)
0.598703 + 0.800971i \(0.295683\pi\)
\(132\) 0.831993 + 2.48160i 0.0724157 + 0.215995i
\(133\) −0.0261727 + 0.984084i −0.00226946 + 0.0853309i
\(134\) 6.62562i 0.572366i
\(135\) 5.84780 8.54161i 0.503299 0.735144i
\(136\) 1.10115i 0.0944231i
\(137\) 7.71208i 0.658887i 0.944175 + 0.329444i \(0.106861\pi\)
−0.944175 + 0.329444i \(0.893139\pi\)
\(138\) 1.64221 0.550576i 0.139795 0.0468682i
\(139\) 14.9440i 1.26753i 0.773524 + 0.633767i \(0.218492\pi\)
−0.773524 + 0.633767i \(0.781508\pi\)
\(140\) 5.26892 + 0.140132i 0.445305 + 0.0118433i
\(141\) 9.86259 3.30658i 0.830580 0.278464i
\(142\) −13.6887 −1.14873
\(143\) −7.81441 −0.653474
\(144\) 2.39373 1.80833i 0.199478 0.150694i
\(145\) 2.63469i 0.218799i
\(146\) 9.75254 0.807126
\(147\) −11.6841 + 3.23755i −0.963689 + 0.267029i
\(148\) 10.7679 0.885114
\(149\) 10.9768i 0.899251i −0.893217 0.449626i \(-0.851557\pi\)
0.893217 0.449626i \(-0.148443\pi\)
\(150\) 0.567791 + 1.69356i 0.0463599 + 0.138279i
\(151\) −2.93475 −0.238826 −0.119413 0.992845i \(-0.538101\pi\)
−0.119413 + 0.992845i \(0.538101\pi\)
\(152\) 0.372080 0.0301797
\(153\) 2.63586 1.99125i 0.213097 0.160983i
\(154\) −3.99666 0.106295i −0.322060 0.00856550i
\(155\) 4.30780i 0.346011i
\(156\) 2.84716 + 8.49227i 0.227955 + 0.679926i
\(157\) 13.1983i 1.05334i −0.850070 0.526670i \(-0.823440\pi\)
0.850070 0.526670i \(-0.176560\pi\)
\(158\) 3.85596i 0.306764i
\(159\) −1.97372 5.88704i −0.156526 0.466873i
\(160\) 1.99217i 0.157495i
\(161\) −0.0703415 + 2.64482i −0.00554368 + 0.208441i
\(162\) 8.65730 + 2.45990i 0.680182 + 0.193268i
\(163\) −13.9521 −1.09282 −0.546408 0.837519i \(-0.684005\pi\)
−0.546408 + 0.837519i \(0.684005\pi\)
\(164\) −5.04520 −0.393964
\(165\) 1.65747 + 4.94376i 0.129034 + 0.384871i
\(166\) 0.708838i 0.0550165i
\(167\) 5.28517 0.408979 0.204489 0.978869i \(-0.434447\pi\)
0.204489 + 0.978869i \(0.434447\pi\)
\(168\) 1.34066 + 4.38208i 0.103434 + 0.338085i
\(169\) −13.7417 −1.05705
\(170\) 2.19368i 0.168248i
\(171\) 0.672844 + 0.890661i 0.0514536 + 0.0681105i
\(172\) 1.65782 0.126407
\(173\) −5.96305 −0.453362 −0.226681 0.973969i \(-0.572788\pi\)
−0.226681 + 0.973969i \(0.572788\pi\)
\(174\) 2.17187 0.728150i 0.164649 0.0552009i
\(175\) −2.72751 0.0725408i −0.206180 0.00548357i
\(176\) 1.51113i 0.113906i
\(177\) 19.1794 6.43018i 1.44161 0.483322i
\(178\) 9.89948i 0.741997i
\(179\) 5.06422i 0.378518i −0.981927 0.189259i \(-0.939391\pi\)
0.981927 0.189259i \(-0.0606086\pi\)
\(180\) 4.76872 3.60249i 0.355439 0.268514i
\(181\) 2.03182i 0.151024i −0.997145 0.0755119i \(-0.975941\pi\)
0.997145 0.0755119i \(-0.0240591\pi\)
\(182\) −13.6770 0.363752i −1.01380 0.0269631i
\(183\) 3.14488 + 9.38028i 0.232476 + 0.693410i
\(184\) 1.00000 0.0737210
\(185\) 21.4514 1.57714
\(186\) −3.55107 + 1.19055i −0.260377 + 0.0872953i
\(187\) 1.66399i 0.121683i
\(188\) 6.00567 0.438008
\(189\) −8.06518 + 11.1334i −0.586655 + 0.809837i
\(190\) 0.741247 0.0537757
\(191\) 2.46441i 0.178319i 0.996017 + 0.0891593i \(0.0284180\pi\)
−0.996017 + 0.0891593i \(0.971582\pi\)
\(192\) 1.64221 0.550576i 0.118517 0.0397344i
\(193\) −1.23713 −0.0890502 −0.0445251 0.999008i \(-0.514177\pi\)
−0.0445251 + 0.999008i \(0.514177\pi\)
\(194\) 1.06712 0.0766149
\(195\) 5.67202 + 16.9180i 0.406182 + 1.21153i
\(196\) −6.99010 0.372080i −0.499293 0.0265772i
\(197\) 4.06740i 0.289790i 0.989447 + 0.144895i \(0.0462845\pi\)
−0.989447 + 0.144895i \(0.953716\pi\)
\(198\) −3.61724 + 2.73262i −0.257066 + 0.194199i
\(199\) 3.97727i 0.281941i 0.990014 + 0.140971i \(0.0450223\pi\)
−0.990014 + 0.140971i \(0.954978\pi\)
\(200\) 1.03127i 0.0729215i
\(201\) 10.8807 3.64791i 0.767464 0.257304i
\(202\) 4.85686i 0.341727i
\(203\) −0.0930282 + 3.49783i −0.00652930 + 0.245500i
\(204\) 1.80833 0.606269i 0.126608 0.0424473i
\(205\) −10.0509 −0.701984
\(206\) −16.7641 −1.16801
\(207\) 1.80833 + 2.39373i 0.125687 + 0.166376i
\(208\) 5.17124i 0.358561i
\(209\) −0.562262 −0.0388925
\(210\) 2.67082 + 8.72984i 0.184304 + 0.602416i
\(211\) 19.5402 1.34520 0.672601 0.740006i \(-0.265177\pi\)
0.672601 + 0.740006i \(0.265177\pi\)
\(212\) 3.58482i 0.246206i
\(213\) −7.53669 22.4798i −0.516405 1.54029i
\(214\) −6.16806 −0.421640
\(215\) 3.30265 0.225239
\(216\) 4.28759 + 2.93540i 0.291734 + 0.199728i
\(217\) 0.152104 5.71907i 0.0103255 0.388236i
\(218\) 5.38632i 0.364807i
\(219\) 5.36952 + 16.0157i 0.362838 + 1.08224i
\(220\) 3.01042i 0.202963i
\(221\) 5.69432i 0.383041i
\(222\) 5.92854 + 17.6831i 0.397897 + 1.18681i
\(223\) 26.3878i 1.76706i 0.468374 + 0.883530i \(0.344840\pi\)
−0.468374 + 0.883530i \(0.655160\pi\)
\(224\) −0.0703415 + 2.64482i −0.00469989 + 0.176714i
\(225\) −2.46857 + 1.86487i −0.164572 + 0.124325i
\(226\) −16.8518 −1.12097
\(227\) −5.16418 −0.342759 −0.171379 0.985205i \(-0.554822\pi\)
−0.171379 + 0.985205i \(0.554822\pi\)
\(228\) 0.204859 + 0.611036i 0.0135671 + 0.0404668i
\(229\) 13.1393i 0.868269i 0.900848 + 0.434134i \(0.142946\pi\)
−0.900848 + 0.434134i \(0.857054\pi\)
\(230\) 1.99217 0.131360
\(231\) −2.02591 6.62189i −0.133295 0.435689i
\(232\) 1.32252 0.0868279
\(233\) 21.2452i 1.39182i −0.718129 0.695910i \(-0.755001\pi\)
0.718129 0.695910i \(-0.244999\pi\)
\(234\) −12.3785 + 9.35129i −0.809211 + 0.611313i
\(235\) 11.9643 0.780465
\(236\) 11.6790 0.760238
\(237\) 6.33231 2.12300i 0.411328 0.137904i
\(238\) −0.0774567 + 2.91235i −0.00502077 + 0.188779i
\(239\) 30.1168i 1.94809i −0.226346 0.974047i \(-0.572678\pi\)
0.226346 0.974047i \(-0.427322\pi\)
\(240\) 3.27157 1.09684i 0.211179 0.0708008i
\(241\) 3.61167i 0.232648i −0.993211 0.116324i \(-0.962889\pi\)
0.993211 0.116324i \(-0.0371112\pi\)
\(242\) 8.71649i 0.560317i
\(243\) 0.726829 + 15.5715i 0.0466261 + 0.998912i
\(244\) 5.71197i 0.365671i
\(245\) −13.9255 0.741247i −0.889665 0.0473565i
\(246\) −2.77777 8.28529i −0.177104 0.528251i
\(247\) −1.92412 −0.122429
\(248\) −2.16237 −0.137311
\(249\) −1.16406 + 0.390269i −0.0737695 + 0.0247323i
\(250\) 12.0153i 0.759914i
\(251\) 26.3289 1.66186 0.830932 0.556373i \(-0.187808\pi\)
0.830932 + 0.556373i \(0.187808\pi\)
\(252\) −6.45818 + 4.61432i −0.406827 + 0.290675i
\(253\) −1.51113 −0.0950039
\(254\) 13.2753i 0.832965i
\(255\) 3.60249 1.20779i 0.225597 0.0756347i
\(256\) 1.00000 0.0625000
\(257\) 24.5168 1.52932 0.764659 0.644435i \(-0.222907\pi\)
0.764659 + 0.644435i \(0.222907\pi\)
\(258\) 0.912756 + 2.72249i 0.0568257 + 0.169495i
\(259\) −28.4790 0.757428i −1.76960 0.0470643i
\(260\) 10.3020i 0.638901i
\(261\) 2.39156 + 3.16576i 0.148034 + 0.195956i
\(262\) 13.7049i 0.846693i
\(263\) 10.1241i 0.624278i 0.950036 + 0.312139i \(0.101045\pi\)
−0.950036 + 0.312139i \(0.898955\pi\)
\(264\) −2.48160 + 0.831993i −0.152732 + 0.0512056i
\(265\) 7.14157i 0.438703i
\(266\) −0.984084 0.0261727i −0.0603381 0.00160475i
\(267\) 16.2571 5.45042i 0.994916 0.333560i
\(268\) 6.62562 0.404724
\(269\) −0.339791 −0.0207174 −0.0103587 0.999946i \(-0.503297\pi\)
−0.0103587 + 0.999946i \(0.503297\pi\)
\(270\) 8.54161 + 5.84780i 0.519826 + 0.355886i
\(271\) 15.1379i 0.919561i −0.888033 0.459780i \(-0.847928\pi\)
0.888033 0.459780i \(-0.152072\pi\)
\(272\) 1.10115 0.0667672
\(273\) −6.93286 22.6608i −0.419596 1.37149i
\(274\) −7.71208 −0.465904
\(275\) 1.55838i 0.0939737i
\(276\) 0.550576 + 1.64221i 0.0331408 + 0.0988496i
\(277\) 25.5666 1.53615 0.768073 0.640362i \(-0.221216\pi\)
0.768073 + 0.640362i \(0.221216\pi\)
\(278\) −14.9440 −0.896282
\(279\) −3.91027 5.17613i −0.234102 0.309887i
\(280\) −0.140132 + 5.26892i −0.00837449 + 0.314878i
\(281\) 16.9275i 1.00981i −0.863175 0.504904i \(-0.831528\pi\)
0.863175 0.504904i \(-0.168472\pi\)
\(282\) 3.30658 + 9.86259i 0.196904 + 0.587309i
\(283\) 20.4813i 1.21748i 0.793368 + 0.608742i \(0.208326\pi\)
−0.793368 + 0.608742i \(0.791674\pi\)
\(284\) 13.6887i 0.812276i
\(285\) 0.408113 + 1.21729i 0.0241745 + 0.0721058i
\(286\) 7.81441i 0.462076i
\(287\) 13.3436 + 0.354887i 0.787649 + 0.0209483i
\(288\) 1.80833 + 2.39373i 0.106557 + 0.141052i
\(289\) −15.7875 −0.928674
\(290\) 2.63469 0.154714
\(291\) 0.587532 + 1.75244i 0.0344417 + 0.102730i
\(292\) 9.75254i 0.570724i
\(293\) 18.9978 1.10986 0.554932 0.831895i \(-0.312744\pi\)
0.554932 + 0.831895i \(0.312744\pi\)
\(294\) −3.23755 11.6841i −0.188818 0.681431i
\(295\) 23.2665 1.35463
\(296\) 10.7679i 0.625870i
\(297\) −6.47911 4.43576i −0.375956 0.257389i
\(298\) 10.9768 0.635867
\(299\) −5.17124 −0.299060
\(300\) −1.69356 + 0.567791i −0.0977777 + 0.0327814i
\(301\) −4.38462 0.116613i −0.252726 0.00672148i
\(302\) 2.93475i 0.168876i
\(303\) 7.97600 2.67407i 0.458209 0.153621i
\(304\) 0.372080i 0.0213403i
\(305\) 11.3792i 0.651571i
\(306\) 1.99125 + 2.63586i 0.113832 + 0.150682i
\(307\) 17.1863i 0.980873i 0.871477 + 0.490436i \(0.163163\pi\)
−0.871477 + 0.490436i \(0.836837\pi\)
\(308\) 0.106295 3.99666i 0.00605673 0.227731i
\(309\) −9.22993 27.5303i −0.525073 1.56614i
\(310\) −4.30780 −0.244667
\(311\) −19.2329 −1.09060 −0.545298 0.838242i \(-0.683583\pi\)
−0.545298 + 0.838242i \(0.683583\pi\)
\(312\) −8.49227 + 2.84716i −0.480780 + 0.161189i
\(313\) 22.8922i 1.29394i −0.762515 0.646971i \(-0.776036\pi\)
0.762515 0.646971i \(-0.223964\pi\)
\(314\) 13.1983 0.744825
\(315\) −12.8658 + 9.19250i −0.724905 + 0.517938i
\(316\) 3.85596 0.216915
\(317\) 14.7130i 0.826364i −0.910648 0.413182i \(-0.864417\pi\)
0.910648 0.413182i \(-0.135583\pi\)
\(318\) 5.88704 1.97372i 0.330129 0.110681i
\(319\) −1.99850 −0.111895
\(320\) 1.99217 0.111366
\(321\) −3.39599 10.1293i −0.189546 0.565361i
\(322\) −2.64482 0.0703415i −0.147390 0.00391998i
\(323\) 0.409717i 0.0227973i
\(324\) −2.45990 + 8.65730i −0.136661 + 0.480961i
\(325\) 5.33292i 0.295817i
\(326\) 13.9521i 0.772737i
\(327\) 8.84548 2.96558i 0.489156 0.163997i
\(328\) 5.04520i 0.278574i
\(329\) −15.8839 0.422447i −0.875707 0.0232903i
\(330\) −4.94376 + 1.65747i −0.272145 + 0.0912407i
\(331\) −20.0559 −1.10237 −0.551185 0.834383i \(-0.685824\pi\)
−0.551185 + 0.834383i \(0.685824\pi\)
\(332\) −0.708838 −0.0389025
\(333\) −25.7754 + 19.4718i −1.41248 + 1.06705i
\(334\) 5.28517i 0.289192i
\(335\) 13.1993 0.721157
\(336\) −4.38208 + 1.34066i −0.239062 + 0.0731389i
\(337\) −10.7491 −0.585543 −0.292771 0.956182i \(-0.594577\pi\)
−0.292771 + 0.956182i \(0.594577\pi\)
\(338\) 13.7417i 0.747449i
\(339\) −9.27822 27.6743i −0.503924 1.50306i
\(340\) 2.19368 0.118969
\(341\) 3.26762 0.176952
\(342\) −0.890661 + 0.672844i −0.0481614 + 0.0363832i
\(343\) 18.4614 + 1.47578i 0.996820 + 0.0796846i
\(344\) 1.65782i 0.0893836i
\(345\) 1.09684 + 3.27157i 0.0590519 + 0.176135i
\(346\) 5.96305i 0.320576i
\(347\) 21.6678i 1.16319i 0.813478 + 0.581595i \(0.197571\pi\)
−0.813478 + 0.581595i \(0.802429\pi\)
\(348\) 0.728150 + 2.17187i 0.0390329 + 0.116424i
\(349\) 15.5372i 0.831687i 0.909436 + 0.415843i \(0.136514\pi\)
−0.909436 + 0.415843i \(0.863486\pi\)
\(350\) 0.0725408 2.72751i 0.00387747 0.145792i
\(351\) −22.1722 15.1796i −1.18346 0.810228i
\(352\) −1.51113 −0.0805435
\(353\) 14.7290 0.783943 0.391972 0.919977i \(-0.371793\pi\)
0.391972 + 0.919977i \(0.371793\pi\)
\(354\) 6.43018 + 19.1794i 0.341760 + 1.01937i
\(355\) 27.2702i 1.44735i
\(356\) 9.89948 0.524671
\(357\) −4.82534 + 1.47627i −0.255384 + 0.0781324i
\(358\) 5.06422 0.267653
\(359\) 29.7728i 1.57135i 0.618641 + 0.785674i \(0.287684\pi\)
−0.618641 + 0.785674i \(0.712316\pi\)
\(360\) 3.60249 + 4.76872i 0.189868 + 0.251333i
\(361\) 18.8616 0.992713
\(362\) 2.03182 0.106790
\(363\) −14.3143 + 4.79909i −0.751308 + 0.251887i
\(364\) 0.363752 13.6770i 0.0190658 0.716868i
\(365\) 19.4287i 1.01694i
\(366\) −9.38028 + 3.14488i −0.490315 + 0.164385i
\(367\) 20.2090i 1.05490i 0.849586 + 0.527449i \(0.176852\pi\)
−0.849586 + 0.527449i \(0.823148\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 12.0768 9.12337i 0.628696 0.474944i
\(370\) 21.4514i 1.11521i
\(371\) −0.252162 + 9.48119i −0.0130916 + 0.492239i
\(372\) −1.19055 3.55107i −0.0617271 0.184115i
\(373\) 36.6965 1.90007 0.950036 0.312141i \(-0.101046\pi\)
0.950036 + 0.312141i \(0.101046\pi\)
\(374\) −1.66399 −0.0860426
\(375\) −19.7317 + 6.61534i −1.01894 + 0.341615i
\(376\) 6.00567i 0.309719i
\(377\) −6.83908 −0.352230
\(378\) −11.1334 8.06518i −0.572641 0.414828i
\(379\) −4.31615 −0.221706 −0.110853 0.993837i \(-0.535358\pi\)
−0.110853 + 0.993837i \(0.535358\pi\)
\(380\) 0.741247i 0.0380252i
\(381\) 21.8008 7.30905i 1.11689 0.374454i
\(382\) −2.46441 −0.126090
\(383\) −10.0077 −0.511369 −0.255685 0.966760i \(-0.582301\pi\)
−0.255685 + 0.966760i \(0.582301\pi\)
\(384\) 0.550576 + 1.64221i 0.0280965 + 0.0838039i
\(385\) 0.211758 7.96202i 0.0107922 0.405782i
\(386\) 1.23713i 0.0629680i
\(387\) −3.96837 + 2.99788i −0.201724 + 0.152391i
\(388\) 1.06712i 0.0541749i
\(389\) 3.27499i 0.166049i 0.996548 + 0.0830244i \(0.0264579\pi\)
−0.996548 + 0.0830244i \(0.973542\pi\)
\(390\) −16.9180 + 5.67202i −0.856678 + 0.287214i
\(391\) 1.10115i 0.0556877i
\(392\) 0.372080 6.99010i 0.0187929 0.353054i
\(393\) −22.5064 + 7.54561i −1.13530 + 0.380626i
\(394\) −4.06740 −0.204913
\(395\) 7.68172 0.386509
\(396\) −2.73262 3.61724i −0.137319 0.181773i
\(397\) 5.59615i 0.280863i −0.990090 0.140431i \(-0.955151\pi\)
0.990090 0.140431i \(-0.0448490\pi\)
\(398\) −3.97727 −0.199363
\(399\) −0.498833 1.63049i −0.0249729 0.0816264i
\(400\) −1.03127 −0.0515633
\(401\) 1.91564i 0.0956623i −0.998855 0.0478312i \(-0.984769\pi\)
0.998855 0.0478312i \(-0.0152309\pi\)
\(402\) 3.64791 + 10.8807i 0.181941 + 0.542679i
\(403\) 11.1821 0.557021
\(404\) 4.85686 0.241638
\(405\) −4.90053 + 17.2468i −0.243509 + 0.857001i
\(406\) −3.49783 0.0930282i −0.173594 0.00461691i
\(407\) 16.2717i 0.806556i
\(408\) 0.606269 + 1.80833i 0.0300148 + 0.0895256i
\(409\) 28.2363i 1.39619i −0.716003 0.698097i \(-0.754030\pi\)
0.716003 0.698097i \(-0.245970\pi\)
\(410\) 10.0509i 0.496378i
\(411\) −4.24609 12.6649i −0.209444 0.624713i
\(412\) 16.7641i 0.825909i
\(413\) −30.8888 0.821518i −1.51994 0.0404242i
\(414\) −2.39373 + 1.80833i −0.117645 + 0.0888745i
\(415\) −1.41212 −0.0693184
\(416\) −5.17124 −0.253541
\(417\) −8.22782 24.5413i −0.402918 1.20179i
\(418\) 0.562262i 0.0275011i
\(419\) −37.2658 −1.82055 −0.910277 0.413999i \(-0.864132\pi\)
−0.910277 + 0.413999i \(0.864132\pi\)
\(420\) −8.72984 + 2.67082i −0.425973 + 0.130322i
\(421\) −20.6006 −1.00401 −0.502005 0.864865i \(-0.667404\pi\)
−0.502005 + 0.864865i \(0.667404\pi\)
\(422\) 19.5402i 0.951201i
\(423\) −14.3760 + 10.8602i −0.698983 + 0.528042i
\(424\) 3.58482 0.174094
\(425\) −1.13558 −0.0550838
\(426\) 22.4798 7.53669i 1.08915 0.365154i
\(427\) 0.401788 15.1071i 0.0194439 0.731084i
\(428\) 6.16806i 0.298144i
\(429\) 12.8329 4.30243i 0.619580 0.207723i
\(430\) 3.30265i 0.159268i
\(431\) 37.1134i 1.78769i −0.448377 0.893845i \(-0.647998\pi\)
0.448377 0.893845i \(-0.352002\pi\)
\(432\) −2.93540 + 4.28759i −0.141229 + 0.206287i
\(433\) 40.1533i 1.92965i −0.262901 0.964823i \(-0.584679\pi\)
0.262901 0.964823i \(-0.415321\pi\)
\(434\) 5.71907 + 0.152104i 0.274524 + 0.00730124i
\(435\) 1.45060 + 4.32672i 0.0695508 + 0.207450i
\(436\) 5.38632 0.257958
\(437\) −0.372080 −0.0177990
\(438\) −16.0157 + 5.36952i −0.765262 + 0.256565i
\(439\) 17.1510i 0.818573i 0.912406 + 0.409287i \(0.134222\pi\)
−0.912406 + 0.409287i \(0.865778\pi\)
\(440\) −3.01042 −0.143516
\(441\) 17.4053 11.7497i 0.828823 0.559512i
\(442\) −5.69432 −0.270851
\(443\) 1.89816i 0.0901842i 0.998983 + 0.0450921i \(0.0143581\pi\)
−0.998983 + 0.0450921i \(0.985642\pi\)
\(444\) −17.6831 + 5.92854i −0.839205 + 0.281356i
\(445\) 19.7214 0.934885
\(446\) −26.3878 −1.24950
\(447\) 6.04355 + 18.0262i 0.285850 + 0.852609i
\(448\) −2.64482 0.0703415i −0.124956 0.00332332i
\(449\) 19.3704i 0.914148i 0.889429 + 0.457074i \(0.151102\pi\)
−0.889429 + 0.457074i \(0.848898\pi\)
\(450\) −1.86487 2.46857i −0.0879107 0.116370i
\(451\) 7.62395i 0.358998i
\(452\) 16.8518i 0.792643i
\(453\) 4.81948 1.61580i 0.226439 0.0759170i
\(454\) 5.16418i 0.242367i
\(455\) 0.724656 27.2468i 0.0339724 1.27735i
\(456\) −0.611036 + 0.204859i −0.0286144 + 0.00959339i
\(457\) −2.69634 −0.126129 −0.0630647 0.998009i \(-0.520087\pi\)
−0.0630647 + 0.998009i \(0.520087\pi\)
\(458\) −13.1393 −0.613959
\(459\) −3.23232 + 4.72130i −0.150872 + 0.220371i
\(460\) 1.99217i 0.0928853i
\(461\) 22.6634 1.05554 0.527770 0.849387i \(-0.323028\pi\)
0.527770 + 0.849387i \(0.323028\pi\)
\(462\) 6.62189 2.02591i 0.308078 0.0942538i
\(463\) 38.9153 1.80855 0.904273 0.426955i \(-0.140414\pi\)
0.904273 + 0.426955i \(0.140414\pi\)
\(464\) 1.32252i 0.0613966i
\(465\) −2.37177 7.07433i −0.109988 0.328064i
\(466\) 21.2452 0.984165
\(467\) 13.0789 0.605219 0.302610 0.953115i \(-0.402142\pi\)
0.302610 + 0.953115i \(0.402142\pi\)
\(468\) −9.35129 12.3785i −0.432264 0.572199i
\(469\) −17.5235 0.466056i −0.809162 0.0215204i
\(470\) 11.9643i 0.551872i
\(471\) 7.26669 + 21.6745i 0.334831 + 0.998707i
\(472\) 11.6790i 0.537569i
\(473\) 2.50518i 0.115188i
\(474\) 2.12300 + 6.33231i 0.0975126 + 0.290853i
\(475\) 0.383714i 0.0176060i
\(476\) −2.91235 0.0774567i −0.133487 0.00355022i
\(477\) 6.48253 + 8.58110i 0.296815 + 0.392901i
\(478\) 30.1168 1.37751
\(479\) −20.6284 −0.942536 −0.471268 0.881990i \(-0.656204\pi\)
−0.471268 + 0.881990i \(0.656204\pi\)
\(480\) 1.09684 + 3.27157i 0.0500637 + 0.149326i
\(481\) 55.6832i 2.53894i
\(482\) 3.61167 0.164507
\(483\) −1.34066 4.38208i −0.0610020 0.199392i
\(484\) −8.71649 −0.396204
\(485\) 2.12589i 0.0965315i
\(486\) −15.5715 + 0.726829i −0.706338 + 0.0329696i
\(487\) 15.9670 0.723536 0.361768 0.932268i \(-0.382173\pi\)
0.361768 + 0.932268i \(0.382173\pi\)
\(488\) −5.71197 −0.258569
\(489\) 22.9124 7.68172i 1.03613 0.347379i
\(490\) 0.741247 13.9255i 0.0334861 0.629088i
\(491\) 6.00786i 0.271131i 0.990768 + 0.135566i \(0.0432851\pi\)
−0.990768 + 0.135566i \(0.956715\pi\)
\(492\) 8.28529 2.77777i 0.373530 0.125231i
\(493\) 1.45630i 0.0655885i
\(494\) 1.92412i 0.0865701i
\(495\) −5.44384 7.20615i −0.244682 0.323892i
\(496\) 2.16237i 0.0970932i
\(497\) −0.962885 + 36.2042i −0.0431913 + 1.62398i
\(498\) −0.390269 1.16406i −0.0174884 0.0521629i
\(499\) 26.5494 1.18852 0.594258 0.804275i \(-0.297446\pi\)
0.594258 + 0.804275i \(0.297446\pi\)
\(500\) −12.0153 −0.537340
\(501\) −8.67938 + 2.90989i −0.387766 + 0.130004i
\(502\) 26.3289i 1.17512i
\(503\) −41.9026 −1.86834 −0.934171 0.356825i \(-0.883859\pi\)
−0.934171 + 0.356825i \(0.883859\pi\)
\(504\) −4.61432 6.45818i −0.205538 0.287670i
\(505\) 9.67568 0.430562
\(506\) 1.51113i 0.0671779i
\(507\) 22.5668 7.56584i 1.00223 0.336011i
\(508\) 13.2753 0.588995
\(509\) −8.32516 −0.369006 −0.184503 0.982832i \(-0.559068\pi\)
−0.184503 + 0.982832i \(0.559068\pi\)
\(510\) 1.20779 + 3.60249i 0.0534818 + 0.159521i
\(511\) 0.686008 25.7937i 0.0303472 1.14104i
\(512\) 1.00000i 0.0441942i
\(513\) −1.59533 1.09220i −0.0704355 0.0482220i
\(514\) 24.5168i 1.08139i
\(515\) 33.3970i 1.47165i
\(516\) −2.72249 + 0.912756i −0.119851 + 0.0401818i
\(517\) 9.07534i 0.399133i
\(518\) 0.757428 28.4790i 0.0332795 1.25130i
\(519\) 9.79260 3.28312i 0.429848 0.144113i
\(520\) −10.3020 −0.451771
\(521\) −27.3282 −1.19727 −0.598634 0.801023i \(-0.704290\pi\)
−0.598634 + 0.801023i \(0.704290\pi\)
\(522\) −3.16576 + 2.39156i −0.138562 + 0.104676i
\(523\) 22.3056i 0.975356i −0.873023 0.487678i \(-0.837844\pi\)
0.873023 0.487678i \(-0.162156\pi\)
\(524\) −13.7049 −0.598703
\(525\) 4.51909 1.38257i 0.197229 0.0603405i
\(526\) −10.1241 −0.441431
\(527\) 2.38110i 0.103722i
\(528\) −0.831993 2.48160i −0.0362078 0.107998i
\(529\) −1.00000 −0.0434783
\(530\) 7.14157 0.310210
\(531\) −27.9564 + 21.1195i −1.21320 + 0.916506i
\(532\) 0.0261727 0.984084i 0.00113473 0.0426655i
\(533\) 26.0899i 1.13008i
\(534\) 5.45042 + 16.2571i 0.235863 + 0.703512i
\(535\) 12.2878i 0.531248i
\(536\) 6.62562i 0.286183i
\(537\) 2.78824 + 8.31654i 0.120322 + 0.358885i
\(538\) 0.339791i 0.0146494i
\(539\) −0.562262 + 10.5630i −0.0242183 + 0.454979i
\(540\) −5.84780 + 8.54161i −0.251649 + 0.367572i
\(541\) 29.2687 1.25836 0.629180 0.777259i \(-0.283391\pi\)
0.629180 + 0.777259i \(0.283391\pi\)
\(542\) 15.1379 0.650228
\(543\) 1.11867 + 3.33668i 0.0480068 + 0.143191i
\(544\) 1.10115i 0.0472115i
\(545\) 10.7305 0.459642
\(546\) 22.6608 6.93286i 0.969792 0.296699i
\(547\) −43.0965 −1.84267 −0.921336 0.388768i \(-0.872901\pi\)
−0.921336 + 0.388768i \(0.872901\pi\)
\(548\) 7.71208i 0.329444i
\(549\) −10.3291 13.6729i −0.440836 0.583546i
\(550\) 1.55838 0.0664494
\(551\) −0.492085 −0.0209635
\(552\) −1.64221 + 0.550576i −0.0698973 + 0.0234341i
\(553\) −10.1983 0.271234i −0.433676 0.0115340i
\(554\) 25.5666i 1.08622i
\(555\) −35.2278 + 11.8106i −1.49534 + 0.501334i
\(556\) 14.9440i 0.633767i
\(557\) 35.2668i 1.49430i 0.664654 + 0.747151i \(0.268579\pi\)
−0.664654 + 0.747151i \(0.731421\pi\)
\(558\) 5.17613 3.91027i 0.219123 0.165535i
\(559\) 8.57297i 0.362598i
\(560\) −5.26892 0.140132i −0.222652 0.00592166i
\(561\) −0.916151 2.73262i −0.0386799 0.115371i
\(562\) 16.9275 0.714042
\(563\) 0.979062 0.0412625 0.0206313 0.999787i \(-0.493432\pi\)
0.0206313 + 0.999787i \(0.493432\pi\)
\(564\) −9.86259 + 3.30658i −0.415290 + 0.139232i
\(565\) 33.5717i 1.41237i
\(566\) −20.4813 −0.860892
\(567\) 7.11495 22.7239i 0.298800 0.954316i
\(568\) 13.6887 0.574366
\(569\) 16.0706i 0.673715i 0.941556 + 0.336857i \(0.109364\pi\)
−0.941556 + 0.336857i \(0.890636\pi\)
\(570\) −1.21729 + 0.408113i −0.0509865 + 0.0170940i
\(571\) 12.1219 0.507285 0.253643 0.967298i \(-0.418371\pi\)
0.253643 + 0.967298i \(0.418371\pi\)
\(572\) 7.81441 0.326737
\(573\) −1.35685 4.04709i −0.0566831 0.169070i
\(574\) −0.354887 + 13.3436i −0.0148127 + 0.556952i
\(575\) 1.03127i 0.0430068i
\(576\) −2.39373 + 1.80833i −0.0997388 + 0.0753470i
\(577\) 36.3260i 1.51227i 0.654414 + 0.756136i \(0.272915\pi\)
−0.654414 + 0.756136i \(0.727085\pi\)
\(578\) 15.7875i 0.656672i
\(579\) 2.03162 0.681132i 0.0844314 0.0283069i
\(580\) 2.63469i 0.109399i
\(581\) 1.87475 + 0.0498607i 0.0777775 + 0.00206857i
\(582\) −1.75244 + 0.587532i −0.0726411 + 0.0243540i
\(583\) −5.41713 −0.224355
\(584\) −9.75254 −0.403563
\(585\) −18.6293 24.6601i −0.770229 1.01957i
\(586\) 18.9978i 0.784793i
\(587\) 33.4043 1.37874 0.689372 0.724408i \(-0.257887\pi\)
0.689372 + 0.724408i \(0.257887\pi\)
\(588\) 11.6841 3.23755i 0.481844 0.133514i
\(589\) 0.804575 0.0331519
\(590\) 23.2665i 0.957867i
\(591\) −2.23941 6.67954i −0.0921172 0.274759i
\(592\) −10.7679 −0.442557
\(593\) 13.6187 0.559253 0.279626 0.960109i \(-0.409789\pi\)
0.279626 + 0.960109i \(0.409789\pi\)
\(594\) 4.43576 6.47911i 0.182002 0.265841i
\(595\) −5.80188 0.154307i −0.237854 0.00632596i
\(596\) 10.9768i 0.449626i
\(597\) −2.18979 6.53153i −0.0896222 0.267318i
\(598\) 5.17124i 0.211468i
\(599\) 11.6957i 0.477873i −0.971035 0.238937i \(-0.923201\pi\)
0.971035 0.238937i \(-0.0767988\pi\)
\(600\) −0.567791 1.69356i −0.0231800 0.0691393i
\(601\) 46.6845i 1.90430i 0.305629 + 0.952151i \(0.401133\pi\)
−0.305629 + 0.952151i \(0.598867\pi\)
\(602\) 0.116613 4.38462i 0.00475281 0.178704i
\(603\) −15.8599 + 11.9813i −0.645867 + 0.487916i
\(604\) 2.93475 0.119413
\(605\) −17.3647 −0.705976
\(606\) 2.67407 + 7.97600i 0.108627 + 0.324003i
\(607\) 34.3837i 1.39559i 0.716297 + 0.697796i \(0.245836\pi\)
−0.716297 + 0.697796i \(0.754164\pi\)
\(608\) −0.372080 −0.0150899
\(609\) −1.77305 5.79540i −0.0718476 0.234842i
\(610\) −11.3792 −0.460731
\(611\) 31.0567i 1.25642i
\(612\) −2.63586 + 1.99125i −0.106548 + 0.0804913i
\(613\) 4.03328 0.162903 0.0814513 0.996677i \(-0.474045\pi\)
0.0814513 + 0.996677i \(0.474045\pi\)
\(614\) −17.1863 −0.693582
\(615\) 16.5057 5.53378i 0.665574 0.223144i
\(616\) 3.99666 + 0.106295i 0.161030 + 0.00428275i
\(617\) 3.14403i 0.126574i 0.997995 + 0.0632869i \(0.0201583\pi\)
−0.997995 + 0.0632869i \(0.979842\pi\)
\(618\) 27.5303 9.22993i 1.10743 0.371282i
\(619\) 46.9319i 1.88635i −0.332295 0.943175i \(-0.607823\pi\)
0.332295 0.943175i \(-0.392177\pi\)
\(620\) 4.30780i 0.173006i
\(621\) −4.28759 2.93540i −0.172055 0.117793i
\(622\) 19.2329i 0.771168i
\(623\) −26.1823 0.696344i −1.04897 0.0278984i
\(624\) −2.84716 8.49227i −0.113978 0.339963i
\(625\) −18.7802 −0.751206
\(626\) 22.8922 0.914955
\(627\) 0.923354 0.309568i 0.0368752 0.0123630i
\(628\) 13.1983i 0.526670i
\(629\) −11.8571 −0.472772
\(630\) −9.19250 12.8658i −0.366238 0.512585i
\(631\) 6.79460 0.270489 0.135244 0.990812i \(-0.456818\pi\)
0.135244 + 0.990812i \(0.456818\pi\)
\(632\) 3.85596i 0.153382i
\(633\) −32.0891 + 10.7584i −1.27543 + 0.427606i
\(634\) 14.7130 0.584328
\(635\) 26.4466 1.04950
\(636\) 1.97372 + 5.88704i 0.0782630 + 0.233436i
\(637\) −1.92412 + 36.1475i −0.0762362 + 1.43222i
\(638\) 1.99850i 0.0791215i
\(639\) 24.7537 + 32.7671i 0.979241 + 1.29625i
\(640\) 1.99217i 0.0787474i
\(641\) 41.1142i 1.62391i 0.583717 + 0.811957i \(0.301598\pi\)
−0.583717 + 0.811957i \(0.698402\pi\)
\(642\) 10.1293 3.39599i 0.399770 0.134029i
\(643\) 30.5897i 1.20634i 0.797613 + 0.603170i \(0.206096\pi\)
−0.797613 + 0.603170i \(0.793904\pi\)
\(644\) 0.0703415 2.64482i 0.00277184 0.104220i
\(645\) −5.42366 + 1.81836i −0.213556 + 0.0715980i
\(646\) −0.409717 −0.0161201
\(647\) −19.7951 −0.778224 −0.389112 0.921190i \(-0.627218\pi\)
−0.389112 + 0.921190i \(0.627218\pi\)
\(648\) −8.65730 2.45990i −0.340091 0.0966339i
\(649\) 17.6485i 0.692763i
\(650\) 5.33292 0.209174
\(651\) 2.89900 + 9.47568i 0.113621 + 0.371381i
\(652\) 13.9521 0.546408
\(653\) 24.0068i 0.939459i 0.882810 + 0.469730i \(0.155649\pi\)
−0.882810 + 0.469730i \(0.844351\pi\)
\(654\) 2.96558 + 8.84548i 0.115963 + 0.345886i
\(655\) −27.3025 −1.06680
\(656\) 5.04520 0.196982
\(657\) −17.6358 23.3449i −0.688038 0.910773i
\(658\) 0.422447 15.8839i 0.0164687 0.619218i
\(659\) 40.1169i 1.56273i −0.624072 0.781367i \(-0.714523\pi\)
0.624072 0.781367i \(-0.285477\pi\)
\(660\) −1.65747 4.94376i −0.0645169 0.192436i
\(661\) 19.0674i 0.741635i 0.928706 + 0.370818i \(0.120923\pi\)
−0.928706 + 0.370818i \(0.879077\pi\)
\(662\) 20.0559i 0.779493i
\(663\) −3.13516 9.35129i −0.121759 0.363174i
\(664\) 0.708838i 0.0275082i
\(665\) 0.0521404 1.96046i 0.00202192 0.0760234i
\(666\) −19.4718 25.7754i −0.754519 0.998776i
\(667\) −1.32252 −0.0512083
\(668\) −5.28517 −0.204489
\(669\) −14.5285 43.3345i −0.561705 1.67541i
\(670\) 13.1993i 0.509935i
\(671\) 8.63153 0.333216
\(672\) −1.34066 4.38208i −0.0517170 0.169042i
\(673\) −13.5361 −0.521779 −0.260890 0.965369i \(-0.584016\pi\)
−0.260890 + 0.965369i \(0.584016\pi\)
\(674\) 10.7491i 0.414041i
\(675\) 3.02717 4.42165i 0.116516 0.170189i
\(676\) 13.7417 0.528526
\(677\) −11.7065 −0.449917 −0.224959 0.974368i \(-0.572225\pi\)
−0.224959 + 0.974368i \(0.572225\pi\)
\(678\) 27.6743 9.27822i 1.06283 0.356328i
\(679\) 0.0750629 2.82234i 0.00288065 0.108312i
\(680\) 2.19368i 0.0841238i
\(681\) 8.48069 2.84328i 0.324981 0.108955i
\(682\) 3.26762i 0.125124i
\(683\) 33.6577i 1.28788i 0.765078 + 0.643938i \(0.222701\pi\)
−0.765078 + 0.643938i \(0.777299\pi\)
\(684\) −0.672844 0.890661i −0.0257268 0.0340553i
\(685\) 15.3638i 0.587019i
\(686\) −1.47578 + 18.4614i −0.0563455 + 0.704858i
\(687\) −7.23418 21.5775i −0.276001 0.823234i
\(688\) −1.65782 −0.0632037
\(689\) −18.5380 −0.706240
\(690\) −3.27157 + 1.09684i −0.124546 + 0.0417560i
\(691\) 1.22804i 0.0467168i 0.999727 + 0.0233584i \(0.00743588\pi\)
−0.999727 + 0.0233584i \(0.992564\pi\)
\(692\) 5.96305 0.226681
\(693\) 6.97283 + 9.75915i 0.264876 + 0.370719i
\(694\) −21.6678 −0.822500
\(695\) 29.7710i 1.12928i
\(696\) −2.17187 + 0.728150i −0.0823243 + 0.0276005i
\(697\) 5.55553 0.210431
\(698\) −15.5372 −0.588091
\(699\) 11.6971 + 34.8891i 0.442425 + 1.31963i
\(700\) 2.72751 + 0.0725408i 0.103090 + 0.00274178i
\(701\) 28.8736i 1.09054i −0.838260 0.545270i \(-0.816427\pi\)
0.838260 0.545270i \(-0.183573\pi\)
\(702\) 15.1796 22.1722i 0.572918 0.836834i
\(703\) 4.00651i 0.151109i
\(704\) 1.51113i 0.0569529i
\(705\) −19.6479 + 6.58726i −0.739984 + 0.248091i
\(706\) 14.7290i 0.554332i
\(707\) −12.8455 0.341639i −0.483105 0.0128486i
\(708\) −19.1794 + 6.43018i −0.720806 + 0.241661i
\(709\) −23.0384 −0.865225 −0.432613 0.901580i \(-0.642408\pi\)
−0.432613 + 0.901580i \(0.642408\pi\)
\(710\) 27.2702 1.02343
\(711\) −9.23013 + 6.97284i −0.346157 + 0.261502i
\(712\) 9.89948i 0.370999i
\(713\) 2.16237 0.0809814
\(714\) −1.47627 4.82534i −0.0552480 0.180584i
\(715\) 15.5676 0.582196
\(716\) 5.06422i 0.189259i
\(717\) 16.5816 + 49.4582i 0.619251 + 1.84705i
\(718\) −29.7728 −1.11111
\(719\) 31.1227 1.16068 0.580340 0.814374i \(-0.302920\pi\)
0.580340 + 0.814374i \(0.302920\pi\)
\(720\) −4.76872 + 3.60249i −0.177720 + 0.134257i
\(721\) −1.17921 + 44.3380i −0.0439162 + 1.65123i
\(722\) 18.8616i 0.701954i
\(723\) 1.98850 + 5.93114i 0.0739532 + 0.220581i
\(724\) 2.03182i 0.0755119i
\(725\) 1.36387i 0.0506530i
\(726\) −4.79909 14.3143i −0.178111 0.531255i
\(727\) 33.9221i 1.25810i 0.777365 + 0.629050i \(0.216556\pi\)
−0.777365 + 0.629050i \(0.783444\pi\)
\(728\) 13.6770 + 0.363752i 0.506902 + 0.0134816i
\(729\) −9.76691 25.1716i −0.361737 0.932280i
\(730\) −19.4287 −0.719088
\(731\) −1.82551 −0.0675190
\(732\) −3.14488 9.38028i −0.116238 0.346705i
\(733\) 13.5652i 0.501040i 0.968111 + 0.250520i \(0.0806017\pi\)
−0.968111 + 0.250520i \(0.919398\pi\)
\(734\) −20.2090 −0.745926
\(735\) 23.2767 6.44975i 0.858574 0.237902i
\(736\) −1.00000 −0.0368605
\(737\) 10.0122i 0.368803i
\(738\) 9.12337 + 12.0768i 0.335836 + 0.444555i
\(739\) 26.2623 0.966076 0.483038 0.875599i \(-0.339533\pi\)
0.483038 + 0.875599i \(0.339533\pi\)
\(740\) −21.4514 −0.788570
\(741\) 3.15981 1.05937i 0.116078 0.0389170i
\(742\) −9.48119 0.252162i −0.348065 0.00925714i
\(743\) 13.8311i 0.507415i −0.967281 0.253707i \(-0.918350\pi\)
0.967281 0.253707i \(-0.0816500\pi\)
\(744\) 3.55107 1.19055i 0.130189 0.0436477i
\(745\) 21.8676i 0.801165i
\(746\) 36.6965i 1.34355i
\(747\) 1.69677 1.28181i 0.0620814 0.0468990i
\(748\) 1.66399i 0.0608413i
\(749\) −0.433870 + 16.3134i −0.0158533 + 0.596078i
\(750\) −6.61534 19.7317i −0.241558 0.720499i
\(751\) 5.93861 0.216703 0.108351 0.994113i \(-0.465443\pi\)
0.108351 + 0.994113i \(0.465443\pi\)
\(752\) −6.00567 −0.219004
\(753\) −43.2377 + 14.4961i −1.57567 + 0.528266i
\(754\) 6.83908i 0.249065i
\(755\) 5.84651 0.212776
\(756\) 8.06518 11.1334i 0.293328 0.404918i
\(757\) 30.3634 1.10358 0.551788 0.833985i \(-0.313946\pi\)
0.551788 + 0.833985i \(0.313946\pi\)
\(758\) 4.31615i 0.156770i
\(759\) 2.48160 0.831993i 0.0900763 0.0301994i
\(760\) −0.741247 −0.0268879
\(761\) 7.92613 0.287322 0.143661 0.989627i \(-0.454113\pi\)
0.143661 + 0.989627i \(0.454113\pi\)
\(762\) 7.30905 + 21.8008i 0.264779 + 0.789761i
\(763\) −14.2458 0.378882i −0.515733 0.0137164i
\(764\) 2.46441i 0.0891593i
\(765\) −5.25108 + 3.96690i −0.189853 + 0.143423i
\(766\) 10.0077i 0.361593i
\(767\) 60.3948i 2.18073i
\(768\) −1.64221 + 0.550576i −0.0592583 + 0.0198672i
\(769\) 40.0002i 1.44244i −0.692704 0.721222i \(-0.743581\pi\)
0.692704 0.721222i \(-0.256419\pi\)
\(770\) 7.96202 + 0.211758i 0.286931 + 0.00763122i
\(771\) −40.2619 + 13.4984i −1.45000 + 0.486133i
\(772\) 1.23713 0.0445251
\(773\) 0.612052 0.0220140 0.0110070 0.999939i \(-0.496496\pi\)
0.0110070 + 0.999939i \(0.496496\pi\)
\(774\) −2.99788 3.96837i −0.107757 0.142640i
\(775\) 2.22998i 0.0801032i
\(776\) −1.06712 −0.0383074
\(777\) 47.1857 14.4360i 1.69278 0.517890i
\(778\) −3.27499 −0.117414
\(779\) 1.87722i 0.0672584i
\(780\) −5.67202 16.9180i −0.203091 0.605763i
\(781\) −20.6854 −0.740183
\(782\) −1.10115 −0.0393771
\(783\) −5.67044 3.88213i −0.202645 0.138736i
\(784\) 6.99010 + 0.372080i 0.249647 + 0.0132886i
\(785\) 26.2933i 0.938447i
\(786\) −7.54561 22.5064i −0.269143 0.802777i
\(787\) 6.88190i 0.245313i 0.992449 + 0.122657i \(0.0391414\pi\)
−0.992449 + 0.122657i \(0.960859\pi\)
\(788\) 4.06740i 0.144895i
\(789\) −5.57408 16.6259i −0.198443 0.591898i
\(790\) 7.68172i 0.273303i
\(791\) −1.18538 + 44.5700i −0.0421473 + 1.58473i
\(792\) 3.61724 2.73262i 0.128533 0.0970994i
\(793\) 29.5379 1.04892
\(794\) 5.59615 0.198600
\(795\) 3.93198 + 11.7280i 0.139453 + 0.415948i
\(796\) 3.97727i 0.140971i
\(797\) 40.2239 1.42480 0.712401 0.701772i \(-0.247608\pi\)
0.712401 + 0.701772i \(0.247608\pi\)
\(798\) 1.63049 0.498833i 0.0577186 0.0176585i
\(799\) −6.61316 −0.233957
\(800\) 1.03127i 0.0364608i
\(801\) −23.6967 + 17.9015i −0.837281 + 0.632519i
\(802\) 1.91564 0.0676435
\(803\) 14.7373 0.520070
\(804\) −10.8807 + 3.64791i −0.383732 + 0.128652i
\(805\) 0.140132 5.26892i 0.00493901 0.185705i
\(806\) 11.1821i 0.393873i
\(807\) 0.558010 0.187081i 0.0196429 0.00658557i
\(808\) 4.85686i 0.170864i
\(809\) 16.9551i 0.596109i 0.954549 + 0.298054i \(0.0963377\pi\)
−0.954549 + 0.298054i \(0.903662\pi\)
\(810\) −17.2468 4.90053i −0.605991 0.172187i
\(811\) 30.8341i 1.08273i −0.840787 0.541366i \(-0.817907\pi\)
0.840787 0.541366i \(-0.182093\pi\)
\(812\) 0.0930282 3.49783i 0.00326465 0.122750i
\(813\) 8.33456 + 24.8596i 0.292306 + 0.871865i
\(814\) 16.2717 0.570321
\(815\) 27.7950 0.973617
\(816\) −1.80833 + 0.606269i −0.0633041 + 0.0212237i
\(817\) 0.616842i 0.0215806i
\(818\) 28.2363 0.987259
\(819\) 23.8617 + 33.3968i 0.833796 + 1.16698i
\(820\) 10.0509 0.350992
\(821\) 3.15438i 0.110089i 0.998484 + 0.0550443i \(0.0175300\pi\)
−0.998484 + 0.0550443i \(0.982470\pi\)
\(822\) 12.6649 4.24609i 0.441738 0.148099i
\(823\) 13.0983 0.456579 0.228290 0.973593i \(-0.426687\pi\)
0.228290 + 0.973593i \(0.426687\pi\)
\(824\) 16.7641 0.584006
\(825\) 0.858006 + 2.55919i 0.0298719 + 0.0890995i
\(826\) 0.821518 30.8888i 0.0285843 1.07476i
\(827\) 26.0225i 0.904889i −0.891792 0.452445i \(-0.850552\pi\)
0.891792 0.452445i \(-0.149448\pi\)
\(828\) −1.80833 2.39373i −0.0628437 0.0831879i
\(829\) 14.1499i 0.491446i 0.969340 + 0.245723i \(0.0790254\pi\)
−0.969340 + 0.245723i \(0.920975\pi\)
\(830\) 1.41212i 0.0490155i
\(831\) −41.9858 + 14.0764i −1.45647 + 0.488303i
\(832\) 5.17124i 0.179280i
\(833\) 7.69717 + 0.409717i 0.266691 + 0.0141959i
\(834\) 24.5413 8.22782i 0.849794 0.284906i
\(835\) −10.5289 −0.364369
\(836\) 0.562262 0.0194462
\(837\) 9.27136 + 6.34741i 0.320465 + 0.219398i
\(838\) 37.2658i 1.28733i
\(839\) 2.73390 0.0943847 0.0471923 0.998886i \(-0.484973\pi\)
0.0471923 + 0.998886i \(0.484973\pi\)
\(840\) −2.67082 8.72984i −0.0921519 0.301208i
\(841\) 27.2509 0.939687
\(842\) 20.6006i 0.709942i
\(843\) 9.31987 + 27.7985i 0.320993 + 0.957432i
\(844\) −19.5402 −0.672601
\(845\) 27.3757 0.941754
\(846\) −10.8602 14.3760i −0.373382 0.494255i
\(847\) 23.0535 + 0.613130i 0.792128 + 0.0210674i
\(848\) 3.58482i 0.123103i
\(849\) −11.2765 33.6346i −0.387008 1.15434i
\(850\) 1.13558i 0.0389501i
\(851\) 10.7679i 0.369118i
\(852\) 7.53669 + 22.4798i 0.258203 + 0.770145i
\(853\) 32.3900i 1.10901i 0.832179 + 0.554507i \(0.187093\pi\)
−0.832179 + 0.554507i \(0.812907\pi\)
\(854\) 15.1071 + 0.401788i 0.516955 + 0.0137489i
\(855\) −1.34042 1.77435i −0.0458413 0.0606813i
\(856\) 6.16806 0.210820
\(857\) 28.3268 0.967624 0.483812 0.875172i \(-0.339252\pi\)
0.483812 + 0.875172i \(0.339252\pi\)
\(858\) 4.30243 + 12.8329i 0.146883 + 0.438109i
\(859\) 18.2415i 0.622393i 0.950346 + 0.311196i \(0.100730\pi\)
−0.950346 + 0.311196i \(0.899270\pi\)
\(860\) −3.30265 −0.112620
\(861\) −22.1085 + 6.76388i −0.753455 + 0.230513i
\(862\) 37.1134 1.26409
\(863\) 17.4332i 0.593432i 0.954966 + 0.296716i \(0.0958914\pi\)
−0.954966 + 0.296716i \(0.904109\pi\)
\(864\) −4.28759 2.93540i −0.145867 0.0998642i
\(865\) 11.8794 0.403912
\(866\) 40.1533 1.36447
\(867\) 25.9264 8.69220i 0.880506 0.295203i
\(868\) −0.152104 + 5.71907i −0.00516275 + 0.194118i
\(869\) 5.82685i 0.197663i
\(870\) −4.32672 + 1.45060i −0.146690 + 0.0491799i
\(871\) 34.2626i 1.16094i
\(872\) 5.38632i 0.182404i
\(873\) −1.92971 2.55440i −0.0653107 0.0864534i
\(874\) 0.372080i 0.0125858i
\(875\) 31.7782 + 0.845174i 1.07430 + 0.0285721i
\(876\) −5.36952 16.0157i −0.181419 0.541122i
\(877\) −47.3073 −1.59745 −0.798727 0.601694i \(-0.794493\pi\)
−0.798727 + 0.601694i \(0.794493\pi\)
\(878\) −17.1510 −0.578819
\(879\) −31.1985 + 10.4598i −1.05230 + 0.352799i
\(880\) 3.01042i 0.101481i
\(881\) −8.43256 −0.284100 −0.142050 0.989859i \(-0.545369\pi\)
−0.142050 + 0.989859i \(0.545369\pi\)
\(882\) 11.7497 + 17.4053i 0.395634 + 0.586066i
\(883\) 27.2561 0.917240 0.458620 0.888632i \(-0.348344\pi\)
0.458620 + 0.888632i \(0.348344\pi\)
\(884\) 5.69432i 0.191521i
\(885\) −38.2086 + 12.8100i −1.28437 + 0.430603i
\(886\) −1.89816 −0.0637699
\(887\) 11.6157 0.390016 0.195008 0.980802i \(-0.437527\pi\)
0.195008 + 0.980802i \(0.437527\pi\)
\(888\) −5.92854 17.6831i −0.198949 0.593407i
\(889\) −35.1107 0.933802i −1.17757 0.0313187i
\(890\) 19.7214i 0.661064i
\(891\) 13.0823 + 3.71723i 0.438274 + 0.124532i
\(892\) 26.3878i 0.883530i
\(893\) 2.23459i 0.0747778i
\(894\) −18.0262 + 6.04355i −0.602886 + 0.202126i
\(895\) 10.0888i 0.337231i
\(896\) 0.0703415 2.64482i 0.00234994 0.0883571i
\(897\) 8.49227 2.84716i 0.283549 0.0950639i
\(898\) −19.3704 −0.646400
\(899\) 2.85978 0.0953791
\(900\) 2.46857 1.86487i 0.0822858 0.0621623i
\(901\) 3.94744i 0.131508i
\(902\) −7.62395 −0.253850
\(903\) 7.26470 2.22257i 0.241754 0.0739624i
\(904\) 16.8518 0.560483
\(905\) 4.04772i 0.134551i
\(906\) 1.61580 + 4.81948i 0.0536814 + 0.160116i
\(907\) 42.8792 1.42378 0.711890 0.702291i \(-0.247840\pi\)
0.711890 + 0.702291i \(0.247840\pi\)
\(908\) 5.16418 0.171379
\(909\) −11.6260 + 8.78280i −0.385611 + 0.291307i
\(910\) 27.2468 + 0.724656i 0.903223 + 0.0240221i
\(911\) 27.3966i 0.907691i −0.891080 0.453845i \(-0.850052\pi\)
0.891080 0.453845i \(-0.149948\pi\)
\(912\) −0.204859 0.611036i −0.00678355 0.0202334i
\(913\) 1.07115i 0.0354497i
\(914\) 2.69634i 0.0891869i
\(915\) −6.26512 18.6871i −0.207119 0.617776i
\(916\) 13.1393i 0.434134i
\(917\) 36.2470 + 0.964025i 1.19698 + 0.0318349i
\(918\) −4.72130 3.23232i −0.155826 0.106682i
\(919\) −12.2243 −0.403241 −0.201620 0.979464i \(-0.564621\pi\)
−0.201620 + 0.979464i \(0.564621\pi\)
\(920\) −1.99217 −0.0656798
\(921\) −9.46236 28.2235i −0.311795 0.929997i
\(922\) 22.6634i 0.746379i
\(923\) −70.7876 −2.33000
\(924\) 2.02591 + 6.62189i 0.0666475 + 0.217844i
\(925\) 11.1045 0.365115
\(926\) 38.9153i 1.27883i
\(927\) 30.3150 + 40.1288i 0.995677 + 1.31800i
\(928\) −1.32252 −0.0434139
\(929\) 3.01871 0.0990406 0.0495203 0.998773i \(-0.484231\pi\)
0.0495203 + 0.998773i \(0.484231\pi\)
\(930\) 7.07433 2.37177i 0.231976 0.0777736i
\(931\) −0.138444 + 2.60088i −0.00453732 + 0.0852404i
\(932\) 21.2452i 0.695910i
\(933\) 31.5845 10.5892i 1.03403 0.346674i
\(934\) 13.0789i 0.427955i
\(935\) 3.31494i 0.108410i
\(936\) 12.3785 9.35129i 0.404606 0.305657i
\(937\) 1.21195i 0.0395928i 0.999804 + 0.0197964i \(0.00630181\pi\)
−0.999804 + 0.0197964i \(0.993698\pi\)
\(938\) 0.466056 17.5235i 0.0152173 0.572164i
\(939\) 12.6039 + 37.5938i 0.411312 + 1.22683i
\(940\) −11.9643 −0.390232
\(941\) −12.7187 −0.414618 −0.207309 0.978276i \(-0.566470\pi\)
−0.207309 + 0.978276i \(0.566470\pi\)
\(942\) −21.6745 + 7.26669i −0.706192 + 0.236761i
\(943\) 5.04520i 0.164294i
\(944\) −11.6790 −0.380119
\(945\) 16.0672 22.1796i 0.522666 0.721504i
\(946\) 2.50518 0.0814504
\(947\) 1.64646i 0.0535027i 0.999642 + 0.0267513i \(0.00851623\pi\)
−0.999642 + 0.0267513i \(0.991484\pi\)
\(948\) −6.33231 + 2.12300i −0.205664 + 0.0689518i
\(949\) 50.4327 1.63711
\(950\) 0.383714 0.0124493
\(951\) 8.10063 + 24.1619i 0.262681 + 0.783503i
\(952\) 0.0774567 2.91235i 0.00251039 0.0943897i
\(953\) 11.8018i 0.382298i −0.981561 0.191149i \(-0.938779\pi\)
0.981561 0.191149i \(-0.0612214\pi\)
\(954\) −8.58110 + 6.48253i −0.277823 + 0.209880i
\(955\) 4.90952i 0.158868i
\(956\) 30.1168i 0.974047i
\(957\) 3.28197 1.10033i 0.106091 0.0355686i
\(958\) 20.6284i 0.666474i
\(959\) −0.542479 + 20.3970i −0.0175176 + 0.658655i
\(960\) −3.27157 + 1.09684i −0.105589 + 0.0354004i
\(961\) 26.3242 0.849166
\(962\) 55.6832 1.79530
\(963\) 11.1539 + 14.7647i 0.359429 + 0.475785i
\(964\) 3.61167i 0.116324i
\(965\) 2.46456 0.0793370
\(966\) 4.38208 1.34066i 0.140991 0.0431350i
\(967\) 12.6572 0.407027 0.203514 0.979072i \(-0.434764\pi\)
0.203514 + 0.979072i \(0.434764\pi\)
\(968\) 8.71649i 0.280158i
\(969\) −0.225581 0.672844i −0.00724670 0.0216149i
\(970\) −2.12589 −0.0682581
\(971\) −23.2660 −0.746642 −0.373321 0.927702i \(-0.621781\pi\)
−0.373321 + 0.927702i \(0.621781\pi\)
\(972\) −0.726829 15.5715i −0.0233131 0.499456i
\(973\) −1.05118 + 39.5241i −0.0336994 + 1.26709i
\(974\) 15.9670i 0.511617i
\(975\) 2.93618 + 8.75779i 0.0940330 + 0.280474i
\(976\) 5.71197i 0.182836i
\(977\) 39.8202i 1.27396i 0.770880 + 0.636981i \(0.219817\pi\)
−0.770880 + 0.636981i \(0.780183\pi\)
\(978\) 7.68172 + 22.9124i 0.245634 + 0.732658i
\(979\) 14.9594i 0.478104i
\(980\) 13.9255 + 0.741247i 0.444833 + 0.0236783i
\(981\) −12.8934 + 9.74023i −0.411654 + 0.310982i
\(982\) −6.00786 −0.191719
\(983\) 44.6488 1.42407 0.712037 0.702141i \(-0.247773\pi\)
0.712037 + 0.702141i \(0.247773\pi\)
\(984\) 2.77777 + 8.28529i 0.0885520 + 0.264125i
\(985\) 8.10294i 0.258181i
\(986\) −1.45630 −0.0463780
\(987\) 26.3173 8.05154i 0.837690 0.256283i
\(988\) 1.92412 0.0612143
\(989\) 1.65782i 0.0527156i
\(990\) 7.20615 5.44384i 0.229026 0.173016i
\(991\) 49.9489 1.58668 0.793339 0.608780i \(-0.208341\pi\)
0.793339 + 0.608780i \(0.208341\pi\)
\(992\) 2.16237 0.0686553
\(993\) 32.9360 11.0423i 1.04519 0.350416i
\(994\) −36.2042 0.962885i −1.14833 0.0305409i
\(995\) 7.92339i 0.251188i
\(996\) 1.16406 0.390269i 0.0368847 0.0123662i
\(997\) 32.2007i 1.01981i 0.860232 + 0.509903i \(0.170319\pi\)
−0.860232 + 0.509903i \(0.829681\pi\)
\(998\) 26.5494i 0.840407i
\(999\) 31.6080 46.1683i 1.00003 1.46070i
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 966.2.f.c.461.15 yes 28
3.2 odd 2 inner 966.2.f.c.461.14 yes 28
7.6 odd 2 inner 966.2.f.c.461.28 yes 28
21.20 even 2 inner 966.2.f.c.461.1 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.f.c.461.1 28 21.20 even 2 inner
966.2.f.c.461.14 yes 28 3.2 odd 2 inner
966.2.f.c.461.15 yes 28 1.1 even 1 trivial
966.2.f.c.461.28 yes 28 7.6 odd 2 inner