Properties

Label 531.2.i.c.19.5
Level $531$
Weight $2$
Character 531.19
Analytic conductor $4.240$
Analytic rank $0$
Dimension $140$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [531,2,Mod(19,531)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(531, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("531.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.i (of order \(29\), degree \(28\), 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: \(4.24005634733\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(5\) over \(\Q(\zeta_{29})\)
Twist minimal: no (minimal twist has level 177)
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 19.5
Character \(\chi\) \(=\) 531.19
Dual form 531.2.i.c.28.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.07727 - 2.03195i) q^{2} +(-1.84595 - 2.72257i) q^{4} +(3.23491 - 0.712057i) q^{5} +(1.31099 - 0.996592i) q^{7} +(-2.94796 + 0.320610i) q^{8} +O(q^{10})\) \(q+(1.07727 - 2.03195i) q^{2} +(-1.84595 - 2.72257i) q^{4} +(3.23491 - 0.712057i) q^{5} +(1.31099 - 0.996592i) q^{7} +(-2.94796 + 0.320610i) q^{8} +(2.03802 - 7.34027i) q^{10} +(0.922770 + 2.31598i) q^{11} +(0.119964 + 2.21261i) q^{13} +(-0.612729 - 3.73748i) q^{14} +(-0.0892630 + 0.224033i) q^{16} +(2.34147 + 1.77994i) q^{17} +(-6.93750 + 2.33752i) q^{19} +(-7.91009 - 7.49283i) q^{20} +(5.70004 + 0.619916i) q^{22} +(-2.37337 + 1.42801i) q^{23} +(5.41973 - 2.50743i) q^{25} +(4.62515 + 2.13982i) q^{26} +(-5.13331 - 1.72961i) q^{28} +(-1.14256 - 2.15509i) q^{29} +(-7.57979 - 2.55393i) q^{31} +(-3.48038 - 4.09742i) q^{32} +(6.13915 - 2.84027i) q^{34} +(3.53132 - 4.15739i) q^{35} +(-9.97984 - 1.08537i) q^{37} +(-2.72386 + 16.6148i) q^{38} +(-9.30809 + 3.13626i) q^{40} +(9.34133 + 5.62049i) q^{41} +(-2.62534 + 6.58910i) q^{43} +(4.60202 - 6.78747i) q^{44} +(0.344881 + 6.36095i) q^{46} +(-6.67879 - 1.47011i) q^{47} +(-1.14719 + 4.13180i) q^{49} +(0.743543 - 13.7138i) q^{50} +(5.80252 - 4.41096i) q^{52} +(-0.271871 - 0.979189i) q^{53} +(4.63418 + 6.83491i) q^{55} +(-3.54524 + 3.35823i) q^{56} -5.60990 q^{58} +(-0.287330 - 7.67577i) q^{59} +(1.09816 - 2.07134i) q^{61} +(-13.3550 + 12.6505i) q^{62} +(-12.5461 + 2.76162i) q^{64} +(1.96357 + 7.07216i) q^{65} +(16.2238 - 1.76445i) q^{67} +(0.523775 - 9.66046i) q^{68} +(-4.64343 - 11.6541i) q^{70} +(6.36506 + 1.40106i) q^{71} +(-1.45289 - 8.86226i) q^{73} +(-12.9564 + 19.1093i) q^{74} +(19.1703 + 14.5729i) q^{76} +(3.51783 + 2.11661i) q^{77} +(9.22548 + 8.73884i) q^{79} +(-0.129233 + 0.788288i) q^{80} +(21.4838 - 12.9263i) q^{82} +(-0.0827415 + 0.0974108i) q^{83} +(8.84184 + 4.09067i) q^{85} +(10.5605 + 12.4328i) q^{86} +(-3.46281 - 6.53156i) q^{88} +(-3.29319 - 6.21161i) q^{89} +(2.36234 + 2.78116i) q^{91} +(8.26897 + 3.82564i) q^{92} +(-10.1821 + 11.9873i) q^{94} +(-20.7777 + 12.5016i) q^{95} +(-2.41950 + 14.7583i) q^{97} +(7.15979 + 6.78211i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).

\(n\) \(119\) \(415\)
\(\chi(n)\) \(1\) \(e\left(\frac{19}{29}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07727 2.03195i 0.761748 1.43681i −0.133411 0.991061i \(-0.542593\pi\)
0.895159 0.445748i \(-0.147062\pi\)
\(3\) 0 0
\(4\) −1.84595 2.72257i −0.922973 1.36128i
\(5\) 3.23491 0.712057i 1.44670 0.318442i 0.578914 0.815388i \(-0.303477\pi\)
0.867781 + 0.496947i \(0.165546\pi\)
\(6\) 0 0
\(7\) 1.31099 0.996592i 0.495509 0.376676i −0.327367 0.944897i \(-0.606161\pi\)
0.822876 + 0.568221i \(0.192368\pi\)
\(8\) −2.94796 + 0.320610i −1.04226 + 0.113353i
\(9\) 0 0
\(10\) 2.03802 7.34027i 0.644477 2.32120i
\(11\) 0.922770 + 2.31598i 0.278226 + 0.698293i 0.999981 + 0.00614541i \(0.00195616\pi\)
−0.721756 + 0.692148i \(0.756665\pi\)
\(12\) 0 0
\(13\) 0.119964 + 2.21261i 0.0332720 + 0.613666i 0.966858 + 0.255314i \(0.0821787\pi\)
−0.933586 + 0.358353i \(0.883339\pi\)
\(14\) −0.612729 3.73748i −0.163759 0.998884i
\(15\) 0 0
\(16\) −0.0892630 + 0.224033i −0.0223158 + 0.0560083i
\(17\) 2.34147 + 1.77994i 0.567889 + 0.431698i 0.849316 0.527885i \(-0.177015\pi\)
−0.281427 + 0.959583i \(0.590808\pi\)
\(18\) 0 0
\(19\) −6.93750 + 2.33752i −1.59157 + 0.536263i −0.969161 0.246428i \(-0.920743\pi\)
−0.622411 + 0.782691i \(0.713847\pi\)
\(20\) −7.91009 7.49283i −1.76875 1.67545i
\(21\) 0 0
\(22\) 5.70004 + 0.619916i 1.21525 + 0.132167i
\(23\) −2.37337 + 1.42801i −0.494883 + 0.297761i −0.741031 0.671471i \(-0.765663\pi\)
0.246148 + 0.969232i \(0.420835\pi\)
\(24\) 0 0
\(25\) 5.41973 2.50743i 1.08395 0.501487i
\(26\) 4.62515 + 2.13982i 0.907066 + 0.419653i
\(27\) 0 0
\(28\) −5.13331 1.72961i −0.970104 0.326866i
\(29\) −1.14256 2.15509i −0.212168 0.400191i 0.754471 0.656333i \(-0.227893\pi\)
−0.966639 + 0.256142i \(0.917549\pi\)
\(30\) 0 0
\(31\) −7.57979 2.55393i −1.36137 0.458699i −0.458532 0.888678i \(-0.651624\pi\)
−0.902839 + 0.429979i \(0.858521\pi\)
\(32\) −3.48038 4.09742i −0.615250 0.724329i
\(33\) 0 0
\(34\) 6.13915 2.84027i 1.05286 0.487103i
\(35\) 3.53132 4.15739i 0.596901 0.702727i
\(36\) 0 0
\(37\) −9.97984 1.08537i −1.64068 0.178434i −0.759264 0.650783i \(-0.774441\pi\)
−0.881412 + 0.472349i \(0.843406\pi\)
\(38\) −2.72386 + 16.6148i −0.441869 + 2.69528i
\(39\) 0 0
\(40\) −9.30809 + 3.13626i −1.47174 + 0.495886i
\(41\) 9.34133 + 5.62049i 1.45887 + 0.877773i 0.999943 0.0107003i \(-0.00340608\pi\)
0.458928 + 0.888474i \(0.348234\pi\)
\(42\) 0 0
\(43\) −2.62534 + 6.58910i −0.400360 + 1.00483i 0.581215 + 0.813750i \(0.302578\pi\)
−0.981575 + 0.191078i \(0.938802\pi\)
\(44\) 4.60202 6.78747i 0.693780 1.02325i
\(45\) 0 0
\(46\) 0.344881 + 6.36095i 0.0508499 + 0.937871i
\(47\) −6.67879 1.47011i −0.974201 0.214438i −0.300777 0.953694i \(-0.597246\pi\)
−0.673424 + 0.739256i \(0.735177\pi\)
\(48\) 0 0
\(49\) −1.14719 + 4.13180i −0.163884 + 0.590257i
\(50\) 0.743543 13.7138i 0.105153 1.93943i
\(51\) 0 0
\(52\) 5.80252 4.41096i 0.804664 0.611690i
\(53\) −0.271871 0.979189i −0.0373443 0.134502i 0.942528 0.334127i \(-0.108441\pi\)
−0.979872 + 0.199625i \(0.936028\pi\)
\(54\) 0 0
\(55\) 4.63418 + 6.83491i 0.624873 + 0.921619i
\(56\) −3.54524 + 3.35823i −0.473753 + 0.448763i
\(57\) 0 0
\(58\) −5.60990 −0.736616
\(59\) −0.287330 7.67577i −0.0374072 0.999300i
\(60\) 0 0
\(61\) 1.09816 2.07134i 0.140605 0.265208i −0.803202 0.595707i \(-0.796872\pi\)
0.943807 + 0.330499i \(0.107217\pi\)
\(62\) −13.3550 + 12.6505i −1.69608 + 1.60662i
\(63\) 0 0
\(64\) −12.5461 + 2.76162i −1.56827 + 0.345202i
\(65\) 1.96357 + 7.07216i 0.243551 + 0.877193i
\(66\) 0 0
\(67\) 16.2238 1.76445i 1.98206 0.215562i 0.982485 0.186344i \(-0.0596638\pi\)
0.999573 0.0292179i \(-0.00930167\pi\)
\(68\) 0.523775 9.66046i 0.0635170 1.17150i
\(69\) 0 0
\(70\) −4.64343 11.6541i −0.554995 1.39293i
\(71\) 6.36506 + 1.40106i 0.755394 + 0.166275i 0.575940 0.817492i \(-0.304636\pi\)
0.179454 + 0.983766i \(0.442567\pi\)
\(72\) 0 0
\(73\) −1.45289 8.86226i −0.170048 1.03725i −0.924581 0.380987i \(-0.875584\pi\)
0.754532 0.656263i \(-0.227864\pi\)
\(74\) −12.9564 + 19.1093i −1.50616 + 2.22141i
\(75\) 0 0
\(76\) 19.1703 + 14.5729i 2.19898 + 1.67162i
\(77\) 3.51783 + 2.11661i 0.400894 + 0.241210i
\(78\) 0 0
\(79\) 9.22548 + 8.73884i 1.03795 + 0.983196i 0.999871 0.0160790i \(-0.00511834\pi\)
0.0380764 + 0.999275i \(0.487877\pi\)
\(80\) −0.129233 + 0.788288i −0.0144487 + 0.0881332i
\(81\) 0 0
\(82\) 21.4838 12.9263i 2.37248 1.42748i
\(83\) −0.0827415 + 0.0974108i −0.00908206 + 0.0106922i −0.766684 0.642024i \(-0.778095\pi\)
0.757602 + 0.652716i \(0.226371\pi\)
\(84\) 0 0
\(85\) 8.84184 + 4.09067i 0.959033 + 0.443696i
\(86\) 10.5605 + 12.4328i 1.13877 + 1.34067i
\(87\) 0 0
\(88\) −3.46281 6.53156i −0.369137 0.696267i
\(89\) −3.29319 6.21161i −0.349077 0.658430i 0.645346 0.763890i \(-0.276713\pi\)
−0.994423 + 0.105461i \(0.966368\pi\)
\(90\) 0 0
\(91\) 2.36234 + 2.78116i 0.247640 + 0.291545i
\(92\) 8.26897 + 3.82564i 0.862100 + 0.398850i
\(93\) 0 0
\(94\) −10.1821 + 11.9873i −1.05020 + 1.23639i
\(95\) −20.7777 + 12.5016i −2.13175 + 1.28263i
\(96\) 0 0
\(97\) −2.41950 + 14.7583i −0.245663 + 1.49848i 0.519407 + 0.854527i \(0.326153\pi\)
−0.765069 + 0.643948i \(0.777295\pi\)
\(98\) 7.15979 + 6.78211i 0.723248 + 0.685097i
\(99\) 0 0
\(100\) −16.8312 10.1270i −1.68312 1.01270i
\(101\) 8.04581 + 6.11627i 0.800588 + 0.608591i 0.923400 0.383839i \(-0.125398\pi\)
−0.122812 + 0.992430i \(0.539191\pi\)
\(102\) 0 0
\(103\) 1.38787 2.04695i 0.136751 0.201692i −0.753147 0.657852i \(-0.771465\pi\)
0.889898 + 0.456160i \(0.150776\pi\)
\(104\) −1.06303 6.48421i −0.104239 0.635829i
\(105\) 0 0
\(106\) −2.28255 0.502427i −0.221701 0.0488000i
\(107\) −4.54178 11.3990i −0.439070 1.10198i −0.967470 0.252987i \(-0.918587\pi\)
0.528399 0.848996i \(-0.322792\pi\)
\(108\) 0 0
\(109\) 0.851925 15.7128i 0.0815997 1.50502i −0.615554 0.788095i \(-0.711068\pi\)
0.697153 0.716922i \(-0.254450\pi\)
\(110\) 18.8805 2.05338i 1.80019 0.195782i
\(111\) 0 0
\(112\) 0.106246 + 0.382665i 0.0100393 + 0.0361585i
\(113\) 5.10089 1.12279i 0.479851 0.105623i 0.0315432 0.999502i \(-0.489958\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(114\) 0 0
\(115\) −6.66082 + 6.30947i −0.621125 + 0.588361i
\(116\) −3.75829 + 7.08888i −0.348948 + 0.658186i
\(117\) 0 0
\(118\) −15.9063 7.68507i −1.46430 0.707468i
\(119\) 4.84352 0.444005
\(120\) 0 0
\(121\) 3.47370 3.29047i 0.315791 0.299133i
\(122\) −3.02586 4.46281i −0.273948 0.404044i
\(123\) 0 0
\(124\) 7.03864 + 25.3509i 0.632089 + 2.27658i
\(125\) 2.56221 1.94774i 0.229171 0.174211i
\(126\) 0 0
\(127\) −0.197707 + 3.64649i −0.0175436 + 0.323573i 0.976568 + 0.215210i \(0.0690437\pi\)
−0.994111 + 0.108363i \(0.965439\pi\)
\(128\) −5.02767 + 18.1080i −0.444387 + 1.60054i
\(129\) 0 0
\(130\) 16.4856 + 3.62876i 1.44588 + 0.318263i
\(131\) −0.561485 10.3560i −0.0490572 0.904807i −0.914697 0.404140i \(-0.867571\pi\)
0.865640 0.500667i \(-0.166912\pi\)
\(132\) 0 0
\(133\) −6.76547 + 9.97833i −0.586641 + 0.865231i
\(134\) 13.8922 34.8669i 1.20011 3.01204i
\(135\) 0 0
\(136\) −7.47322 4.49648i −0.640823 0.385570i
\(137\) 10.6203 3.57838i 0.907351 0.305722i 0.173342 0.984862i \(-0.444544\pi\)
0.734009 + 0.679140i \(0.237647\pi\)
\(138\) 0 0
\(139\) −0.283066 + 1.72663i −0.0240094 + 0.146451i −0.996111 0.0881107i \(-0.971917\pi\)
0.972101 + 0.234561i \(0.0753654\pi\)
\(140\) −17.8374 1.93993i −1.50753 0.163954i
\(141\) 0 0
\(142\) 9.70380 11.4242i 0.814325 0.958697i
\(143\) −5.01364 + 2.31956i −0.419262 + 0.193971i
\(144\) 0 0
\(145\) −5.23062 6.15797i −0.434380 0.511391i
\(146\) −19.5729 6.59487i −1.61986 0.545796i
\(147\) 0 0
\(148\) 15.4672 + 29.1743i 1.27140 + 2.39811i
\(149\) 8.50392 + 2.86531i 0.696668 + 0.234735i 0.645283 0.763944i \(-0.276740\pi\)
0.0513859 + 0.998679i \(0.483636\pi\)
\(150\) 0 0
\(151\) −14.7204 6.81037i −1.19793 0.554220i −0.283501 0.958972i \(-0.591496\pi\)
−0.914427 + 0.404751i \(0.867358\pi\)
\(152\) 19.7021 9.11514i 1.59805 0.739336i
\(153\) 0 0
\(154\) 8.09052 4.86790i 0.651953 0.392267i
\(155\) −26.3385 2.86448i −2.11556 0.230081i
\(156\) 0 0
\(157\) −13.7517 13.0263i −1.09750 1.03961i −0.999011 0.0444738i \(-0.985839\pi\)
−0.0984939 0.995138i \(-0.531403\pi\)
\(158\) 27.6953 9.33163i 2.20332 0.742384i
\(159\) 0 0
\(160\) −14.1763 10.7766i −1.12074 0.851961i
\(161\) −1.68833 + 4.23740i −0.133059 + 0.333954i
\(162\) 0 0
\(163\) −0.748385 4.56495i −0.0586181 0.357554i −0.999806 0.0196722i \(-0.993738\pi\)
0.941188 0.337882i \(-0.109711\pi\)
\(164\) −1.94143 35.8075i −0.151600 2.79610i
\(165\) 0 0
\(166\) 0.108799 + 0.273065i 0.00844445 + 0.0211940i
\(167\) −2.34446 + 8.44398i −0.181420 + 0.653414i 0.815762 + 0.578388i \(0.196318\pi\)
−0.997182 + 0.0750266i \(0.976096\pi\)
\(168\) 0 0
\(169\) 8.04256 0.874681i 0.618659 0.0672832i
\(170\) 17.8371 13.5594i 1.36805 1.03996i
\(171\) 0 0
\(172\) 22.7855 5.01546i 1.73738 0.382426i
\(173\) 3.08678 + 4.55266i 0.234684 + 0.346133i 0.926735 0.375716i \(-0.122603\pi\)
−0.692051 + 0.721848i \(0.743293\pi\)
\(174\) 0 0
\(175\) 4.60635 8.68849i 0.348207 0.656788i
\(176\) −0.601225 −0.0453190
\(177\) 0 0
\(178\) −16.1694 −1.21195
\(179\) 3.47244 6.54971i 0.259542 0.489549i −0.719157 0.694848i \(-0.755472\pi\)
0.978699 + 0.205299i \(0.0658166\pi\)
\(180\) 0 0
\(181\) 7.59459 + 11.2012i 0.564501 + 0.832577i 0.997634 0.0687531i \(-0.0219021\pi\)
−0.433132 + 0.901330i \(0.642592\pi\)
\(182\) 8.19607 1.80409i 0.607533 0.133728i
\(183\) 0 0
\(184\) 6.53878 4.97065i 0.482045 0.366441i
\(185\) −33.0567 + 3.59513i −2.43038 + 0.264320i
\(186\) 0 0
\(187\) −1.96166 + 7.06525i −0.143451 + 0.516662i
\(188\) 8.32620 + 20.8972i 0.607250 + 1.52408i
\(189\) 0 0
\(190\) 3.01926 + 55.6870i 0.219040 + 4.03996i
\(191\) 1.01560 + 6.19490i 0.0734864 + 0.448247i 0.997782 + 0.0665692i \(0.0212053\pi\)
−0.924295 + 0.381678i \(0.875346\pi\)
\(192\) 0 0
\(193\) 2.77074 6.95404i 0.199442 0.500562i −0.794906 0.606733i \(-0.792480\pi\)
0.994348 + 0.106171i \(0.0338590\pi\)
\(194\) 27.3817 + 20.8150i 1.96589 + 1.49443i
\(195\) 0 0
\(196\) 13.3667 4.50378i 0.954767 0.321698i
\(197\) 13.9693 + 13.2324i 0.995272 + 0.942772i 0.998361 0.0572232i \(-0.0182247\pi\)
−0.00308911 + 0.999995i \(0.500983\pi\)
\(198\) 0 0
\(199\) −12.5469 1.36456i −0.889427 0.0967311i −0.348016 0.937489i \(-0.613144\pi\)
−0.541412 + 0.840758i \(0.682110\pi\)
\(200\) −15.1732 + 9.12944i −1.07291 + 0.645549i
\(201\) 0 0
\(202\) 21.0955 9.75983i 1.48428 0.686699i
\(203\) −3.64564 1.68665i −0.255874 0.118380i
\(204\) 0 0
\(205\) 34.2205 + 11.5302i 2.39006 + 0.805305i
\(206\) −2.66420 5.02521i −0.185623 0.350123i
\(207\) 0 0
\(208\) −0.506406 0.170628i −0.0351129 0.0118309i
\(209\) −11.8154 13.9101i −0.817285 0.962182i
\(210\) 0 0
\(211\) −10.7657 + 4.98073i −0.741140 + 0.342888i −0.753863 0.657031i \(-0.771812\pi\)
0.0127236 + 0.999919i \(0.495950\pi\)
\(212\) −2.16405 + 2.54772i −0.148628 + 0.174978i
\(213\) 0 0
\(214\) −28.0550 3.05116i −1.91780 0.208573i
\(215\) −3.80091 + 23.1845i −0.259220 + 1.58117i
\(216\) 0 0
\(217\) −12.4823 + 4.20577i −0.847353 + 0.285506i
\(218\) −31.0100 18.6581i −2.10026 1.26369i
\(219\) 0 0
\(220\) 10.0540 25.2337i 0.677843 1.70126i
\(221\) −3.65740 + 5.39427i −0.246024 + 0.362858i
\(222\) 0 0
\(223\) 0.358488 + 6.61193i 0.0240062 + 0.442767i 0.985686 + 0.168592i \(0.0539221\pi\)
−0.961680 + 0.274175i \(0.911595\pi\)
\(224\) −8.64622 1.90318i −0.577700 0.127161i
\(225\) 0 0
\(226\) 3.21360 11.5743i 0.213765 0.769913i
\(227\) 0.267345 4.93089i 0.0177443 0.327275i −0.976162 0.217044i \(-0.930358\pi\)
0.993906 0.110230i \(-0.0351589\pi\)
\(228\) 0 0
\(229\) 0.733073 0.557268i 0.0484429 0.0368253i −0.580673 0.814137i \(-0.697210\pi\)
0.629115 + 0.777312i \(0.283417\pi\)
\(230\) 5.64502 + 20.3315i 0.372221 + 1.34062i
\(231\) 0 0
\(232\) 4.05916 + 5.98682i 0.266497 + 0.393054i
\(233\) −2.35861 + 2.23419i −0.154517 + 0.146367i −0.761053 0.648690i \(-0.775317\pi\)
0.606536 + 0.795056i \(0.292559\pi\)
\(234\) 0 0
\(235\) −22.6521 −1.47766
\(236\) −20.3674 + 14.9513i −1.32580 + 0.973248i
\(237\) 0 0
\(238\) 5.21780 9.84181i 0.338219 0.637950i
\(239\) −11.9293 + 11.3000i −0.771641 + 0.730937i −0.968369 0.249521i \(-0.919727\pi\)
0.196729 + 0.980458i \(0.436968\pi\)
\(240\) 0 0
\(241\) 3.76281 0.828256i 0.242384 0.0533527i −0.0921170 0.995748i \(-0.529363\pi\)
0.334501 + 0.942396i \(0.391432\pi\)
\(242\) −2.94395 10.6031i −0.189244 0.681596i
\(243\) 0 0
\(244\) −7.66650 + 0.833782i −0.490798 + 0.0533774i
\(245\) −0.768972 + 14.1829i −0.0491278 + 0.906109i
\(246\) 0 0
\(247\) −6.00425 15.0695i −0.382041 0.958852i
\(248\) 23.1637 + 5.09873i 1.47090 + 0.323769i
\(249\) 0 0
\(250\) −1.19752 7.30454i −0.0757377 0.461980i
\(251\) −8.48180 + 12.5097i −0.535366 + 0.789606i −0.995144 0.0984277i \(-0.968619\pi\)
0.459778 + 0.888034i \(0.347929\pi\)
\(252\) 0 0
\(253\) −5.49732 4.17895i −0.345614 0.262729i
\(254\) 7.19651 + 4.32999i 0.451549 + 0.271688i
\(255\) 0 0
\(256\) 12.7255 + 12.0543i 0.795345 + 0.753391i
\(257\) 3.23780 19.7497i 0.201968 1.23195i −0.669990 0.742370i \(-0.733701\pi\)
0.871958 0.489581i \(-0.162850\pi\)
\(258\) 0 0
\(259\) −14.1652 + 8.52291i −0.880182 + 0.529588i
\(260\) 15.6298 18.4008i 0.969316 1.14117i
\(261\) 0 0
\(262\) −21.6478 10.0153i −1.33740 0.618749i
\(263\) −14.6913 17.2960i −0.905905 1.06651i −0.997496 0.0707176i \(-0.977471\pi\)
0.0915909 0.995797i \(-0.470805\pi\)
\(264\) 0 0
\(265\) −1.57672 2.97400i −0.0968569 0.182691i
\(266\) 12.9872 + 24.4965i 0.796299 + 1.50198i
\(267\) 0 0
\(268\) −34.7522 40.9134i −2.12283 2.49918i
\(269\) 13.6637 + 6.32150i 0.833090 + 0.385429i 0.789597 0.613625i \(-0.210289\pi\)
0.0434927 + 0.999054i \(0.486151\pi\)
\(270\) 0 0
\(271\) −2.21100 + 2.60300i −0.134309 + 0.158121i −0.825205 0.564833i \(-0.808940\pi\)
0.690896 + 0.722954i \(0.257216\pi\)
\(272\) −0.607771 + 0.365684i −0.0368515 + 0.0221728i
\(273\) 0 0
\(274\) 4.16982 25.4348i 0.251908 1.53657i
\(275\) 10.8083 + 10.2382i 0.651767 + 0.617386i
\(276\) 0 0
\(277\) 4.32147 + 2.60014i 0.259652 + 0.156227i 0.639428 0.768851i \(-0.279171\pi\)
−0.379776 + 0.925078i \(0.623999\pi\)
\(278\) 3.20349 + 2.43523i 0.192132 + 0.146055i
\(279\) 0 0
\(280\) −9.07728 + 13.3880i −0.542471 + 0.800085i
\(281\) −0.602315 3.67396i −0.0359311 0.219170i 0.962758 0.270366i \(-0.0871448\pi\)
−0.998689 + 0.0511964i \(0.983697\pi\)
\(282\) 0 0
\(283\) −4.99083 1.09856i −0.296674 0.0653029i 0.0641394 0.997941i \(-0.479570\pi\)
−0.360813 + 0.932638i \(0.617501\pi\)
\(284\) −7.93509 19.9156i −0.470861 1.18177i
\(285\) 0 0
\(286\) −0.687831 + 12.6863i −0.0406723 + 0.750157i
\(287\) 17.8478 1.94106i 1.05352 0.114577i
\(288\) 0 0
\(289\) −2.23369 8.04503i −0.131394 0.473237i
\(290\) −18.1475 + 3.99457i −1.06566 + 0.234569i
\(291\) 0 0
\(292\) −21.4461 + 20.3149i −1.25504 + 1.18884i
\(293\) 11.4836 21.6603i 0.670878 1.26541i −0.281228 0.959641i \(-0.590742\pi\)
0.952106 0.305769i \(-0.0989134\pi\)
\(294\) 0 0
\(295\) −6.39507 24.6258i −0.372336 1.43377i
\(296\) 29.7682 1.73024
\(297\) 0 0
\(298\) 14.9832 14.1929i 0.867955 0.822171i
\(299\) −3.44435 5.08003i −0.199192 0.293786i
\(300\) 0 0
\(301\) 3.12484 + 11.2547i 0.180113 + 0.648708i
\(302\) −29.6963 + 22.5745i −1.70883 + 1.29902i
\(303\) 0 0
\(304\) 0.0955808 1.76288i 0.00548194 0.101108i
\(305\) 2.07752 7.48255i 0.118958 0.428450i
\(306\) 0 0
\(307\) 6.09492 + 1.34159i 0.347856 + 0.0765688i 0.385462 0.922724i \(-0.374042\pi\)
−0.0376061 + 0.999293i \(0.511973\pi\)
\(308\) −0.731117 13.4847i −0.0416593 0.768360i
\(309\) 0 0
\(310\) −34.1943 + 50.4327i −1.94210 + 2.86439i
\(311\) −11.8739 + 29.8013i −0.673308 + 1.68988i 0.0494517 + 0.998777i \(0.484253\pi\)
−0.722760 + 0.691099i \(0.757127\pi\)
\(312\) 0 0
\(313\) 18.3380 + 11.0336i 1.03652 + 0.623656i 0.928822 0.370527i \(-0.120823\pi\)
0.107703 + 0.994183i \(0.465650\pi\)
\(314\) −41.2832 + 13.9099i −2.32974 + 0.784982i
\(315\) 0 0
\(316\) 6.76233 41.2484i 0.380411 2.32040i
\(317\) −27.9293 3.03749i −1.56866 0.170602i −0.717898 0.696148i \(-0.754896\pi\)
−0.850766 + 0.525545i \(0.823861\pi\)
\(318\) 0 0
\(319\) 3.93683 4.63480i 0.220420 0.259499i
\(320\) −38.6192 + 17.8671i −2.15888 + 0.998804i
\(321\) 0 0
\(322\) 6.79141 + 7.99546i 0.378470 + 0.445570i
\(323\) −20.4046 6.87509i −1.13534 0.382540i
\(324\) 0 0
\(325\) 6.19814 + 11.6909i 0.343811 + 0.648496i
\(326\) −10.0820 3.39702i −0.558389 0.188143i
\(327\) 0 0
\(328\) −29.3399 13.5741i −1.62002 0.749502i
\(329\) −10.2210 + 4.72872i −0.563499 + 0.260703i
\(330\) 0 0
\(331\) 16.6324 10.0074i 0.914200 0.550056i 0.0210321 0.999779i \(-0.493305\pi\)
0.893168 + 0.449723i \(0.148477\pi\)
\(332\) 0.417944 + 0.0454541i 0.0229376 + 0.00249462i
\(333\) 0 0
\(334\) 14.6321 + 13.8603i 0.800636 + 0.758402i
\(335\) 51.2263 17.2601i 2.79879 0.943022i
\(336\) 0 0
\(337\) −5.17764 3.93594i −0.282044 0.214404i 0.454581 0.890705i \(-0.349789\pi\)
−0.736626 + 0.676301i \(0.763582\pi\)
\(338\) 6.88673 17.2844i 0.374589 0.940147i
\(339\) 0 0
\(340\) −5.18444 31.6237i −0.281166 1.71503i
\(341\) −1.07956 19.9113i −0.0584614 1.07826i
\(342\) 0 0
\(343\) 6.88053 + 17.2688i 0.371513 + 0.932428i
\(344\) 5.62686 20.2661i 0.303380 1.09268i
\(345\) 0 0
\(346\) 12.5761 1.36773i 0.676096 0.0735299i
\(347\) 28.9733 22.0249i 1.55537 1.18236i 0.648288 0.761395i \(-0.275485\pi\)
0.907078 0.420963i \(-0.138308\pi\)
\(348\) 0 0
\(349\) −19.8007 + 4.35847i −1.05991 + 0.233303i −0.710522 0.703675i \(-0.751541\pi\)
−0.349386 + 0.936979i \(0.613610\pi\)
\(350\) −12.6923 18.7198i −0.678433 1.00061i
\(351\) 0 0
\(352\) 6.27795 11.8415i 0.334616 0.631152i
\(353\) −10.5120 −0.559498 −0.279749 0.960073i \(-0.590251\pi\)
−0.279749 + 0.960073i \(0.590251\pi\)
\(354\) 0 0
\(355\) 21.5880 1.14577
\(356\) −10.8325 + 20.4322i −0.574120 + 1.08291i
\(357\) 0 0
\(358\) −9.56795 14.1117i −0.505682 0.745825i
\(359\) 3.75805 0.827208i 0.198342 0.0436584i −0.114688 0.993402i \(-0.536587\pi\)
0.313030 + 0.949743i \(0.398656\pi\)
\(360\) 0 0
\(361\) 27.5392 20.9347i 1.44943 1.10183i
\(362\) 30.9417 3.36512i 1.62626 0.176867i
\(363\) 0 0
\(364\) 3.21114 11.5655i 0.168309 0.606196i
\(365\) −11.0104 27.6341i −0.576312 1.44643i
\(366\) 0 0
\(367\) 0.990788 + 18.2740i 0.0517187 + 0.953896i 0.903122 + 0.429384i \(0.141269\pi\)
−0.851403 + 0.524512i \(0.824248\pi\)
\(368\) −0.108068 0.659183i −0.00563341 0.0343623i
\(369\) 0 0
\(370\) −28.3060 + 71.0427i −1.47156 + 3.69333i
\(371\) −1.33227 1.01277i −0.0691682 0.0525803i
\(372\) 0 0
\(373\) −6.52367 + 2.19808i −0.337783 + 0.113812i −0.483081 0.875576i \(-0.660482\pi\)
0.145298 + 0.989388i \(0.453586\pi\)
\(374\) 12.2430 + 11.5972i 0.633072 + 0.599678i
\(375\) 0 0
\(376\) 20.1601 + 2.19255i 1.03968 + 0.113072i
\(377\) 4.63131 2.78657i 0.238525 0.143515i
\(378\) 0 0
\(379\) 3.31802 1.53508i 0.170435 0.0788517i −0.332816 0.942992i \(-0.607999\pi\)
0.503252 + 0.864140i \(0.332137\pi\)
\(380\) 72.3909 + 33.4916i 3.71357 + 1.71808i
\(381\) 0 0
\(382\) 13.6818 + 4.60995i 0.700023 + 0.235865i
\(383\) −6.85564 12.9311i −0.350307 0.660749i 0.644265 0.764803i \(-0.277164\pi\)
−0.994572 + 0.104053i \(0.966819\pi\)
\(384\) 0 0
\(385\) 12.8870 + 4.34214i 0.656783 + 0.221296i
\(386\) −11.1454 13.1214i −0.567288 0.667863i
\(387\) 0 0
\(388\) 44.6466 20.6557i 2.26659 1.04864i
\(389\) −14.5352 + 17.1121i −0.736963 + 0.867620i −0.995139 0.0984780i \(-0.968603\pi\)
0.258176 + 0.966098i \(0.416878\pi\)
\(390\) 0 0
\(391\) −8.09894 0.880813i −0.409581 0.0445446i
\(392\) 2.05717 12.5482i 0.103903 0.633779i
\(393\) 0 0
\(394\) 41.9365 14.1300i 2.11273 0.711861i
\(395\) 36.0661 + 21.7003i 1.81468 + 1.09186i
\(396\) 0 0
\(397\) 9.48004 23.7931i 0.475790 1.19414i −0.473796 0.880634i \(-0.657117\pi\)
0.949586 0.313507i \(-0.101504\pi\)
\(398\) −16.2892 + 24.0248i −0.816503 + 1.20425i
\(399\) 0 0
\(400\) 0.0779673 + 1.43802i 0.00389836 + 0.0719011i
\(401\) 21.5722 + 4.74841i 1.07727 + 0.237124i 0.717952 0.696092i \(-0.245080\pi\)
0.359314 + 0.933217i \(0.383011\pi\)
\(402\) 0 0
\(403\) 4.74153 17.0775i 0.236193 0.850689i
\(404\) 1.79981 33.1955i 0.0895439 1.65154i
\(405\) 0 0
\(406\) −7.35455 + 5.59078i −0.365000 + 0.277466i
\(407\) −6.69539 24.1146i −0.331878 1.19532i
\(408\) 0 0
\(409\) −0.0878626 0.129588i −0.00434453 0.00640770i 0.825511 0.564387i \(-0.190887\pi\)
−0.829855 + 0.557979i \(0.811577\pi\)
\(410\) 60.2937 57.1132i 2.97769 2.82062i
\(411\) 0 0
\(412\) −8.13488 −0.400777
\(413\) −8.02630 9.77654i −0.394948 0.481072i
\(414\) 0 0
\(415\) −0.198299 + 0.374032i −0.00973412 + 0.0183605i
\(416\) 8.64846 8.19225i 0.424026 0.401658i
\(417\) 0 0
\(418\) −40.9931 + 9.02326i −2.00504 + 0.441342i
\(419\) −1.96214 7.06701i −0.0958570 0.345246i 0.900032 0.435823i \(-0.143543\pi\)
−0.995889 + 0.0905771i \(0.971129\pi\)
\(420\) 0 0
\(421\) −24.2330 + 2.63550i −1.18104 + 0.128446i −0.677499 0.735523i \(-0.736936\pi\)
−0.503544 + 0.863969i \(0.667971\pi\)
\(422\) −1.47696 + 27.2410i −0.0718974 + 1.32607i
\(423\) 0 0
\(424\) 1.11540 + 2.79945i 0.0541687 + 0.135953i
\(425\) 17.1532 + 3.77570i 0.832052 + 0.183148i
\(426\) 0 0
\(427\) −0.624607 3.80993i −0.0302268 0.184376i
\(428\) −22.6507 + 33.4072i −1.09486 + 1.61480i
\(429\) 0 0
\(430\) 43.0153 + 32.6994i 2.07438 + 1.57690i
\(431\) −18.3953 11.0681i −0.886071 0.533131i −0.00174341 0.999998i \(-0.500555\pi\)
−0.884327 + 0.466867i \(0.845383\pi\)
\(432\) 0 0
\(433\) −5.27017 4.99217i −0.253268 0.239909i 0.550523 0.834820i \(-0.314428\pi\)
−0.803791 + 0.594912i \(0.797187\pi\)
\(434\) −4.90091 + 29.8942i −0.235251 + 1.43497i
\(435\) 0 0
\(436\) −44.3518 + 26.6856i −2.12407 + 1.27801i
\(437\) 13.1273 15.4546i 0.627963 0.739295i
\(438\) 0 0
\(439\) 8.14734 + 3.76936i 0.388851 + 0.179902i 0.604567 0.796555i \(-0.293346\pi\)
−0.215715 + 0.976456i \(0.569208\pi\)
\(440\) −15.8527 18.6633i −0.755750 0.889737i
\(441\) 0 0
\(442\) 7.02088 + 13.2428i 0.333949 + 0.629895i
\(443\) −1.00406 1.89386i −0.0477044 0.0899800i 0.858514 0.512791i \(-0.171388\pi\)
−0.906218 + 0.422811i \(0.861044\pi\)
\(444\) 0 0
\(445\) −15.0762 17.7491i −0.714680 0.841386i
\(446\) 13.8213 + 6.39443i 0.654459 + 0.302785i
\(447\) 0 0
\(448\) −13.6957 + 16.1238i −0.647062 + 0.761780i
\(449\) 13.3209 8.01492i 0.628652 0.378247i −0.165286 0.986246i \(-0.552855\pi\)
0.793938 + 0.607998i \(0.208027\pi\)
\(450\) 0 0
\(451\) −4.39703 + 26.8207i −0.207048 + 1.26294i
\(452\) −12.4728 11.8149i −0.586673 0.555726i
\(453\) 0 0
\(454\) −9.73134 5.85515i −0.456714 0.274796i
\(455\) 9.62229 + 7.31467i 0.451100 + 0.342917i
\(456\) 0 0
\(457\) −4.81325 + 7.09901i −0.225154 + 0.332078i −0.923441 0.383741i \(-0.874636\pi\)
0.698287 + 0.715818i \(0.253946\pi\)
\(458\) −0.342622 2.08990i −0.0160097 0.0976547i
\(459\) 0 0
\(460\) 29.4734 + 6.48760i 1.37421 + 0.302486i
\(461\) 11.2734 + 28.2942i 0.525056 + 1.31779i 0.917398 + 0.397972i \(0.130286\pi\)
−0.392341 + 0.919820i \(0.628335\pi\)
\(462\) 0 0
\(463\) 1.87299 34.5452i 0.0870450 1.60545i −0.550364 0.834925i \(-0.685511\pi\)
0.637409 0.770526i \(-0.280006\pi\)
\(464\) 0.584801 0.0636010i 0.0271487 0.00295260i
\(465\) 0 0
\(466\) 1.99891 + 7.19942i 0.0925976 + 0.333507i
\(467\) 20.1323 4.43145i 0.931610 0.205063i 0.276862 0.960910i \(-0.410706\pi\)
0.654748 + 0.755847i \(0.272775\pi\)
\(468\) 0 0
\(469\) 19.5109 18.4817i 0.900931 0.853407i
\(470\) −24.4025 + 46.0280i −1.12560 + 2.12311i
\(471\) 0 0
\(472\) 3.30797 + 22.5358i 0.152262 + 1.03729i
\(473\) −17.6828 −0.813055
\(474\) 0 0
\(475\) −31.7382 + 30.0640i −1.45625 + 1.37943i
\(476\) −8.94087 13.1868i −0.409804 0.604416i
\(477\) 0 0
\(478\) 10.1100 + 36.4129i 0.462421 + 1.66549i
\(479\) 19.3772 14.7302i 0.885368 0.673040i −0.0602971 0.998180i \(-0.519205\pi\)
0.945666 + 0.325141i \(0.105412\pi\)
\(480\) 0 0
\(481\) 1.20428 22.2117i 0.0549105 1.01276i
\(482\) 2.37059 8.53811i 0.107978 0.388900i
\(483\) 0 0
\(484\) −15.3708 3.38336i −0.698672 0.153789i
\(485\) 2.68189 + 49.4645i 0.121778 + 2.24607i
\(486\) 0 0
\(487\) −16.5241 + 24.3712i −0.748778 + 1.10436i 0.242185 + 0.970230i \(0.422136\pi\)
−0.990963 + 0.134135i \(0.957175\pi\)
\(488\) −2.57323 + 6.45832i −0.116485 + 0.292354i
\(489\) 0 0
\(490\) 27.9905 + 16.8413i 1.26448 + 0.760814i
\(491\) −7.97632 + 2.68754i −0.359966 + 0.121287i −0.493473 0.869761i \(-0.664273\pi\)
0.133507 + 0.991048i \(0.457376\pi\)
\(492\) 0 0
\(493\) 1.16067 7.07976i 0.0522739 0.318856i
\(494\) −37.0888 4.03365i −1.66871 0.181483i
\(495\) 0 0
\(496\) 1.24876 1.47015i 0.0560710 0.0660119i
\(497\) 9.74084 4.50659i 0.436936 0.202148i
\(498\) 0 0
\(499\) −18.1083 21.3187i −0.810639 0.954358i 0.188980 0.981981i \(-0.439482\pi\)
−0.999618 + 0.0276234i \(0.991206\pi\)
\(500\) −10.0325 3.38036i −0.448669 0.151174i
\(501\) 0 0
\(502\) 16.2820 + 30.7110i 0.726699 + 1.37070i
\(503\) 25.8744 + 8.71810i 1.15368 + 0.388721i 0.830174 0.557504i \(-0.188241\pi\)
0.323509 + 0.946225i \(0.395138\pi\)
\(504\) 0 0
\(505\) 30.3826 + 14.0565i 1.35201 + 0.625505i
\(506\) −14.4136 + 6.66843i −0.640761 + 0.296448i
\(507\) 0 0
\(508\) 10.2928 6.19294i 0.456667 0.274767i
\(509\) 2.73734 + 0.297703i 0.121330 + 0.0131955i 0.168583 0.985688i \(-0.446081\pi\)
−0.0472524 + 0.998883i \(0.515046\pi\)
\(510\) 0 0
\(511\) −10.7368 10.1704i −0.474968 0.449914i
\(512\) 2.58401 0.870655i 0.114198 0.0384779i
\(513\) 0 0
\(514\) −36.6425 27.8549i −1.61623 1.22863i
\(515\) 3.03207 7.60993i 0.133609 0.335334i
\(516\) 0 0
\(517\) −2.75824 16.8245i −0.121307 0.739940i
\(518\) 2.05838 + 37.9645i 0.0904399 + 1.66807i
\(519\) 0 0
\(520\) −8.05595 20.2189i −0.353277 0.886657i
\(521\) −7.30611 + 26.3142i −0.320086 + 1.15285i 0.612074 + 0.790801i \(0.290336\pi\)
−0.932160 + 0.362046i \(0.882078\pi\)
\(522\) 0 0
\(523\) 30.4037 3.30660i 1.32946 0.144588i 0.584335 0.811512i \(-0.301355\pi\)
0.745125 + 0.666925i \(0.232390\pi\)
\(524\) −27.1584 + 20.6453i −1.18642 + 0.901893i
\(525\) 0 0
\(526\) −50.9712 + 11.2196i −2.22245 + 0.489198i
\(527\) −13.2020 19.4715i −0.575088 0.848191i
\(528\) 0 0
\(529\) −7.17971 + 13.5424i −0.312161 + 0.588798i
\(530\) −7.74159 −0.336273
\(531\) 0 0
\(532\) 39.6554 1.71928
\(533\) −11.3153 + 21.3429i −0.490120 + 0.924465i
\(534\) 0 0
\(535\) −22.8090 33.6407i −0.986118 1.45442i
\(536\) −47.2616 + 10.4031i −2.04139 + 0.449344i
\(537\) 0 0
\(538\) 27.5645 20.9540i 1.18839 0.903392i
\(539\) −10.6277 + 1.15584i −0.457769 + 0.0497854i
\(540\) 0 0
\(541\) −1.85601 + 6.68474i −0.0797960 + 0.287399i −0.992672 0.120837i \(-0.961442\pi\)
0.912876 + 0.408236i \(0.133856\pi\)
\(542\) 2.90731 + 7.29680i 0.124880 + 0.313424i
\(543\) 0 0
\(544\) −0.856045 15.7888i −0.0367026 0.676940i
\(545\) −8.43254 51.4362i −0.361210 2.20329i
\(546\) 0 0
\(547\) 4.54991 11.4194i 0.194540 0.488259i −0.799055 0.601258i \(-0.794666\pi\)
0.993595 + 0.112999i \(0.0360458\pi\)
\(548\) −29.3468 22.3089i −1.25363 0.952988i
\(549\) 0 0
\(550\) 32.4471 10.9327i 1.38355 0.466171i
\(551\) 12.9641 + 12.2802i 0.552288 + 0.523155i
\(552\) 0 0
\(553\) 20.8036 + 2.26253i 0.884659 + 0.0962125i
\(554\) 9.93877 5.97996i 0.422258 0.254064i
\(555\) 0 0
\(556\) 5.22338 2.41659i 0.221521 0.102486i
\(557\) 13.6858 + 6.33174i 0.579887 + 0.268284i 0.687829 0.725873i \(-0.258564\pi\)
−0.107942 + 0.994157i \(0.534426\pi\)
\(558\) 0 0
\(559\) −14.8940 5.01838i −0.629950 0.212255i
\(560\) 0.616177 + 1.16223i 0.0260382 + 0.0491133i
\(561\) 0 0
\(562\) −8.11417 2.73398i −0.342276 0.115326i
\(563\) 12.0959 + 14.2404i 0.509782 + 0.600162i 0.955493 0.295015i \(-0.0953247\pi\)
−0.445710 + 0.895177i \(0.647049\pi\)
\(564\) 0 0
\(565\) 15.7014 7.26425i 0.660563 0.305609i
\(566\) −7.60872 + 8.95768i −0.319818 + 0.376519i
\(567\) 0 0
\(568\) −19.2131 2.08956i −0.806166 0.0876758i
\(569\) −3.99832 + 24.3887i −0.167618 + 1.02243i 0.760280 + 0.649595i \(0.225062\pi\)
−0.927899 + 0.372832i \(0.878387\pi\)
\(570\) 0 0
\(571\) −15.6373 + 5.26883i −0.654402 + 0.220494i −0.626866 0.779127i \(-0.715663\pi\)
−0.0275360 + 0.999621i \(0.508766\pi\)
\(572\) 15.5701 + 9.36820i 0.651017 + 0.391704i
\(573\) 0 0
\(574\) 15.2828 38.3569i 0.637891 1.60099i
\(575\) −9.28240 + 13.6905i −0.387103 + 0.570934i
\(576\) 0 0
\(577\) 2.39235 + 44.1243i 0.0995949 + 1.83692i 0.441588 + 0.897218i \(0.354415\pi\)
−0.341993 + 0.939703i \(0.611102\pi\)
\(578\) −18.7534 4.12794i −0.780040 0.171700i
\(579\) 0 0
\(580\) −7.11002 + 25.6080i −0.295228 + 1.06331i
\(581\) −0.0113948 + 0.210164i −0.000472735 + 0.00871909i
\(582\) 0 0
\(583\) 2.01691 1.53321i 0.0835317 0.0634992i
\(584\) 7.12441 + 25.6598i 0.294810 + 1.06181i
\(585\) 0 0
\(586\) −31.6418 46.6682i −1.30711 1.92785i
\(587\) −19.8997 + 18.8500i −0.821347 + 0.778021i −0.977772 0.209669i \(-0.932761\pi\)
0.156426 + 0.987690i \(0.450003\pi\)
\(588\) 0 0
\(589\) 58.5547 2.41270
\(590\) −56.9278 13.5343i −2.34368 0.557196i
\(591\) 0 0
\(592\) 1.13399 2.13893i 0.0466067 0.0879096i
\(593\) 30.4879 28.8797i 1.25199 1.18595i 0.277694 0.960670i \(-0.410430\pi\)
0.974295 0.225277i \(-0.0723287\pi\)
\(594\) 0 0
\(595\) 15.6683 3.44886i 0.642339 0.141390i
\(596\) −7.89679 28.4417i −0.323465 1.16502i
\(597\) 0 0
\(598\) −14.0329 + 1.52617i −0.573848 + 0.0624097i
\(599\) −1.00798 + 18.5910i −0.0411848 + 0.759610i 0.902889 + 0.429875i \(0.141442\pi\)
−0.944073 + 0.329735i \(0.893041\pi\)
\(600\) 0 0
\(601\) −2.81985 7.07730i −0.115024 0.288689i 0.860182 0.509987i \(-0.170350\pi\)
−0.975206 + 0.221298i \(0.928971\pi\)
\(602\) 26.2353 + 5.77482i 1.06927 + 0.235364i
\(603\) 0 0
\(604\) 8.63133 + 52.6488i 0.351204 + 2.14225i
\(605\) 8.89411 13.1178i 0.361597 0.533316i
\(606\) 0 0
\(607\) −11.0411 8.39322i −0.448144 0.340670i 0.356636 0.934243i \(-0.383924\pi\)
−0.804780 + 0.593573i \(0.797717\pi\)
\(608\) 33.7229 + 20.2904i 1.36765 + 0.822885i
\(609\) 0 0
\(610\) −12.9661 12.2822i −0.524984 0.497291i
\(611\) 2.45156 14.9539i 0.0991797 0.604969i
\(612\) 0 0
\(613\) −14.6348 + 8.80548i −0.591095 + 0.355650i −0.779463 0.626449i \(-0.784508\pi\)
0.188368 + 0.982099i \(0.439680\pi\)
\(614\) 9.29196 10.9393i 0.374993 0.441476i
\(615\) 0 0
\(616\) −11.0490 5.11183i −0.445178 0.205961i
\(617\) 2.57683 + 3.03368i 0.103739 + 0.122131i 0.811581 0.584239i \(-0.198607\pi\)
−0.707842 + 0.706371i \(0.750331\pi\)
\(618\) 0 0
\(619\) 6.10790 + 11.5207i 0.245497 + 0.463057i 0.975385 0.220511i \(-0.0707723\pi\)
−0.729887 + 0.683567i \(0.760428\pi\)
\(620\) 40.8206 + 76.9959i 1.63940 + 3.09223i
\(621\) 0 0
\(622\) 47.7634 + 56.2314i 1.91514 + 2.25467i
\(623\) −10.5078 4.86142i −0.420986 0.194769i
\(624\) 0 0
\(625\) −12.4282 + 14.6317i −0.497130 + 0.585267i
\(626\) 42.1748 25.3758i 1.68565 1.01422i
\(627\) 0 0
\(628\) −10.0801 + 61.4857i −0.402239 + 2.45355i
\(629\) −21.4356 20.3048i −0.854692 0.809607i
\(630\) 0 0
\(631\) 16.4816 + 9.91663i 0.656121 + 0.394775i 0.804331 0.594181i \(-0.202524\pi\)
−0.148210 + 0.988956i \(0.547351\pi\)
\(632\) −29.9981 22.8040i −1.19326 0.907093i
\(633\) 0 0
\(634\) −36.2595 + 53.4788i −1.44005 + 2.12391i
\(635\) 1.95694 + 11.9368i 0.0776589 + 0.473698i
\(636\) 0 0
\(637\) −9.27966 2.04261i −0.367673 0.0809311i
\(638\) −5.17665 12.9924i −0.204945 0.514374i
\(639\) 0 0
\(640\) −3.37010 + 62.1578i −0.133215 + 2.45700i
\(641\) 24.8197 2.69931i 0.980320 0.106616i 0.396096 0.918209i \(-0.370365\pi\)
0.584224 + 0.811593i \(0.301399\pi\)
\(642\) 0 0
\(643\) 3.56498 + 12.8399i 0.140589 + 0.506356i 0.999988 0.00495015i \(-0.00157569\pi\)
−0.859399 + 0.511306i \(0.829162\pi\)
\(644\) 14.6532 3.22541i 0.577416 0.127099i
\(645\) 0 0
\(646\) −35.9512 + 34.0548i −1.41448 + 1.33987i
\(647\) −18.9087 + 35.6656i −0.743377 + 1.40216i 0.165975 + 0.986130i \(0.446923\pi\)
−0.909352 + 0.416028i \(0.863422\pi\)
\(648\) 0 0
\(649\) 17.5118 7.74842i 0.687397 0.304152i
\(650\) 30.4325 1.19366
\(651\) 0 0
\(652\) −11.0469 + 10.4642i −0.432630 + 0.409809i
\(653\) −12.6247 18.6200i −0.494041 0.728656i 0.496171 0.868225i \(-0.334739\pi\)
−0.990212 + 0.139568i \(0.955429\pi\)
\(654\) 0 0
\(655\) −9.19041 33.1009i −0.359099 1.29336i
\(656\) −2.09301 + 1.59107i −0.0817184 + 0.0621207i
\(657\) 0 0
\(658\) −1.40223 + 25.8626i −0.0546647 + 1.00823i
\(659\) −5.10327 + 18.3803i −0.198795 + 0.715996i 0.795178 + 0.606376i \(0.207377\pi\)
−0.993974 + 0.109620i \(0.965037\pi\)
\(660\) 0 0
\(661\) −30.4956 6.71259i −1.18614 0.261089i −0.422277 0.906467i \(-0.638769\pi\)
−0.763864 + 0.645377i \(0.776700\pi\)
\(662\) −2.41690 44.5770i −0.0939353 1.73254i
\(663\) 0 0
\(664\) 0.212688 0.313691i 0.00825389 0.0121736i
\(665\) −14.7806 + 37.0964i −0.573165 + 1.43854i
\(666\) 0 0
\(667\) 5.78922 + 3.48326i 0.224160 + 0.134872i
\(668\) 27.3170 9.20418i 1.05693 0.356120i
\(669\) 0 0
\(670\) 20.1129 122.683i 0.777029 4.73967i
\(671\) 5.81053 + 0.631933i 0.224313 + 0.0243955i
\(672\) 0 0
\(673\) 6.29442 7.41036i 0.242632 0.285649i −0.627344 0.778742i \(-0.715858\pi\)
0.869976 + 0.493094i \(0.164134\pi\)
\(674\) −13.5754 + 6.28065i −0.522905 + 0.241922i
\(675\) 0 0
\(676\) −17.2275 20.2818i −0.662596 0.780069i
\(677\) −5.30152 1.78629i −0.203754 0.0686527i 0.215574 0.976488i \(-0.430838\pi\)
−0.419328 + 0.907835i \(0.637734\pi\)
\(678\) 0 0
\(679\) 11.5360 + 21.7593i 0.442712 + 0.835044i
\(680\) −27.3769 9.22436i −1.04986 0.353738i
\(681\) 0 0
\(682\) −41.6219 19.2563i −1.59378 0.737363i
\(683\) 15.0737 6.97382i 0.576778 0.266846i −0.109738 0.993961i \(-0.535001\pi\)
0.686516 + 0.727115i \(0.259139\pi\)
\(684\) 0 0
\(685\) 31.8076 19.1380i 1.21531 0.731225i
\(686\) 42.5017 + 4.62233i 1.62272 + 0.176482i
\(687\) 0 0
\(688\) −1.24183 1.17633i −0.0473444 0.0448470i
\(689\) 2.13395 0.719010i 0.0812968 0.0273921i
\(690\) 0 0
\(691\) 29.0878 + 22.1120i 1.10655 + 0.841180i 0.988409 0.151816i \(-0.0485121\pi\)
0.118145 + 0.992996i \(0.462305\pi\)
\(692\) 6.69689 16.8079i 0.254578 0.638942i
\(693\) 0 0
\(694\) −13.5414 82.5992i −0.514026 3.13542i
\(695\) 0.313764 + 5.78704i 0.0119018 + 0.219515i
\(696\) 0 0
\(697\) 11.8683 + 29.7872i 0.449543 + 1.12827i
\(698\) −12.4746 + 44.9294i −0.472170 + 1.70060i
\(699\) 0 0
\(700\) −32.1581 + 3.49740i −1.21546 + 0.132189i
\(701\) 11.1921 8.50803i 0.422720 0.321344i −0.372095 0.928195i \(-0.621361\pi\)
0.794816 + 0.606851i \(0.207567\pi\)
\(702\) 0 0
\(703\) 71.7722 15.7983i 2.70694 0.595843i
\(704\) −17.9730 26.5083i −0.677385 0.999067i
\(705\) 0 0
\(706\) −11.3243 + 21.3599i −0.426197 + 0.803892i
\(707\) 16.6434 0.625941
\(708\) 0 0
\(709\) 8.71519 0.327306 0.163653 0.986518i \(-0.447672\pi\)
0.163653 + 0.986518i \(0.447672\pi\)
\(710\) 23.2562 43.8659i 0.872790 1.64626i
\(711\) 0 0
\(712\) 11.6997 + 17.2558i 0.438465 + 0.646687i
\(713\) 21.6367 4.76260i 0.810301 0.178361i
\(714\) 0 0
\(715\) −14.5670 + 11.0736i −0.544776 + 0.414128i
\(716\) −24.2420 + 2.63647i −0.905965 + 0.0985296i
\(717\) 0 0
\(718\) 2.36760 8.52731i 0.0883579 0.318236i
\(719\) 1.41106 + 3.54149i 0.0526236 + 0.132075i 0.952938 0.303164i \(-0.0980430\pi\)
−0.900315 + 0.435239i \(0.856664\pi\)
\(720\) 0 0
\(721\) −0.220489 4.06667i −0.00821143 0.151451i
\(722\) −12.8712 78.5108i −0.479016 2.92187i
\(723\) 0 0
\(724\) 16.4768 41.3535i 0.612354 1.53689i
\(725\) −11.5961 8.81514i −0.430669 0.327386i
\(726\) 0 0
\(727\) −11.4538 + 3.85923i −0.424797 + 0.143131i −0.523577 0.851978i \(-0.675403\pi\)
0.0987796 + 0.995109i \(0.468506\pi\)
\(728\) −7.85574 7.44136i −0.291153 0.275795i
\(729\) 0 0
\(730\) −68.0124 7.39680i −2.51725 0.273768i
\(731\) −17.8753 + 10.7552i −0.661142 + 0.397796i
\(732\) 0 0
\(733\) 38.8273 17.9634i 1.43412 0.663495i 0.459668 0.888091i \(-0.347968\pi\)
0.974452 + 0.224596i \(0.0721063\pi\)
\(734\) 38.1993 + 17.6729i 1.40996 + 0.652318i
\(735\) 0 0
\(736\) 14.1114 + 4.75469i 0.520154 + 0.175260i
\(737\) 19.0573 + 35.9459i 0.701984 + 1.32408i
\(738\) 0 0
\(739\) −39.8067 13.4125i −1.46431 0.493385i −0.529435 0.848350i \(-0.677596\pi\)
−0.934879 + 0.354965i \(0.884493\pi\)
\(740\) 70.8089 + 83.3627i 2.60299 + 3.06447i
\(741\) 0 0
\(742\) −3.49312 + 1.61609i −0.128236 + 0.0593285i
\(743\) 9.99369 11.7655i 0.366633 0.431634i −0.547651 0.836707i \(-0.684478\pi\)
0.914284 + 0.405073i \(0.132754\pi\)
\(744\) 0 0
\(745\) 29.5497 + 3.21372i 1.08262 + 0.117742i
\(746\) −2.56138 + 15.6237i −0.0937788 + 0.572025i
\(747\) 0 0
\(748\) 22.8567 7.70133i 0.835725 0.281588i
\(749\) −17.3144 10.4177i −0.632654 0.380655i
\(750\) 0 0
\(751\) 7.17407 18.0056i 0.261785 0.657032i −0.738058 0.674738i \(-0.764257\pi\)
0.999843 + 0.0177055i \(0.00563614\pi\)
\(752\) 0.925523 1.36504i 0.0337503 0.0497780i
\(753\) 0 0
\(754\) −0.672986 12.4125i −0.0245087 0.452037i
\(755\) −52.4685 11.5492i −1.90952 0.420318i
\(756\) 0 0
\(757\) 5.06755 18.2517i 0.184183 0.663368i −0.812571 0.582862i \(-0.801933\pi\)
0.996754 0.0805054i \(-0.0256534\pi\)
\(758\) 0.455205 8.39576i 0.0165338 0.304948i
\(759\) 0 0
\(760\) 57.2438 43.5156i 2.07645 1.57848i
\(761\) −10.1850 36.6829i −0.369205 1.32976i −0.882002 0.471245i \(-0.843805\pi\)
0.512797 0.858510i \(-0.328609\pi\)
\(762\) 0 0
\(763\) −14.5424 21.4485i −0.526471 0.776487i
\(764\) 14.9913 14.2005i 0.542365 0.513756i
\(765\) 0 0
\(766\) −33.6608 −1.21622
\(767\) 16.9490 1.55656i 0.611992 0.0562043i
\(768\) 0 0
\(769\) −25.3965 + 47.9029i −0.915822 + 1.72742i −0.271913 + 0.962322i \(0.587656\pi\)
−0.643909 + 0.765102i \(0.722689\pi\)
\(770\) 22.7059 21.5081i 0.818262 0.775099i
\(771\) 0 0
\(772\) −24.0475 + 5.29324i −0.865487 + 0.190508i
\(773\) −8.57083 30.8693i −0.308271 1.11029i −0.941689 0.336483i \(-0.890762\pi\)
0.633418 0.773810i \(-0.281651\pi\)
\(774\) 0 0
\(775\) −47.4842 + 5.16422i −1.70568 + 0.185504i
\(776\) 2.40093 44.2825i 0.0861883 1.58965i
\(777\) 0 0
\(778\) 19.1127 + 47.9693i 0.685224 + 1.71978i
\(779\) −77.9435 17.1567i −2.79261 0.614701i
\(780\) 0 0
\(781\) 2.62867 + 16.0342i 0.0940613 + 0.573748i
\(782\) −10.5146 + 15.5078i −0.376000 + 0.554558i
\(783\) 0 0
\(784\) −0.823259 0.625825i −0.0294021 0.0223509i
\(785\) −53.7609 32.3469i −1.91881 1.15451i
\(786\) 0 0
\(787\) −6.37008 6.03406i −0.227069 0.215091i 0.565704 0.824609i \(-0.308605\pi\)
−0.792773 + 0.609517i \(0.791363\pi\)
\(788\) 10.2396 62.4587i 0.364770 2.22500i
\(789\) 0 0
\(790\) 82.9471 49.9076i 2.95112 1.77563i
\(791\) 5.56827 6.55547i 0.197985 0.233086i
\(792\) 0 0
\(793\) 4.71480 + 2.18130i 0.167428 + 0.0774602i
\(794\) −38.1339 44.8947i −1.35332 1.59325i
\(795\) 0 0
\(796\) 19.4458 + 36.6787i 0.689239 + 1.30004i
\(797\) −11.4172 21.5350i −0.404417 0.762811i 0.594738 0.803920i \(-0.297256\pi\)
−0.999155 + 0.0411089i \(0.986911\pi\)
\(798\) 0 0
\(799\) −13.0214 15.3300i −0.460666 0.542338i
\(800\) −29.1368 13.4801i −1.03014 0.476593i
\(801\) 0 0
\(802\) 32.8878 38.7185i 1.16131 1.36720i
\(803\) 19.1841 11.5427i 0.676993 0.407333i
\(804\) 0 0
\(805\) −2.44434 + 14.9098i −0.0861515 + 0.525501i
\(806\) −29.5927 28.0317i −1.04236 0.987374i
\(807\) 0 0
\(808\) −25.6797 15.4510i −0.903408 0.543563i
\(809\) −26.4405 20.0995i −0.929597 0.706661i 0.0265194 0.999648i \(-0.491558\pi\)
−0.956116 + 0.292987i \(0.905351\pi\)
\(810\) 0 0
\(811\) −3.35793 + 4.95258i −0.117913 + 0.173909i −0.882065 0.471127i \(-0.843847\pi\)
0.764152 + 0.645036i \(0.223158\pi\)
\(812\) 2.13763 + 13.0390i 0.0750160 + 0.457578i
\(813\) 0 0
\(814\) −56.2126 12.3733i −1.97025 0.433685i
\(815\) −5.67146 14.2343i −0.198663 0.498606i
\(816\) 0 0
\(817\) 2.81115 51.8487i 0.0983498 1.81395i
\(818\) −0.357968 + 0.0389314i −0.0125161 + 0.00136121i
\(819\) 0 0
\(820\) −31.7773 114.452i −1.10971 3.99682i
\(821\) −10.4010 + 2.28944i −0.362998 + 0.0799018i −0.392724 0.919656i \(-0.628467\pi\)
0.0297266 + 0.999558i \(0.490536\pi\)
\(822\) 0 0
\(823\) 6.26048 5.93024i 0.218227 0.206715i −0.570775 0.821107i \(-0.693357\pi\)
0.789001 + 0.614391i \(0.210598\pi\)
\(824\) −3.43510 + 6.47929i −0.119667 + 0.225717i
\(825\) 0 0
\(826\) −28.5120 + 5.77706i −0.992059 + 0.201010i
\(827\) 34.9004 1.21361 0.606803 0.794852i \(-0.292452\pi\)
0.606803 + 0.794852i \(0.292452\pi\)
\(828\) 0 0
\(829\) −36.9188 + 34.9713i −1.28224 + 1.21461i −0.318454 + 0.947938i \(0.603164\pi\)
−0.963789 + 0.266667i \(0.914078\pi\)
\(830\) 0.546393 + 0.805869i 0.0189656 + 0.0279721i
\(831\) 0 0
\(832\) −7.61545 27.4284i −0.264018 0.950908i
\(833\) −10.0404 + 7.63254i −0.347881 + 0.264452i
\(834\) 0 0
\(835\) −1.57151 + 28.9849i −0.0543845 + 1.00306i
\(836\) −16.0607 + 57.8454i −0.555470 + 2.00062i
\(837\) 0 0
\(838\) −16.4736 3.62611i −0.569071 0.125262i
\(839\) 1.78615 + 32.9436i 0.0616648 + 1.13734i 0.851615 + 0.524168i \(0.175624\pi\)
−0.789950 + 0.613171i \(0.789894\pi\)
\(840\) 0 0
\(841\) 12.9354 19.0783i 0.446049 0.657874i
\(842\) −20.7504 + 52.0795i −0.715105 + 1.79478i
\(843\) 0 0
\(844\) 33.4332 + 20.1161i 1.15082 + 0.692425i
\(845\) 25.3941 8.55628i 0.873585 0.294345i
\(846\) 0 0
\(847\) 1.27475 7.77565i 0.0438010 0.267174i
\(848\) 0.243639 + 0.0264973i 0.00836660 + 0.000909922i
\(849\) 0 0
\(850\) 26.1507 30.7870i 0.896963 1.05599i
\(851\) 25.2358 11.6753i 0.865073 0.400225i
\(852\) 0 0
\(853\) −27.5141 32.3922i −0.942067 1.10909i −0.993884 0.110430i \(-0.964777\pi\)
0.0518174 0.998657i \(-0.483499\pi\)
\(854\) −8.41448 2.83517i −0.287938 0.0970175i
\(855\) 0 0
\(856\) 17.0436 + 32.1477i 0.582539 + 1.09878i
\(857\) 12.1521 + 4.09453i 0.415109 + 0.139867i 0.519104 0.854711i \(-0.326266\pi\)
−0.103995 + 0.994578i \(0.533162\pi\)
\(858\) 0 0
\(859\) −52.6781 24.3715i −1.79735 0.831545i −0.957331 0.288995i \(-0.906679\pi\)
−0.840024 0.542550i \(-0.817459\pi\)
\(860\) 70.1377 32.4491i 2.39167 1.10651i
\(861\) 0 0
\(862\) −42.3066 + 25.4551i −1.44097 + 0.867003i
\(863\) 15.3001 + 1.66398i 0.520820 + 0.0566426i 0.364754 0.931104i \(-0.381153\pi\)
0.156066 + 0.987747i \(0.450119\pi\)
\(864\) 0 0
\(865\) 13.2272 + 12.5295i 0.449739 + 0.426015i
\(866\) −15.8213 + 5.33081i −0.537629 + 0.181148i
\(867\) 0 0
\(868\) 34.4921 + 26.2202i 1.17074 + 0.889972i
\(869\) −11.7260 + 29.4299i −0.397776 + 0.998342i
\(870\) 0 0
\(871\) 5.85031 + 35.6853i 0.198230 + 1.20915i
\(872\) 2.52625 + 46.5940i 0.0855497 + 1.57787i
\(873\) 0 0
\(874\) −17.2614 43.3229i −0.583877 1.46542i
\(875\) 1.41794 5.10695i 0.0479350 0.172646i
\(876\) 0 0
\(877\) 3.59352 0.390819i 0.121345 0.0131970i −0.0472451 0.998883i \(-0.515044\pi\)
0.168590 + 0.985686i \(0.446079\pi\)
\(878\) 16.4361 12.4944i 0.554691 0.421665i
\(879\) 0 0
\(880\) −1.94491 + 0.428107i −0.0655628 + 0.0144315i
\(881\) 27.2385 + 40.1737i 0.917687 + 1.35349i 0.935380 + 0.353644i \(0.115058\pi\)
−0.0176927 + 0.999843i \(0.505632\pi\)
\(882\) 0 0
\(883\) −24.7023 + 46.5936i −0.831300 + 1.56800i −0.00829384 + 0.999966i \(0.502640\pi\)
−0.823006 + 0.568032i \(0.807705\pi\)
\(884\) 21.4376 0.721025
\(885\) 0 0
\(886\) −4.92989 −0.165623
\(887\) −13.8667 + 26.1553i −0.465597 + 0.878209i 0.533870 + 0.845566i \(0.320737\pi\)
−0.999467 + 0.0326425i \(0.989608\pi\)
\(888\) 0 0
\(889\) 3.37487 + 4.97755i 0.113189 + 0.166942i
\(890\) −52.3065 + 11.5135i −1.75332 + 0.385934i
\(891\) 0 0
\(892\) 17.3397 13.1813i 0.580575 0.441341i
\(893\) 49.7705 5.41287i 1.66551 0.181135i
\(894\) 0 0
\(895\) 6.56925 23.6603i 0.219586 0.790877i
\(896\) 11.4551 + 28.7501i 0.382687 + 0.960472i
\(897\) 0 0
\(898\) −1.93569 35.7017i −0.0645949 1.19138i
\(899\) 3.15640 + 19.2532i 0.105272 + 0.642130i
\(900\) 0 0
\(901\) 1.10632 2.77665i 0.0368568 0.0925036i
\(902\) 49.7617 + 37.8278i 1.65688 + 1.25953i
\(903\) 0 0
\(904\) −14.6772 + 4.94534i −0.488158 + 0.164479i
\(905\) 32.5437 + 30.8270i 1.08179 + 1.02472i
\(906\) 0 0
\(907\) 1.42208 + 0.154660i 0.0472192 + 0.00513540i 0.131698 0.991290i \(-0.457957\pi\)
−0.0844789 + 0.996425i \(0.526923\pi\)
\(908\) −13.9182 + 8.37429i −0.461891 + 0.277911i
\(909\) 0 0
\(910\) 25.2289 11.6721i 0.836331 0.386928i
\(911\) −39.2332 18.1512i −1.29985 0.601376i −0.356851 0.934161i \(-0.616150\pi\)
−0.943003 + 0.332785i \(0.892012\pi\)
\(912\) 0 0
\(913\) −0.301953 0.101740i −0.00999317 0.00336709i
\(914\) 9.23967 + 17.4279i 0.305621 + 0.576463i
\(915\) 0 0
\(916\) −2.87041 0.967154i −0.0948411 0.0319557i
\(917\) −11.0568 13.0171i −0.365128 0.429861i
\(918\) 0 0
\(919\) −30.3345 + 14.0342i −1.00064 + 0.462947i −0.850646 0.525739i \(-0.823789\pi\)
−0.149998 + 0.988686i \(0.547927\pi\)
\(920\) 17.6130 20.7356i 0.580682 0.683632i
\(921\) 0 0
\(922\) 69.6371 + 7.57349i 2.29338 + 0.249420i
\(923\) −2.33641 + 14.2514i −0.0769037 + 0.469092i
\(924\) 0 0
\(925\) −56.8095 + 19.1414i −1.86789 + 0.629364i
\(926\) −68.1765 41.0204i −2.24042 1.34802i
\(927\) 0 0
\(928\) −4.85379 + 12.1821i −0.159334 + 0.399897i
\(929\) −8.94476 + 13.1925i −0.293468 + 0.432833i −0.945629 0.325248i \(-0.894552\pi\)
0.652161 + 0.758081i \(0.273863\pi\)
\(930\) 0 0
\(931\) −1.69953 31.3459i −0.0556997 1.02732i
\(932\) 10.4366 + 2.29727i 0.341862 + 0.0752495i
\(933\) 0 0
\(934\) 12.6835 45.6817i 0.415016 1.49475i
\(935\) −1.31492 + 24.2523i −0.0430025 + 0.793134i
\(936\) 0 0
\(937\) −21.5854 + 16.4088i −0.705164 + 0.536052i −0.895167 0.445732i \(-0.852943\pi\)
0.190003 + 0.981784i \(0.439150\pi\)
\(938\) −16.5354 59.5552i −0.539901 1.94455i
\(939\) 0 0
\(940\) 41.8145 + 61.6718i 1.36384 + 2.01151i
\(941\) −7.85497 + 7.44062i −0.256065 + 0.242557i −0.804953 0.593338i \(-0.797810\pi\)
0.548889 + 0.835895i \(0.315051\pi\)
\(942\) 0 0
\(943\) −30.1966 −0.983336
\(944\) 1.74528 + 0.620791i 0.0568039 + 0.0202050i
\(945\) 0 0
\(946\) −19.0492 + 35.9306i −0.619343 + 1.16821i
\(947\) −5.21649 + 4.94132i −0.169513 + 0.160571i −0.767753 0.640745i \(-0.778625\pi\)
0.598240 + 0.801317i \(0.295867\pi\)
\(948\) 0 0
\(949\) 19.4344 4.27783i 0.630867 0.138864i
\(950\) 26.8980 + 96.8779i 0.872686 + 3.14313i
\(951\) 0 0
\(952\) −14.2785 + 1.55288i −0.462769 + 0.0503292i
\(953\) 3.04200 56.1063i 0.0985400 1.81746i −0.364585 0.931170i \(-0.618789\pi\)
0.463125 0.886293i \(-0.346728\pi\)
\(954\) 0 0
\(955\) 7.69650 + 19.3168i 0.249053 + 0.625076i
\(956\) 52.7858 + 11.6190i 1.70721 + 0.375786i
\(957\) 0 0
\(958\) −9.05648 55.2421i −0.292602 1.78479i
\(959\) 10.3569 15.2753i 0.334442 0.493266i
\(960\) 0 0
\(961\) 26.2518 + 19.9561i 0.846832 + 0.643745i
\(962\) −43.8357 26.3751i −1.41332 0.850367i
\(963\) 0 0
\(964\) −9.20092 8.71557i −0.296342 0.280710i
\(965\) 4.01142 24.4686i 0.129132 0.787672i
\(966\) 0 0
\(967\) −9.97401 + 6.00116i −0.320742 + 0.192984i −0.666815 0.745224i \(-0.732343\pi\)
0.346072 + 0.938208i \(0.387515\pi\)
\(968\) −9.18539 + 10.8139i −0.295229 + 0.347571i
\(969\) 0 0
\(970\) 103.399 + 47.8373i 3.31993 + 1.53596i
\(971\) −11.3655 13.3805i −0.364737 0.429402i 0.548928 0.835870i \(-0.315036\pi\)
−0.913665 + 0.406468i \(0.866760\pi\)
\(972\) 0 0
\(973\) 1.34964 + 2.54570i 0.0432676 + 0.0816114i
\(974\) 31.7202 + 59.8307i 1.01638 + 1.91710i
\(975\) 0 0
\(976\) 0.366025 + 0.430918i 0.0117162 + 0.0137933i
\(977\) −29.7631 13.7699i −0.952205 0.440537i −0.118627 0.992939i \(-0.537849\pi\)
−0.833578 + 0.552402i \(0.813711\pi\)
\(978\) 0 0
\(979\) 11.3471 13.3588i 0.362655 0.426950i
\(980\) 40.0332 24.0872i 1.27881 0.769437i
\(981\) 0 0
\(982\) −3.13173 + 19.1027i −0.0999377 + 0.609593i
\(983\) 30.6059 + 28.9915i 0.976178 + 0.924685i 0.997176 0.0750944i \(-0.0239258\pi\)
−0.0209983 + 0.999780i \(0.506684\pi\)
\(984\) 0 0
\(985\) 54.6117 + 32.8588i 1.74007 + 1.04697i
\(986\) −13.1354 9.98527i −0.418316 0.317996i
\(987\) 0 0
\(988\) −29.9443 + 44.1645i −0.952655 + 1.40506i
\(989\) −3.17840 19.3874i −0.101067 0.616484i
\(990\) 0 0
\(991\) 23.1509 + 5.09590i 0.735413 + 0.161877i 0.566858 0.823816i \(-0.308159\pi\)
0.168555 + 0.985692i \(0.446090\pi\)
\(992\) 15.9160 + 39.9462i 0.505335 + 1.26829i
\(993\) 0 0
\(994\) 1.33636 24.6478i 0.0423869 0.781780i
\(995\) −41.5598 + 4.51990i −1.31753 + 0.143290i
\(996\) 0 0
\(997\) 9.03220 + 32.5311i 0.286053 + 1.03027i 0.957314 + 0.289049i \(0.0933389\pi\)
−0.671262 + 0.741220i \(0.734247\pi\)
\(998\) −62.8263 + 13.8291i −1.98873 + 0.437753i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 531.2.i.c.19.5 140
3.2 odd 2 177.2.e.a.19.1 140
59.28 even 29 inner 531.2.i.c.28.5 140
177.146 odd 58 177.2.e.a.28.1 yes 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.2.e.a.19.1 140 3.2 odd 2
177.2.e.a.28.1 yes 140 177.146 odd 58
531.2.i.c.19.5 140 1.1 even 1 trivial
531.2.i.c.28.5 140 59.28 even 29 inner