Properties

Label 804.2.q.b.397.2
Level $804$
Weight $2$
Character 804.397
Analytic conductor $6.420$
Analytic rank $0$
Dimension $60$
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] = [804,2,Mod(25,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.q (of order \(11\), degree \(10\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 397.2
Character \(\chi\) \(=\) 804.397
Dual form 804.2.q.b.241.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.415415 - 0.909632i) q^{3} +(-1.77661 + 0.521660i) q^{5} +(0.707286 - 0.816251i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 - 0.909632i) q^{3} +(-1.77661 + 0.521660i) q^{5} +(0.707286 - 0.816251i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-6.30285 + 1.85068i) q^{11} +(4.21329 - 2.70772i) q^{13} +(1.21255 + 1.39936i) q^{15} +(-0.520776 + 3.62208i) q^{17} +(4.73554 + 5.46510i) q^{19} +(-1.03631 - 0.304287i) q^{21} +(2.13944 + 4.68472i) q^{23} +(-1.32205 + 0.849633i) q^{25} +(0.959493 + 0.281733i) q^{27} +3.56041 q^{29} +(-2.55994 - 1.64517i) q^{31} +(4.30174 + 4.96447i) q^{33} +(-0.830765 + 1.81912i) q^{35} -5.91644 q^{37} +(-4.21329 - 2.70772i) q^{39} +(0.936661 - 6.51462i) q^{41} +(-1.17480 + 8.17090i) q^{43} +(0.769188 - 1.68429i) q^{45} +(5.39652 + 11.8167i) q^{47} +(0.830191 + 5.77410i) q^{49} +(3.51110 - 1.03095i) q^{51} +(-0.207822 - 1.44544i) q^{53} +(10.2323 - 6.57588i) q^{55} +(3.00402 - 6.57788i) q^{57} +(-1.12909 - 0.725625i) q^{59} +(0.203291 + 0.0596917i) q^{61} +(0.153708 + 1.06906i) q^{63} +(-6.07287 + 7.00847i) q^{65} +(-8.00742 + 1.69742i) q^{67} +(3.37262 - 3.89221i) q^{69} +(1.41822 + 9.86395i) q^{71} +(11.6575 + 3.42296i) q^{73} +(1.32205 + 0.849633i) q^{75} +(-2.94729 + 6.45367i) q^{77} +(0.266249 - 0.171108i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(4.67588 - 1.37296i) q^{83} +(-0.964276 - 6.70668i) q^{85} +(-1.47905 - 3.23866i) q^{87} +(-2.91449 + 6.38185i) q^{89} +(0.769823 - 5.35424i) q^{91} +(-0.433064 + 3.01203i) q^{93} +(-11.2641 - 7.23901i) q^{95} +0.508626 q^{97} +(2.72883 - 5.97531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.415415 0.909632i −0.239840 0.525176i
\(4\) 0 0
\(5\) −1.77661 + 0.521660i −0.794524 + 0.233293i −0.653712 0.756743i \(-0.726789\pi\)
−0.140812 + 0.990036i \(0.544971\pi\)
\(6\) 0 0
\(7\) 0.707286 0.816251i 0.267329 0.308514i −0.606175 0.795331i \(-0.707297\pi\)
0.873504 + 0.486817i \(0.161842\pi\)
\(8\) 0 0
\(9\) −0.654861 + 0.755750i −0.218287 + 0.251917i
\(10\) 0 0
\(11\) −6.30285 + 1.85068i −1.90038 + 0.558002i −0.911053 + 0.412289i \(0.864729\pi\)
−0.989327 + 0.145712i \(0.953453\pi\)
\(12\) 0 0
\(13\) 4.21329 2.70772i 1.16856 0.750986i 0.195309 0.980742i \(-0.437429\pi\)
0.973248 + 0.229755i \(0.0737926\pi\)
\(14\) 0 0
\(15\) 1.21255 + 1.39936i 0.313079 + 0.361312i
\(16\) 0 0
\(17\) −0.520776 + 3.62208i −0.126307 + 0.878483i 0.823872 + 0.566776i \(0.191810\pi\)
−0.950178 + 0.311706i \(0.899099\pi\)
\(18\) 0 0
\(19\) 4.73554 + 5.46510i 1.08641 + 1.25378i 0.965301 + 0.261141i \(0.0840987\pi\)
0.121106 + 0.992640i \(0.461356\pi\)
\(20\) 0 0
\(21\) −1.03631 0.304287i −0.226140 0.0664008i
\(22\) 0 0
\(23\) 2.13944 + 4.68472i 0.446104 + 0.976832i 0.990437 + 0.137963i \(0.0440555\pi\)
−0.544333 + 0.838869i \(0.683217\pi\)
\(24\) 0 0
\(25\) −1.32205 + 0.849633i −0.264411 + 0.169927i
\(26\) 0 0
\(27\) 0.959493 + 0.281733i 0.184655 + 0.0542195i
\(28\) 0 0
\(29\) 3.56041 0.661151 0.330575 0.943780i \(-0.392757\pi\)
0.330575 + 0.943780i \(0.392757\pi\)
\(30\) 0 0
\(31\) −2.55994 1.64517i −0.459778 0.295481i 0.290174 0.956974i \(-0.406287\pi\)
−0.749952 + 0.661493i \(0.769923\pi\)
\(32\) 0 0
\(33\) 4.30174 + 4.96447i 0.748836 + 0.864203i
\(34\) 0 0
\(35\) −0.830765 + 1.81912i −0.140425 + 0.307488i
\(36\) 0 0
\(37\) −5.91644 −0.972657 −0.486328 0.873776i \(-0.661664\pi\)
−0.486328 + 0.873776i \(0.661664\pi\)
\(38\) 0 0
\(39\) −4.21329 2.70772i −0.674667 0.433582i
\(40\) 0 0
\(41\) 0.936661 6.51462i 0.146282 1.01741i −0.775955 0.630788i \(-0.782732\pi\)
0.922237 0.386625i \(-0.126359\pi\)
\(42\) 0 0
\(43\) −1.17480 + 8.17090i −0.179155 + 1.24605i 0.679569 + 0.733612i \(0.262167\pi\)
−0.858724 + 0.512438i \(0.828742\pi\)
\(44\) 0 0
\(45\) 0.769188 1.68429i 0.114664 0.251079i
\(46\) 0 0
\(47\) 5.39652 + 11.8167i 0.787163 + 1.72365i 0.684600 + 0.728919i \(0.259977\pi\)
0.102563 + 0.994727i \(0.467296\pi\)
\(48\) 0 0
\(49\) 0.830191 + 5.77410i 0.118599 + 0.824872i
\(50\) 0 0
\(51\) 3.51110 1.03095i 0.491652 0.144362i
\(52\) 0 0
\(53\) −0.207822 1.44544i −0.0285466 0.198546i 0.970557 0.240870i \(-0.0774328\pi\)
−0.999104 + 0.0423243i \(0.986524\pi\)
\(54\) 0 0
\(55\) 10.2323 6.57588i 1.37972 0.886692i
\(56\) 0 0
\(57\) 3.00402 6.57788i 0.397892 0.871262i
\(58\) 0 0
\(59\) −1.12909 0.725625i −0.146996 0.0944683i 0.465076 0.885271i \(-0.346027\pi\)
−0.612071 + 0.790803i \(0.709663\pi\)
\(60\) 0 0
\(61\) 0.203291 + 0.0596917i 0.0260288 + 0.00764274i 0.294721 0.955583i \(-0.404773\pi\)
−0.268692 + 0.963226i \(0.586591\pi\)
\(62\) 0 0
\(63\) 0.153708 + 1.06906i 0.0193654 + 0.134689i
\(64\) 0 0
\(65\) −6.07287 + 7.00847i −0.753247 + 0.869293i
\(66\) 0 0
\(67\) −8.00742 + 1.69742i −0.978262 + 0.207373i
\(68\) 0 0
\(69\) 3.37262 3.89221i 0.406015 0.468567i
\(70\) 0 0
\(71\) 1.41822 + 9.86395i 0.168312 + 1.17064i 0.882372 + 0.470552i \(0.155945\pi\)
−0.714060 + 0.700084i \(0.753146\pi\)
\(72\) 0 0
\(73\) 11.6575 + 3.42296i 1.36441 + 0.400627i 0.880316 0.474388i \(-0.157331\pi\)
0.484095 + 0.875016i \(0.339149\pi\)
\(74\) 0 0
\(75\) 1.32205 + 0.849633i 0.152658 + 0.0981072i
\(76\) 0 0
\(77\) −2.94729 + 6.45367i −0.335875 + 0.735464i
\(78\) 0 0
\(79\) 0.266249 0.171108i 0.0299553 0.0192511i −0.525577 0.850746i \(-0.676151\pi\)
0.555533 + 0.831495i \(0.312514\pi\)
\(80\) 0 0
\(81\) −0.142315 0.989821i −0.0158128 0.109980i
\(82\) 0 0
\(83\) 4.67588 1.37296i 0.513244 0.150702i −0.0148469 0.999890i \(-0.504726\pi\)
0.528091 + 0.849188i \(0.322908\pi\)
\(84\) 0 0
\(85\) −0.964276 6.70668i −0.104590 0.727442i
\(86\) 0 0
\(87\) −1.47905 3.23866i −0.158570 0.347221i
\(88\) 0 0
\(89\) −2.91449 + 6.38185i −0.308936 + 0.676475i −0.998876 0.0473910i \(-0.984909\pi\)
0.689941 + 0.723866i \(0.257637\pi\)
\(90\) 0 0
\(91\) 0.769823 5.35424i 0.0806994 0.561277i
\(92\) 0 0
\(93\) −0.433064 + 3.01203i −0.0449067 + 0.312333i
\(94\) 0 0
\(95\) −11.2641 7.23901i −1.15567 0.742707i
\(96\) 0 0
\(97\) 0.508626 0.0516432 0.0258216 0.999667i \(-0.491780\pi\)
0.0258216 + 0.999667i \(0.491780\pi\)
\(98\) 0 0
\(99\) 2.72883 5.97531i 0.274258 0.600542i
\(100\) 0 0
\(101\) −10.0015 11.5424i −0.995189 1.14851i −0.988908 0.148529i \(-0.952546\pi\)
−0.00628108 0.999980i \(-0.501999\pi\)
\(102\) 0 0
\(103\) −9.45292 6.07503i −0.931424 0.598590i −0.0154733 0.999880i \(-0.504925\pi\)
−0.915951 + 0.401290i \(0.868562\pi\)
\(104\) 0 0
\(105\) 1.99984 0.195165
\(106\) 0 0
\(107\) −9.62937 2.82744i −0.930906 0.273339i −0.219090 0.975705i \(-0.570309\pi\)
−0.711816 + 0.702366i \(0.752127\pi\)
\(108\) 0 0
\(109\) 4.61414 2.96533i 0.441954 0.284027i −0.300679 0.953726i \(-0.597213\pi\)
0.742633 + 0.669699i \(0.233577\pi\)
\(110\) 0 0
\(111\) 2.45778 + 5.38178i 0.233282 + 0.510816i
\(112\) 0 0
\(113\) 0.455474 + 0.133739i 0.0428474 + 0.0125811i 0.303086 0.952963i \(-0.401983\pi\)
−0.260239 + 0.965544i \(0.583801\pi\)
\(114\) 0 0
\(115\) −6.24478 7.20686i −0.582329 0.672043i
\(116\) 0 0
\(117\) −0.712763 + 4.95737i −0.0658950 + 0.458309i
\(118\) 0 0
\(119\) 2.58819 + 2.98693i 0.237259 + 0.273811i
\(120\) 0 0
\(121\) 27.0471 17.3821i 2.45882 1.58019i
\(122\) 0 0
\(123\) −6.31501 + 1.85425i −0.569405 + 0.167192i
\(124\) 0 0
\(125\) 7.96830 9.19591i 0.712706 0.822507i
\(126\) 0 0
\(127\) −2.57508 + 2.97180i −0.228501 + 0.263704i −0.858409 0.512965i \(-0.828547\pi\)
0.629908 + 0.776670i \(0.283092\pi\)
\(128\) 0 0
\(129\) 7.92054 2.32568i 0.697364 0.204765i
\(130\) 0 0
\(131\) −8.67599 18.9978i −0.758025 1.65984i −0.751384 0.659865i \(-0.770614\pi\)
−0.00664048 0.999978i \(-0.502114\pi\)
\(132\) 0 0
\(133\) 7.81028 0.677237
\(134\) 0 0
\(135\) −1.85161 −0.159361
\(136\) 0 0
\(137\) 3.28591 + 7.19515i 0.280735 + 0.614723i 0.996498 0.0836201i \(-0.0266482\pi\)
−0.715763 + 0.698343i \(0.753921\pi\)
\(138\) 0 0
\(139\) −21.0011 + 6.16648i −1.78129 + 0.523034i −0.995441 0.0953838i \(-0.969592\pi\)
−0.785850 + 0.618418i \(0.787774\pi\)
\(140\) 0 0
\(141\) 8.50707 9.81769i 0.716425 0.826798i
\(142\) 0 0
\(143\) −21.5446 + 24.8638i −1.80165 + 2.07922i
\(144\) 0 0
\(145\) −6.32545 + 1.85732i −0.525300 + 0.154242i
\(146\) 0 0
\(147\) 4.90744 3.15382i 0.404759 0.260123i
\(148\) 0 0
\(149\) −7.46522 8.61532i −0.611575 0.705795i 0.362510 0.931980i \(-0.381920\pi\)
−0.974084 + 0.226185i \(0.927375\pi\)
\(150\) 0 0
\(151\) −0.810852 + 5.63960i −0.0659862 + 0.458944i 0.929862 + 0.367910i \(0.119926\pi\)
−0.995848 + 0.0910344i \(0.970983\pi\)
\(152\) 0 0
\(153\) −2.39635 2.76553i −0.193733 0.223580i
\(154\) 0 0
\(155\) 5.40623 + 1.58741i 0.434239 + 0.127504i
\(156\) 0 0
\(157\) 1.28348 + 2.81042i 0.102433 + 0.224296i 0.953908 0.300098i \(-0.0970193\pi\)
−0.851476 + 0.524394i \(0.824292\pi\)
\(158\) 0 0
\(159\) −1.22848 + 0.789498i −0.0974250 + 0.0626113i
\(160\) 0 0
\(161\) 5.33711 + 1.56712i 0.420623 + 0.123506i
\(162\) 0 0
\(163\) −11.7855 −0.923110 −0.461555 0.887112i \(-0.652708\pi\)
−0.461555 + 0.887112i \(0.652708\pi\)
\(164\) 0 0
\(165\) −10.2323 6.57588i −0.796581 0.511932i
\(166\) 0 0
\(167\) 7.28198 + 8.40386i 0.563497 + 0.650310i 0.963974 0.265997i \(-0.0857010\pi\)
−0.400477 + 0.916307i \(0.631156\pi\)
\(168\) 0 0
\(169\) 5.01971 10.9916i 0.386131 0.845510i
\(170\) 0 0
\(171\) −7.23137 −0.552996
\(172\) 0 0
\(173\) −1.33481 0.857833i −0.101484 0.0652199i 0.488914 0.872332i \(-0.337393\pi\)
−0.590398 + 0.807112i \(0.701029\pi\)
\(174\) 0 0
\(175\) −0.241557 + 1.68006i −0.0182600 + 0.127001i
\(176\) 0 0
\(177\) −0.191009 + 1.32850i −0.0143571 + 0.0998559i
\(178\) 0 0
\(179\) −0.482924 + 1.05746i −0.0360954 + 0.0790380i −0.926821 0.375504i \(-0.877470\pi\)
0.890725 + 0.454542i \(0.150197\pi\)
\(180\) 0 0
\(181\) 7.93138 + 17.3673i 0.589535 + 1.29090i 0.935723 + 0.352736i \(0.114749\pi\)
−0.346188 + 0.938165i \(0.612524\pi\)
\(182\) 0 0
\(183\) −0.0301528 0.209717i −0.00222896 0.0155027i
\(184\) 0 0
\(185\) 10.5112 3.08637i 0.772799 0.226914i
\(186\) 0 0
\(187\) −3.42094 23.7932i −0.250164 1.73993i
\(188\) 0 0
\(189\) 0.908600 0.583922i 0.0660909 0.0424741i
\(190\) 0 0
\(191\) −4.85212 + 10.6247i −0.351087 + 0.768774i 0.648882 + 0.760889i \(0.275237\pi\)
−0.999969 + 0.00788471i \(0.997490\pi\)
\(192\) 0 0
\(193\) −17.8992 11.5031i −1.28841 0.828012i −0.296512 0.955029i \(-0.595823\pi\)
−0.991901 + 0.127017i \(0.959460\pi\)
\(194\) 0 0
\(195\) 8.89789 + 2.61266i 0.637191 + 0.187096i
\(196\) 0 0
\(197\) 1.42272 + 9.89523i 0.101365 + 0.705006i 0.975608 + 0.219519i \(0.0704487\pi\)
−0.874244 + 0.485487i \(0.838642\pi\)
\(198\) 0 0
\(199\) −7.24130 + 8.35690i −0.513322 + 0.592405i −0.951946 0.306265i \(-0.900920\pi\)
0.438624 + 0.898671i \(0.355466\pi\)
\(200\) 0 0
\(201\) 4.87043 + 6.57867i 0.343534 + 0.464024i
\(202\) 0 0
\(203\) 2.51822 2.90619i 0.176745 0.203974i
\(204\) 0 0
\(205\) 1.73433 + 12.0626i 0.121131 + 0.842485i
\(206\) 0 0
\(207\) −4.94151 1.45096i −0.343459 0.100849i
\(208\) 0 0
\(209\) −39.9615 25.6817i −2.76420 1.77644i
\(210\) 0 0
\(211\) 9.17122 20.0822i 0.631373 1.38251i −0.275578 0.961279i \(-0.588869\pi\)
0.906951 0.421235i \(-0.138403\pi\)
\(212\) 0 0
\(213\) 8.38342 5.38769i 0.574422 0.369159i
\(214\) 0 0
\(215\) −2.17527 15.1293i −0.148352 1.03181i
\(216\) 0 0
\(217\) −3.15348 + 0.925945i −0.214072 + 0.0628573i
\(218\) 0 0
\(219\) −1.72908 12.0260i −0.116840 0.812642i
\(220\) 0 0
\(221\) 7.61339 + 16.6710i 0.512132 + 1.12141i
\(222\) 0 0
\(223\) 9.62261 21.0706i 0.644377 1.41099i −0.252013 0.967724i \(-0.581092\pi\)
0.896390 0.443266i \(-0.146180\pi\)
\(224\) 0 0
\(225\) 0.223652 1.55553i 0.0149101 0.103702i
\(226\) 0 0
\(227\) 3.51482 24.4461i 0.233287 1.62254i −0.450440 0.892807i \(-0.648733\pi\)
0.683727 0.729738i \(-0.260358\pi\)
\(228\) 0 0
\(229\) 11.9149 + 7.65725i 0.787359 + 0.506005i 0.871468 0.490452i \(-0.163168\pi\)
−0.0841093 + 0.996457i \(0.526804\pi\)
\(230\) 0 0
\(231\) 7.09481 0.466804
\(232\) 0 0
\(233\) 10.2538 22.4527i 0.671748 1.47092i −0.199408 0.979917i \(-0.563902\pi\)
0.871156 0.491006i \(-0.163371\pi\)
\(234\) 0 0
\(235\) −15.7518 18.1786i −1.02753 1.18584i
\(236\) 0 0
\(237\) −0.266249 0.171108i −0.0172947 0.0111146i
\(238\) 0 0
\(239\) 22.2021 1.43614 0.718068 0.695973i \(-0.245027\pi\)
0.718068 + 0.695973i \(0.245027\pi\)
\(240\) 0 0
\(241\) 22.0047 + 6.46117i 1.41745 + 0.416200i 0.898639 0.438689i \(-0.144557\pi\)
0.518810 + 0.854890i \(0.326375\pi\)
\(242\) 0 0
\(243\) −0.841254 + 0.540641i −0.0539664 + 0.0346821i
\(244\) 0 0
\(245\) −4.48704 9.82525i −0.286667 0.627712i
\(246\) 0 0
\(247\) 34.7502 + 10.2036i 2.21110 + 0.649238i
\(248\) 0 0
\(249\) −3.19132 3.68298i −0.202242 0.233399i
\(250\) 0 0
\(251\) −3.72323 + 25.8956i −0.235008 + 1.63452i 0.440919 + 0.897547i \(0.354653\pi\)
−0.675927 + 0.736969i \(0.736256\pi\)
\(252\) 0 0
\(253\) −22.1545 25.5677i −1.39284 1.60743i
\(254\) 0 0
\(255\) −5.70004 + 3.66319i −0.356950 + 0.229398i
\(256\) 0 0
\(257\) −7.77514 + 2.28299i −0.485000 + 0.142409i −0.515086 0.857139i \(-0.672240\pi\)
0.0300863 + 0.999547i \(0.490422\pi\)
\(258\) 0 0
\(259\) −4.18461 + 4.82930i −0.260019 + 0.300078i
\(260\) 0 0
\(261\) −2.33157 + 2.69077i −0.144321 + 0.166555i
\(262\) 0 0
\(263\) 3.00315 0.881805i 0.185182 0.0543744i −0.187827 0.982202i \(-0.560144\pi\)
0.373009 + 0.927828i \(0.378326\pi\)
\(264\) 0 0
\(265\) 1.12325 + 2.45956i 0.0690004 + 0.151090i
\(266\) 0 0
\(267\) 7.01586 0.429364
\(268\) 0 0
\(269\) −4.50112 −0.274438 −0.137219 0.990541i \(-0.543816\pi\)
−0.137219 + 0.990541i \(0.543816\pi\)
\(270\) 0 0
\(271\) 3.63644 + 7.96269i 0.220898 + 0.483699i 0.987341 0.158614i \(-0.0507024\pi\)
−0.766443 + 0.642312i \(0.777975\pi\)
\(272\) 0 0
\(273\) −5.19018 + 1.52398i −0.314124 + 0.0922352i
\(274\) 0 0
\(275\) 6.76031 7.80181i 0.407662 0.470467i
\(276\) 0 0
\(277\) −15.8811 + 18.3277i −0.954200 + 1.10121i 0.0405815 + 0.999176i \(0.487079\pi\)
−0.994781 + 0.102029i \(0.967466\pi\)
\(278\) 0 0
\(279\) 2.91974 0.857313i 0.174800 0.0513260i
\(280\) 0 0
\(281\) −3.01093 + 1.93501i −0.179617 + 0.115433i −0.627360 0.778729i \(-0.715864\pi\)
0.447743 + 0.894163i \(0.352228\pi\)
\(282\) 0 0
\(283\) 1.92622 + 2.22298i 0.114502 + 0.132142i 0.810107 0.586282i \(-0.199409\pi\)
−0.695605 + 0.718425i \(0.744864\pi\)
\(284\) 0 0
\(285\) −1.90555 + 13.2534i −0.112875 + 0.785064i
\(286\) 0 0
\(287\) −4.65508 5.37225i −0.274781 0.317114i
\(288\) 0 0
\(289\) 3.46315 + 1.01687i 0.203714 + 0.0598160i
\(290\) 0 0
\(291\) −0.211291 0.462663i −0.0123861 0.0271218i
\(292\) 0 0
\(293\) −12.4449 + 7.99786i −0.727040 + 0.467240i −0.851079 0.525037i \(-0.824051\pi\)
0.124040 + 0.992277i \(0.460415\pi\)
\(294\) 0 0
\(295\) 2.38449 + 0.700149i 0.138830 + 0.0407643i
\(296\) 0 0
\(297\) −6.56894 −0.381168
\(298\) 0 0
\(299\) 21.6990 + 13.9451i 1.25489 + 0.806466i
\(300\) 0 0
\(301\) 5.83859 + 6.73809i 0.336531 + 0.388377i
\(302\) 0 0
\(303\) −6.34453 + 13.8926i −0.364484 + 0.798108i
\(304\) 0 0
\(305\) −0.392308 −0.0224635
\(306\) 0 0
\(307\) 27.6458 + 17.7669i 1.57783 + 1.01401i 0.976634 + 0.214909i \(0.0689455\pi\)
0.601197 + 0.799101i \(0.294691\pi\)
\(308\) 0 0
\(309\) −1.59915 + 11.1223i −0.0909725 + 0.632728i
\(310\) 0 0
\(311\) −3.71480 + 25.8370i −0.210647 + 1.46508i 0.560358 + 0.828251i \(0.310664\pi\)
−0.771005 + 0.636829i \(0.780246\pi\)
\(312\) 0 0
\(313\) 6.00882 13.1575i 0.339638 0.743704i −0.660335 0.750971i \(-0.729586\pi\)
0.999974 + 0.00726673i \(0.00231309\pi\)
\(314\) 0 0
\(315\) −0.830765 1.81912i −0.0468083 0.102496i
\(316\) 0 0
\(317\) −0.816861 5.68139i −0.0458795 0.319099i −0.999818 0.0190956i \(-0.993921\pi\)
0.953938 0.300003i \(-0.0969878\pi\)
\(318\) 0 0
\(319\) −22.4407 + 6.58918i −1.25644 + 0.368923i
\(320\) 0 0
\(321\) 1.42826 + 9.93374i 0.0797175 + 0.554447i
\(322\) 0 0
\(323\) −22.2612 + 14.3064i −1.23865 + 0.796029i
\(324\) 0 0
\(325\) −3.26964 + 7.15951i −0.181367 + 0.397138i
\(326\) 0 0
\(327\) −4.61414 2.96533i −0.255162 0.163983i
\(328\) 0 0
\(329\) 13.4623 + 3.95289i 0.742200 + 0.217930i
\(330\) 0 0
\(331\) −1.85936 12.9321i −0.102200 0.710814i −0.974914 0.222583i \(-0.928551\pi\)
0.872714 0.488232i \(-0.162358\pi\)
\(332\) 0 0
\(333\) 3.87444 4.47135i 0.212318 0.245028i
\(334\) 0 0
\(335\) 13.3406 7.19280i 0.728874 0.392985i
\(336\) 0 0
\(337\) 8.12315 9.37462i 0.442496 0.510668i −0.490062 0.871688i \(-0.663026\pi\)
0.932558 + 0.361020i \(0.117571\pi\)
\(338\) 0 0
\(339\) −0.0675573 0.469871i −0.00366921 0.0255199i
\(340\) 0 0
\(341\) 19.1796 + 5.63163i 1.03863 + 0.304970i
\(342\) 0 0
\(343\) 11.6605 + 7.49375i 0.629608 + 0.404625i
\(344\) 0 0
\(345\) −3.96142 + 8.67429i −0.213276 + 0.467008i
\(346\) 0 0
\(347\) −11.5268 + 7.40784i −0.618792 + 0.397673i −0.812145 0.583456i \(-0.801700\pi\)
0.193353 + 0.981129i \(0.438064\pi\)
\(348\) 0 0
\(349\) 0.418591 + 2.91137i 0.0224067 + 0.155842i 0.997953 0.0639522i \(-0.0203705\pi\)
−0.975546 + 0.219794i \(0.929461\pi\)
\(350\) 0 0
\(351\) 4.80548 1.41102i 0.256498 0.0753145i
\(352\) 0 0
\(353\) −1.18195 8.22064i −0.0629089 0.437541i −0.996797 0.0799751i \(-0.974516\pi\)
0.933888 0.357566i \(-0.116393\pi\)
\(354\) 0 0
\(355\) −7.66525 16.7846i −0.406829 0.890832i
\(356\) 0 0
\(357\) 1.64183 3.59511i 0.0868950 0.190274i
\(358\) 0 0
\(359\) 1.12157 7.80070i 0.0591943 0.411705i −0.938582 0.345056i \(-0.887860\pi\)
0.997776 0.0666495i \(-0.0212309\pi\)
\(360\) 0 0
\(361\) −4.73804 + 32.9538i −0.249371 + 1.73441i
\(362\) 0 0
\(363\) −27.0471 17.3821i −1.41960 0.912323i
\(364\) 0 0
\(365\) −22.4965 −1.17752
\(366\) 0 0
\(367\) 0.297957 0.652435i 0.0155532 0.0340568i −0.901696 0.432371i \(-0.857677\pi\)
0.917249 + 0.398314i \(0.130404\pi\)
\(368\) 0 0
\(369\) 4.31004 + 4.97405i 0.224372 + 0.258939i
\(370\) 0 0
\(371\) −1.32683 0.852702i −0.0688856 0.0442701i
\(372\) 0 0
\(373\) 13.6530 0.706926 0.353463 0.935449i \(-0.385004\pi\)
0.353463 + 0.935449i \(0.385004\pi\)
\(374\) 0 0
\(375\) −11.6750 3.42810i −0.602897 0.177026i
\(376\) 0 0
\(377\) 15.0010 9.64058i 0.772593 0.496515i
\(378\) 0 0
\(379\) 6.38225 + 13.9752i 0.327834 + 0.717856i 0.999741 0.0227795i \(-0.00725158\pi\)
−0.671906 + 0.740636i \(0.734524\pi\)
\(380\) 0 0
\(381\) 3.77297 + 1.10784i 0.193295 + 0.0567565i
\(382\) 0 0
\(383\) 11.4782 + 13.2465i 0.586507 + 0.676866i 0.968991 0.247097i \(-0.0794765\pi\)
−0.382483 + 0.923962i \(0.624931\pi\)
\(384\) 0 0
\(385\) 1.86957 13.0031i 0.0952820 0.662701i
\(386\) 0 0
\(387\) −5.40582 6.23865i −0.274793 0.317128i
\(388\) 0 0
\(389\) 25.5214 16.4016i 1.29399 0.831595i 0.301443 0.953484i \(-0.402532\pi\)
0.992544 + 0.121889i \(0.0388952\pi\)
\(390\) 0 0
\(391\) −18.0826 + 5.30953i −0.914476 + 0.268514i
\(392\) 0 0
\(393\) −13.6768 + 15.7839i −0.689905 + 0.796193i
\(394\) 0 0
\(395\) −0.383760 + 0.442883i −0.0193091 + 0.0222839i
\(396\) 0 0
\(397\) −31.7750 + 9.32999i −1.59474 + 0.468259i −0.954077 0.299561i \(-0.903160\pi\)
−0.640666 + 0.767820i \(0.721342\pi\)
\(398\) 0 0
\(399\) −3.24451 7.10448i −0.162428 0.355669i
\(400\) 0 0
\(401\) 8.62132 0.430528 0.215264 0.976556i \(-0.430939\pi\)
0.215264 + 0.976556i \(0.430939\pi\)
\(402\) 0 0
\(403\) −15.2404 −0.759180
\(404\) 0 0
\(405\) 0.769188 + 1.68429i 0.0382212 + 0.0836929i
\(406\) 0 0
\(407\) 37.2904 10.9495i 1.84842 0.542744i
\(408\) 0 0
\(409\) −17.1503 + 19.7925i −0.848028 + 0.978676i −0.999953 0.00971574i \(-0.996907\pi\)
0.151925 + 0.988392i \(0.451453\pi\)
\(410\) 0 0
\(411\) 5.17992 5.97795i 0.255507 0.294870i
\(412\) 0 0
\(413\) −1.39088 + 0.408401i −0.0684410 + 0.0200961i
\(414\) 0 0
\(415\) −7.59099 + 4.87843i −0.372627 + 0.239473i
\(416\) 0 0
\(417\) 14.3334 + 16.5416i 0.701910 + 0.810047i
\(418\) 0 0
\(419\) −3.56496 + 24.7949i −0.174160 + 1.21131i 0.695818 + 0.718218i \(0.255042\pi\)
−0.869978 + 0.493090i \(0.835867\pi\)
\(420\) 0 0
\(421\) 10.3091 + 11.8973i 0.502433 + 0.579839i 0.949145 0.314839i \(-0.101951\pi\)
−0.446712 + 0.894678i \(0.647405\pi\)
\(422\) 0 0
\(423\) −12.4644 3.65989i −0.606042 0.177950i
\(424\) 0 0
\(425\) −2.38894 5.23105i −0.115881 0.253743i
\(426\) 0 0
\(427\) 0.192509 0.123718i 0.00931614 0.00598712i
\(428\) 0 0
\(429\) 31.5669 + 9.26887i 1.52406 + 0.447505i
\(430\) 0 0
\(431\) 29.4346 1.41781 0.708907 0.705302i \(-0.249189\pi\)
0.708907 + 0.705302i \(0.249189\pi\)
\(432\) 0 0
\(433\) −13.4260 8.62834i −0.645210 0.414652i 0.176703 0.984264i \(-0.443457\pi\)
−0.821913 + 0.569613i \(0.807093\pi\)
\(434\) 0 0
\(435\) 4.31716 + 4.98227i 0.206992 + 0.238882i
\(436\) 0 0
\(437\) −15.4711 + 33.8769i −0.740082 + 1.62055i
\(438\) 0 0
\(439\) −17.1229 −0.817229 −0.408615 0.912707i \(-0.633988\pi\)
−0.408615 + 0.912707i \(0.633988\pi\)
\(440\) 0 0
\(441\) −4.90744 3.15382i −0.233687 0.150182i
\(442\) 0 0
\(443\) −0.280265 + 1.94928i −0.0133158 + 0.0926133i −0.995396 0.0958524i \(-0.969442\pi\)
0.982080 + 0.188466i \(0.0603514\pi\)
\(444\) 0 0
\(445\) 1.84876 12.8584i 0.0876398 0.609548i
\(446\) 0 0
\(447\) −4.73561 + 10.3695i −0.223987 + 0.490462i
\(448\) 0 0
\(449\) 1.16035 + 2.54082i 0.0547604 + 0.119909i 0.935034 0.354557i \(-0.115368\pi\)
−0.880274 + 0.474466i \(0.842641\pi\)
\(450\) 0 0
\(451\) 6.15286 + 42.7941i 0.289727 + 2.01510i
\(452\) 0 0
\(453\) 5.46680 1.60520i 0.256853 0.0754187i
\(454\) 0 0
\(455\) 1.42541 + 9.91398i 0.0668245 + 0.464774i
\(456\) 0 0
\(457\) 3.41726 2.19614i 0.159853 0.102731i −0.458269 0.888814i \(-0.651530\pi\)
0.618122 + 0.786083i \(0.287894\pi\)
\(458\) 0 0
\(459\) −1.52014 + 3.32864i −0.0709540 + 0.155368i
\(460\) 0 0
\(461\) 8.53402 + 5.48448i 0.397469 + 0.255438i 0.724073 0.689723i \(-0.242268\pi\)
−0.326604 + 0.945161i \(0.605904\pi\)
\(462\) 0 0
\(463\) −0.0372962 0.0109512i −0.00173330 0.000508943i 0.280866 0.959747i \(-0.409378\pi\)
−0.282599 + 0.959238i \(0.591197\pi\)
\(464\) 0 0
\(465\) −0.801868 5.57711i −0.0371857 0.258632i
\(466\) 0 0
\(467\) 10.5560 12.1823i 0.488474 0.563729i −0.456983 0.889475i \(-0.651070\pi\)
0.945457 + 0.325746i \(0.105615\pi\)
\(468\) 0 0
\(469\) −4.27801 + 7.73663i −0.197540 + 0.357244i
\(470\) 0 0
\(471\) 2.02328 2.33498i 0.0932276 0.107590i
\(472\) 0 0
\(473\) −7.71717 53.6741i −0.354836 2.46794i
\(474\) 0 0
\(475\) −10.9040 3.20170i −0.500309 0.146904i
\(476\) 0 0
\(477\) 1.22848 + 0.789498i 0.0562484 + 0.0361486i
\(478\) 0 0
\(479\) 11.0837 24.2699i 0.506427 1.10892i −0.467900 0.883781i \(-0.654989\pi\)
0.974327 0.225138i \(-0.0722834\pi\)
\(480\) 0 0
\(481\) −24.9277 + 16.0201i −1.13661 + 0.730452i
\(482\) 0 0
\(483\) −0.791616 5.50581i −0.0360198 0.250523i
\(484\) 0 0
\(485\) −0.903631 + 0.265330i −0.0410317 + 0.0120480i
\(486\) 0 0
\(487\) 6.22412 + 43.2897i 0.282042 + 1.96164i 0.274197 + 0.961674i \(0.411588\pi\)
0.00784481 + 0.999969i \(0.497503\pi\)
\(488\) 0 0
\(489\) 4.89586 + 10.7204i 0.221399 + 0.484795i
\(490\) 0 0
\(491\) 11.3020 24.7478i 0.510050 1.11685i −0.463020 0.886348i \(-0.653234\pi\)
0.973071 0.230507i \(-0.0740385\pi\)
\(492\) 0 0
\(493\) −1.85417 + 12.8961i −0.0835078 + 0.580809i
\(494\) 0 0
\(495\) −1.73099 + 12.0393i −0.0778024 + 0.541127i
\(496\) 0 0
\(497\) 9.05455 + 5.81901i 0.406152 + 0.261018i
\(498\) 0 0
\(499\) 14.7062 0.658339 0.329169 0.944271i \(-0.393231\pi\)
0.329169 + 0.944271i \(0.393231\pi\)
\(500\) 0 0
\(501\) 4.61937 10.1150i 0.206378 0.451906i
\(502\) 0 0
\(503\) −20.5152 23.6758i −0.914729 1.05565i −0.998249 0.0591472i \(-0.981162\pi\)
0.0835205 0.996506i \(-0.473384\pi\)
\(504\) 0 0
\(505\) 23.7900 + 15.2889i 1.05864 + 0.680347i
\(506\) 0 0
\(507\) −12.0836 −0.536651
\(508\) 0 0
\(509\) 7.30156 + 2.14393i 0.323636 + 0.0950281i 0.439515 0.898235i \(-0.355150\pi\)
−0.115879 + 0.993263i \(0.536968\pi\)
\(510\) 0 0
\(511\) 11.0392 7.09446i 0.488345 0.313841i
\(512\) 0 0
\(513\) 3.00402 + 6.57788i 0.132631 + 0.290421i
\(514\) 0 0
\(515\) 19.9632 + 5.86174i 0.879686 + 0.258299i
\(516\) 0 0
\(517\) −55.8824 64.4917i −2.45771 2.83634i
\(518\) 0 0
\(519\) −0.225811 + 1.57055i −0.00991198 + 0.0689394i
\(520\) 0 0
\(521\) 14.5179 + 16.7546i 0.636041 + 0.734031i 0.978670 0.205440i \(-0.0658627\pi\)
−0.342628 + 0.939471i \(0.611317\pi\)
\(522\) 0 0
\(523\) −20.0776 + 12.9031i −0.877931 + 0.564212i −0.900169 0.435541i \(-0.856557\pi\)
0.0222380 + 0.999753i \(0.492921\pi\)
\(524\) 0 0
\(525\) 1.62858 0.478196i 0.0710773 0.0208702i
\(526\) 0 0
\(527\) 7.29209 8.41552i 0.317648 0.366586i
\(528\) 0 0
\(529\) −2.30762 + 2.66313i −0.100331 + 0.115788i
\(530\) 0 0
\(531\) 1.28779 0.378129i 0.0558853 0.0164094i
\(532\) 0 0
\(533\) −13.6933 29.9842i −0.593124 1.29876i
\(534\) 0 0
\(535\) 18.5826 0.803395
\(536\) 0 0
\(537\) 1.16251 0.0501660
\(538\) 0 0
\(539\) −15.9186 34.8569i −0.685663 1.50139i
\(540\) 0 0
\(541\) 25.8313 7.58477i 1.11058 0.326095i 0.325530 0.945532i \(-0.394457\pi\)
0.785046 + 0.619437i \(0.212639\pi\)
\(542\) 0 0
\(543\) 12.5030 14.4293i 0.536557 0.619220i
\(544\) 0 0
\(545\) −6.65063 + 7.67523i −0.284882 + 0.328771i
\(546\) 0 0
\(547\) −12.6118 + 3.70316i −0.539242 + 0.158336i −0.540002 0.841664i \(-0.681576\pi\)
0.000759759 1.00000i \(0.499758\pi\)
\(548\) 0 0
\(549\) −0.178240 + 0.114548i −0.00760708 + 0.00488877i
\(550\) 0 0
\(551\) 16.8604 + 19.4580i 0.718279 + 0.828938i
\(552\) 0 0
\(553\) 0.0486471 0.338348i 0.00206869 0.0143880i
\(554\) 0 0
\(555\) −7.17397 8.27920i −0.304518 0.351433i
\(556\) 0 0
\(557\) −24.8846 7.30677i −1.05439 0.309598i −0.291802 0.956479i \(-0.594255\pi\)
−0.762591 + 0.646881i \(0.776073\pi\)
\(558\) 0 0
\(559\) 17.1747 + 37.6074i 0.726414 + 1.59062i
\(560\) 0 0
\(561\) −20.2219 + 12.9958i −0.853771 + 0.548685i
\(562\) 0 0
\(563\) 18.0781 + 5.30821i 0.761901 + 0.223714i 0.639526 0.768770i \(-0.279131\pi\)
0.122375 + 0.992484i \(0.460949\pi\)
\(564\) 0 0
\(565\) −0.878966 −0.0369784
\(566\) 0 0
\(567\) −0.908600 0.583922i −0.0381576 0.0245224i
\(568\) 0 0
\(569\) −6.21332 7.17055i −0.260476 0.300605i 0.610415 0.792082i \(-0.291003\pi\)
−0.870891 + 0.491477i \(0.836457\pi\)
\(570\) 0 0
\(571\) 17.7351 38.8346i 0.742193 1.62518i −0.0377207 0.999288i \(-0.512010\pi\)
0.779914 0.625887i \(-0.215263\pi\)
\(572\) 0 0
\(573\) 11.6802 0.487947
\(574\) 0 0
\(575\) −6.80875 4.37572i −0.283945 0.182480i
\(576\) 0 0
\(577\) −4.10699 + 28.5647i −0.170976 + 1.18916i 0.705852 + 0.708360i \(0.250565\pi\)
−0.876828 + 0.480805i \(0.840345\pi\)
\(578\) 0 0
\(579\) −3.02801 + 21.0603i −0.125840 + 0.875234i
\(580\) 0 0
\(581\) 2.18650 4.78777i 0.0907113 0.198630i
\(582\) 0 0
\(583\) 3.98492 + 8.72575i 0.165038 + 0.361384i
\(584\) 0 0
\(585\) −1.31976 9.17914i −0.0545654 0.379511i
\(586\) 0 0
\(587\) 0.103554 0.0304062i 0.00427413 0.00125500i −0.279595 0.960118i \(-0.590200\pi\)
0.283869 + 0.958863i \(0.408382\pi\)
\(588\) 0 0
\(589\) −3.13165 21.7811i −0.129037 0.897474i
\(590\) 0 0
\(591\) 8.41000 5.40478i 0.345941 0.222323i
\(592\) 0 0
\(593\) −5.75662 + 12.6052i −0.236396 + 0.517635i −0.990232 0.139427i \(-0.955474\pi\)
0.753836 + 0.657062i \(0.228201\pi\)
\(594\) 0 0
\(595\) −6.15636 3.95645i −0.252386 0.162199i
\(596\) 0 0
\(597\) 10.6099 + 3.11533i 0.434232 + 0.127502i
\(598\) 0 0
\(599\) 2.65164 + 18.4426i 0.108343 + 0.753543i 0.969480 + 0.245170i \(0.0788438\pi\)
−0.861137 + 0.508373i \(0.830247\pi\)
\(600\) 0 0
\(601\) 14.5061 16.7409i 0.591715 0.682875i −0.378366 0.925656i \(-0.623514\pi\)
0.970081 + 0.242781i \(0.0780595\pi\)
\(602\) 0 0
\(603\) 3.96092 7.16318i 0.161301 0.291707i
\(604\) 0 0
\(605\) −38.9845 + 44.9906i −1.58495 + 1.82913i
\(606\) 0 0
\(607\) −6.12585 42.6062i −0.248641 1.72933i −0.606085 0.795400i \(-0.707261\pi\)
0.357445 0.933934i \(-0.383648\pi\)
\(608\) 0 0
\(609\) −3.68967 1.08338i −0.149513 0.0439009i
\(610\) 0 0
\(611\) 54.7335 + 35.1751i 2.21428 + 1.42303i
\(612\) 0 0
\(613\) 5.59468 12.2506i 0.225967 0.494799i −0.762359 0.647155i \(-0.775959\pi\)
0.988326 + 0.152356i \(0.0486861\pi\)
\(614\) 0 0
\(615\) 10.2520 6.58857i 0.413401 0.265677i
\(616\) 0 0
\(617\) 0.546163 + 3.79865i 0.0219877 + 0.152928i 0.997857 0.0654256i \(-0.0208405\pi\)
−0.975870 + 0.218354i \(0.929931\pi\)
\(618\) 0 0
\(619\) −13.1539 + 3.86232i −0.528699 + 0.155240i −0.535178 0.844739i \(-0.679756\pi\)
0.00647978 + 0.999979i \(0.497937\pi\)
\(620\) 0 0
\(621\) 0.732940 + 5.09771i 0.0294119 + 0.204564i
\(622\) 0 0
\(623\) 3.14781 + 6.89275i 0.126115 + 0.276152i
\(624\) 0 0
\(625\) −6.09524 + 13.3467i −0.243809 + 0.533868i
\(626\) 0 0
\(627\) −6.76029 + 47.0189i −0.269980 + 1.87775i
\(628\) 0 0
\(629\) 3.08114 21.4298i 0.122853 0.854462i
\(630\) 0 0
\(631\) −14.3046 9.19299i −0.569456 0.365967i 0.224005 0.974588i \(-0.428087\pi\)
−0.793461 + 0.608621i \(0.791723\pi\)
\(632\) 0 0
\(633\) −22.0773 −0.877492
\(634\) 0 0
\(635\) 3.02464 6.62304i 0.120029 0.262827i
\(636\) 0 0
\(637\) 19.1325 + 22.0801i 0.758057 + 0.874844i
\(638\) 0 0
\(639\) −8.38342 5.38769i −0.331643 0.213134i
\(640\) 0 0
\(641\) 4.66303 0.184179 0.0920893 0.995751i \(-0.470645\pi\)
0.0920893 + 0.995751i \(0.470645\pi\)
\(642\) 0 0
\(643\) 22.7653 + 6.68450i 0.897776 + 0.263611i 0.697887 0.716208i \(-0.254124\pi\)
0.199889 + 0.979819i \(0.435942\pi\)
\(644\) 0 0
\(645\) −12.8585 + 8.26365i −0.506302 + 0.325381i
\(646\) 0 0
\(647\) −1.66057 3.63614i −0.0652837 0.142951i 0.874178 0.485606i \(-0.161401\pi\)
−0.939461 + 0.342655i \(0.888674\pi\)
\(648\) 0 0
\(649\) 8.45941 + 2.48391i 0.332061 + 0.0975019i
\(650\) 0 0
\(651\) 2.15227 + 2.48385i 0.0843542 + 0.0973499i
\(652\) 0 0
\(653\) 1.02272 7.11316i 0.0400220 0.278359i −0.959976 0.280081i \(-0.909639\pi\)
0.999999 + 0.00172121i \(0.000547878\pi\)
\(654\) 0 0
\(655\) 25.3242 + 29.2257i 0.989499 + 1.14194i
\(656\) 0 0
\(657\) −10.2210 + 6.56861i −0.398758 + 0.256266i
\(658\) 0 0
\(659\) −9.59738 + 2.81805i −0.373861 + 0.109775i −0.463265 0.886220i \(-0.653322\pi\)
0.0894037 + 0.995995i \(0.471504\pi\)
\(660\) 0 0
\(661\) 2.11853 2.44492i 0.0824013 0.0950962i −0.713052 0.701111i \(-0.752688\pi\)
0.795453 + 0.606015i \(0.207233\pi\)
\(662\) 0 0
\(663\) 12.0018 13.8508i 0.466109 0.537919i
\(664\) 0 0
\(665\) −13.8758 + 4.07431i −0.538081 + 0.157995i
\(666\) 0 0
\(667\) 7.61728 + 16.6795i 0.294942 + 0.645833i
\(668\) 0 0
\(669\) −23.1638 −0.895566
\(670\) 0 0
\(671\) −1.39178 −0.0537292
\(672\) 0 0
\(673\) −18.7166 40.9837i −0.721473 1.57981i −0.811829 0.583896i \(-0.801528\pi\)
0.0903556 0.995910i \(-0.471200\pi\)
\(674\) 0 0
\(675\) −1.50787 + 0.442751i −0.0580380 + 0.0170415i
\(676\) 0 0
\(677\) 2.44945 2.82681i 0.0941399 0.108643i −0.706725 0.707489i \(-0.749828\pi\)
0.800865 + 0.598845i \(0.204374\pi\)
\(678\) 0 0
\(679\) 0.359744 0.415167i 0.0138057 0.0159326i
\(680\) 0 0
\(681\) −23.6971 + 6.95808i −0.908073 + 0.266634i
\(682\) 0 0
\(683\) 14.3418 9.21694i 0.548775 0.352676i −0.236687 0.971586i \(-0.576062\pi\)
0.785462 + 0.618910i \(0.212425\pi\)
\(684\) 0 0
\(685\) −9.59121 11.0688i −0.366461 0.422919i
\(686\) 0 0
\(687\) 2.01564 14.0191i 0.0769016 0.534863i
\(688\) 0 0
\(689\) −4.78946 5.52733i −0.182464 0.210574i
\(690\) 0 0
\(691\) −29.6452 8.70462i −1.12776 0.331139i −0.335932 0.941886i \(-0.609051\pi\)
−0.791826 + 0.610747i \(0.790869\pi\)
\(692\) 0 0
\(693\) −2.94729 6.45367i −0.111958 0.245155i
\(694\) 0 0
\(695\) 34.0940 21.9109i 1.29326 0.831126i
\(696\) 0 0
\(697\) 23.1087 + 6.78532i 0.875303 + 0.257012i
\(698\) 0 0
\(699\) −24.6832 −0.933606
\(700\) 0 0
\(701\) −11.7482 7.55013i −0.443725 0.285164i 0.299638 0.954053i \(-0.403134\pi\)
−0.743363 + 0.668888i \(0.766770\pi\)
\(702\) 0 0
\(703\) −28.0175 32.3340i −1.05670 1.21950i
\(704\) 0 0
\(705\) −9.99226 + 21.8800i −0.376330 + 0.824048i
\(706\) 0 0
\(707\) −16.4954 −0.620374
\(708\) 0 0
\(709\) 11.9925 + 7.70714i 0.450389 + 0.289448i 0.746105 0.665828i \(-0.231922\pi\)
−0.295716 + 0.955276i \(0.595558\pi\)
\(710\) 0 0
\(711\) −0.0450413 + 0.313269i −0.00168918 + 0.0117485i
\(712\) 0 0
\(713\) 2.23034 15.5123i 0.0835268 0.580942i
\(714\) 0 0
\(715\) 25.3059 55.4123i 0.946388 2.07230i
\(716\) 0 0
\(717\) −9.22310 20.1958i −0.344443 0.754225i
\(718\) 0 0
\(719\) −6.47060 45.0040i −0.241313 1.67837i −0.645555 0.763714i \(-0.723374\pi\)
0.404243 0.914652i \(-0.367535\pi\)
\(720\) 0 0
\(721\) −11.6447 + 3.41918i −0.433670 + 0.127337i
\(722\) 0 0
\(723\) −3.26380 22.7003i −0.121382 0.844232i
\(724\) 0 0
\(725\) −4.70705 + 3.02504i −0.174816 + 0.112347i
\(726\) 0 0
\(727\) 3.47740 7.61444i 0.128970 0.282404i −0.834121 0.551581i \(-0.814025\pi\)
0.963091 + 0.269178i \(0.0867518\pi\)
\(728\) 0 0
\(729\) 0.841254 + 0.540641i 0.0311575 + 0.0200237i
\(730\) 0 0
\(731\) −28.9838 8.51041i −1.07200 0.314769i
\(732\) 0 0
\(733\) −2.43843 16.9596i −0.0900653 0.626418i −0.983993 0.178207i \(-0.942970\pi\)
0.893928 0.448211i \(-0.147939\pi\)
\(734\) 0 0
\(735\) −7.07338 + 8.16311i −0.260906 + 0.301101i
\(736\) 0 0
\(737\) 47.3281 25.5178i 1.74335 0.939960i
\(738\) 0 0
\(739\) 14.6066 16.8569i 0.537313 0.620092i −0.420567 0.907261i \(-0.638169\pi\)
0.957880 + 0.287169i \(0.0927143\pi\)
\(740\) 0 0
\(741\) −5.15425 35.8486i −0.189346 1.31693i
\(742\) 0 0
\(743\) −17.9183 5.26128i −0.657358 0.193018i −0.0639919 0.997950i \(-0.520383\pi\)
−0.593366 + 0.804933i \(0.702201\pi\)
\(744\) 0 0
\(745\) 17.7570 + 11.4118i 0.650568 + 0.418095i
\(746\) 0 0
\(747\) −2.02443 + 4.43289i −0.0740702 + 0.162191i
\(748\) 0 0
\(749\) −9.11861 + 5.86018i −0.333187 + 0.214126i
\(750\) 0 0
\(751\) 3.63994 + 25.3163i 0.132823 + 0.923807i 0.941850 + 0.336034i \(0.109086\pi\)
−0.809026 + 0.587772i \(0.800005\pi\)
\(752\) 0 0
\(753\) 25.1022 7.37066i 0.914773 0.268602i
\(754\) 0 0
\(755\) −1.50138 10.4424i −0.0546410 0.380036i
\(756\) 0 0
\(757\) 20.4627 + 44.8072i 0.743731 + 1.62854i 0.777318 + 0.629108i \(0.216580\pi\)
−0.0335870 + 0.999436i \(0.510693\pi\)
\(758\) 0 0
\(759\) −14.0538 + 30.7736i −0.510122 + 1.11701i
\(760\) 0 0
\(761\) 4.47973 31.1572i 0.162390 1.12945i −0.731721 0.681604i \(-0.761283\pi\)
0.894111 0.447845i \(-0.147808\pi\)
\(762\) 0 0
\(763\) 0.843062 5.86363i 0.0305209 0.212278i
\(764\) 0 0
\(765\) 5.70004 + 3.66319i 0.206085 + 0.132443i
\(766\) 0 0
\(767\) −6.72200 −0.242717
\(768\) 0 0
\(769\) −17.6486 + 38.6450i −0.636424 + 1.39357i 0.266526 + 0.963828i \(0.414124\pi\)
−0.902950 + 0.429746i \(0.858603\pi\)
\(770\) 0 0
\(771\) 5.30658 + 6.12413i 0.191112 + 0.220555i
\(772\) 0 0
\(773\) 9.10646 + 5.85237i 0.327537 + 0.210495i 0.694066 0.719912i \(-0.255818\pi\)
−0.366529 + 0.930407i \(0.619454\pi\)
\(774\) 0 0
\(775\) 4.78217 0.171781
\(776\) 0 0
\(777\) 6.13124 + 1.80029i 0.219957 + 0.0645852i
\(778\) 0 0
\(779\) 40.0387 25.7313i 1.43453 0.921919i
\(780\) 0 0
\(781\) −27.1939 59.5463i −0.973074 2.13073i
\(782\) 0 0
\(783\) 3.41618 + 1.00308i 0.122084 + 0.0358472i
\(784\) 0 0
\(785\) −3.74632 4.32349i −0.133712 0.154312i
\(786\) 0 0
\(787\) 7.51309 52.2547i 0.267813 1.86268i −0.201284 0.979533i \(-0.564512\pi\)
0.469097 0.883147i \(-0.344579\pi\)
\(788\) 0 0
\(789\) −2.04967 2.36545i −0.0729703 0.0842122i
\(790\) 0 0
\(791\) 0.431315 0.277189i 0.0153358 0.00985572i
\(792\) 0 0
\(793\) 1.01815 0.298957i 0.0361557 0.0106163i
\(794\) 0 0
\(795\) 1.77069 2.04348i 0.0627997 0.0724748i
\(796\) 0 0
\(797\) 6.64013 7.66312i 0.235206 0.271442i −0.625860 0.779935i \(-0.715252\pi\)
0.861066 + 0.508494i \(0.169797\pi\)
\(798\) 0 0
\(799\) −45.6114 + 13.3927i −1.61362 + 0.473801i
\(800\) 0 0
\(801\) −2.91449 6.38185i −0.102979 0.225492i
\(802\) 0 0
\(803\) −79.8104 −2.81645
\(804\) 0 0
\(805\) −10.2995 −0.363008
\(806\) 0 0
\(807\) 1.86983 + 4.09436i 0.0658213 + 0.144128i
\(808\) 0 0
\(809\) 39.4325 11.5784i 1.38637 0.407076i 0.498390 0.866953i \(-0.333925\pi\)
0.887982 + 0.459878i \(0.152107\pi\)
\(810\) 0 0
\(811\) 13.0681 15.0814i 0.458883 0.529579i −0.478403 0.878140i \(-0.658784\pi\)
0.937286 + 0.348561i \(0.113330\pi\)
\(812\) 0 0
\(813\) 5.73248 6.61564i 0.201047 0.232021i
\(814\) 0 0
\(815\) 20.9382 6.14801i 0.733433 0.215355i
\(816\) 0 0
\(817\) −50.2181 + 32.2732i −1.75691 + 1.12910i
\(818\) 0 0
\(819\) 3.54234 + 4.08807i 0.123779 + 0.142849i
\(820\) 0 0
\(821\) 3.92406 27.2925i 0.136951 0.952514i −0.799238 0.601015i \(-0.794763\pi\)
0.936188 0.351499i \(-0.114328\pi\)
\(822\) 0 0
\(823\) −29.7634 34.3488i −1.03749 1.19732i −0.980004 0.198977i \(-0.936238\pi\)
−0.0574825 0.998347i \(-0.518307\pi\)
\(824\) 0 0
\(825\) −9.90511 2.90840i −0.344852 0.101258i
\(826\) 0 0
\(827\) 8.49965 + 18.6116i 0.295562 + 0.647190i 0.997908 0.0646453i \(-0.0205916\pi\)
−0.702347 + 0.711835i \(0.747864\pi\)
\(828\) 0 0
\(829\) 0.0338705 0.0217672i 0.00117637 0.000756008i −0.540052 0.841631i \(-0.681596\pi\)
0.541229 + 0.840875i \(0.317959\pi\)
\(830\) 0 0
\(831\) 23.2687 + 6.83231i 0.807182 + 0.237010i
\(832\) 0 0
\(833\) −21.3466 −0.739616
\(834\) 0 0
\(835\) −17.3212 11.1317i −0.599425 0.385227i
\(836\) 0 0
\(837\) −1.99274 2.29975i −0.0688793 0.0794909i
\(838\) 0 0
\(839\) −19.7584 + 43.2649i −0.682136 + 1.49367i 0.178228 + 0.983989i \(0.442964\pi\)
−0.860364 + 0.509680i \(0.829764\pi\)
\(840\) 0 0
\(841\) −16.3235 −0.562880
\(842\) 0 0
\(843\) 3.01093 + 1.93501i 0.103702 + 0.0666453i
\(844\) 0 0
\(845\) −3.18417 + 22.1464i −0.109539 + 0.761859i
\(846\) 0 0
\(847\) 4.94185 34.3713i 0.169804 1.18101i
\(848\) 0 0
\(849\) 1.22191 2.67561i 0.0419359 0.0918268i
\(850\) 0 0
\(851\) −12.6579 27.7169i −0.433906 0.950123i
\(852\) 0 0
\(853\) 5.37939 + 37.4145i 0.184187 + 1.28105i 0.846730 + 0.532023i \(0.178568\pi\)
−0.662543 + 0.749024i \(0.730523\pi\)
\(854\) 0 0
\(855\) 12.8473 3.77231i 0.439369 0.129010i
\(856\) 0 0
\(857\) 0.327965 + 2.28105i 0.0112031 + 0.0779192i 0.994656 0.103245i \(-0.0329226\pi\)
−0.983453 + 0.181164i \(0.942013\pi\)
\(858\) 0 0
\(859\) 16.9128 10.8692i 0.577058 0.370853i −0.219319 0.975653i \(-0.570383\pi\)
0.796377 + 0.604800i \(0.206747\pi\)
\(860\) 0 0
\(861\) −2.95298 + 6.46612i −0.100637 + 0.220365i
\(862\) 0 0
\(863\) −7.82017 5.02572i −0.266202 0.171077i 0.400730 0.916196i \(-0.368756\pi\)
−0.666932 + 0.745119i \(0.732393\pi\)
\(864\) 0 0
\(865\) 2.81894 + 0.827716i 0.0958469 + 0.0281432i
\(866\) 0 0
\(867\) −0.513664 3.57261i −0.0174449 0.121332i
\(868\) 0 0
\(869\) −1.36146 + 1.57121i −0.0461844 + 0.0532996i
\(870\) 0 0
\(871\) −29.1415 + 28.8336i −0.987421 + 0.976989i
\(872\) 0 0
\(873\) −0.333079 + 0.384394i −0.0112730 + 0.0130098i
\(874\) 0 0
\(875\) −1.87031 13.0083i −0.0632279 0.439760i
\(876\) 0 0
\(877\) −5.52715 1.62292i −0.186639 0.0548021i 0.187078 0.982345i \(-0.440098\pi\)
−0.373716 + 0.927543i \(0.621917\pi\)
\(878\) 0 0
\(879\) 12.4449 + 7.99786i 0.419757 + 0.269761i
\(880\) 0 0
\(881\) −0.590178 + 1.29231i −0.0198836 + 0.0435390i −0.919313 0.393527i \(-0.871255\pi\)
0.899430 + 0.437066i \(0.143982\pi\)
\(882\) 0 0
\(883\) −14.8798 + 9.56264i −0.500744 + 0.321809i −0.766514 0.642228i \(-0.778010\pi\)
0.265770 + 0.964037i \(0.414374\pi\)
\(884\) 0 0
\(885\) −0.353675 2.45986i −0.0118886 0.0826873i
\(886\) 0 0
\(887\) −3.97071 + 1.16591i −0.133323 + 0.0391473i −0.347713 0.937601i \(-0.613042\pi\)
0.214390 + 0.976748i \(0.431224\pi\)
\(888\) 0 0
\(889\) 0.604418 + 4.20382i 0.0202715 + 0.140992i
\(890\) 0 0
\(891\) 2.72883 + 5.97531i 0.0914194 + 0.200181i
\(892\) 0 0
\(893\) −39.0242 + 85.4510i −1.30589 + 2.85951i
\(894\) 0 0
\(895\) 0.306335 2.13061i 0.0102397 0.0712184i
\(896\) 0 0
\(897\) 3.67082 25.5311i 0.122565 0.852459i
\(898\) 0 0
\(899\) −9.11441 5.85748i −0.303983 0.195358i
\(900\) 0 0
\(901\) 5.34371 0.178025
\(902\) 0 0
\(903\) 3.70374 8.11007i 0.123253 0.269886i
\(904\) 0 0
\(905\) −23.1508 26.7174i −0.769558 0.888118i
\(906\) 0 0
\(907\) 35.5736 + 22.8618i 1.18120 + 0.759112i 0.975607 0.219525i \(-0.0704509\pi\)
0.205594 + 0.978637i \(0.434087\pi\)
\(908\) 0 0
\(909\) 15.2728 0.506565
\(910\) 0 0
\(911\) 54.1763 + 15.9076i 1.79494 + 0.527042i 0.997119 0.0758513i \(-0.0241674\pi\)
0.797822 + 0.602893i \(0.205986\pi\)
\(912\) 0 0
\(913\) −26.9304 + 17.3071i −0.891267 + 0.572783i
\(914\) 0 0
\(915\) 0.162971 + 0.356856i 0.00538764 + 0.0117973i
\(916\) 0 0
\(917\) −21.6434 6.35506i −0.714727 0.209863i
\(918\) 0 0
\(919\) 18.2992 + 21.1184i 0.603634 + 0.696631i 0.972514 0.232846i \(-0.0748039\pi\)
−0.368879 + 0.929477i \(0.620258\pi\)
\(920\) 0 0
\(921\) 4.67684 32.5282i 0.154107 1.07184i
\(922\) 0 0
\(923\) 32.6842 + 37.7196i 1.07581 + 1.24156i
\(924\) 0 0
\(925\) 7.82186 5.02680i 0.257181 0.165280i
\(926\) 0 0
\(927\) 10.7815 3.16575i 0.354112 0.103977i
\(928\) 0 0
\(929\) −28.2651 + 32.6197i −0.927349 + 1.07022i 0.0700071 + 0.997546i \(0.477698\pi\)
−0.997356 + 0.0726712i \(0.976848\pi\)
\(930\) 0 0
\(931\) −27.6247 + 31.8806i −0.905362 + 1.04484i
\(932\) 0 0
\(933\) 25.0453 7.35397i 0.819947 0.240758i
\(934\) 0 0
\(935\) 18.4896 + 40.4866i 0.604676 + 1.32405i
\(936\) 0 0
\(937\) −14.6366 −0.478158 −0.239079 0.971000i \(-0.576845\pi\)
−0.239079 + 0.971000i \(0.576845\pi\)
\(938\) 0 0
\(939\) −14.4646 −0.472035
\(940\) 0 0
\(941\) −14.1670 31.0215i −0.461832 1.01127i −0.987066 0.160313i \(-0.948750\pi\)
0.525234 0.850958i \(-0.323978\pi\)
\(942\) 0 0
\(943\) 32.5231 9.54965i 1.05910 0.310979i
\(944\) 0 0
\(945\) −1.30962 + 1.51138i −0.0426019 + 0.0491652i
\(946\) 0 0
\(947\) 16.1148 18.5974i 0.523659 0.604335i −0.430884 0.902407i \(-0.641798\pi\)
0.954543 + 0.298072i \(0.0963437\pi\)
\(948\) 0 0
\(949\) 58.3850 17.1434i 1.89526 0.556498i
\(950\) 0 0
\(951\) −4.82864 + 3.10318i −0.156579 + 0.100627i
\(952\) 0 0
\(953\) −9.77269 11.2783i −0.316568 0.365339i 0.575057 0.818113i \(-0.304980\pi\)
−0.891625 + 0.452774i \(0.850434\pi\)
\(954\) 0 0
\(955\) 3.07787 21.4070i 0.0995975 0.692716i
\(956\) 0 0
\(957\) 15.3159 + 17.6755i 0.495094 + 0.571369i
\(958\) 0 0
\(959\) 8.19713 + 2.40689i 0.264699 + 0.0777227i
\(960\) 0 0
\(961\) −9.03118 19.7755i −0.291328 0.637920i
\(962\) 0 0
\(963\) 8.44273 5.42581i 0.272063 0.174844i
\(964\) 0 0
\(965\) 37.8006 + 11.0993i 1.21684 + 0.357298i
\(966\) 0 0
\(967\) 35.3257 1.13600 0.567999 0.823029i \(-0.307718\pi\)
0.567999 + 0.823029i \(0.307718\pi\)
\(968\) 0 0
\(969\) 22.2612 + 14.3064i 0.715132 + 0.459587i
\(970\) 0 0
\(971\) −10.0936 11.6487i −0.323920 0.373823i 0.570312 0.821428i \(-0.306822\pi\)
−0.894231 + 0.447605i \(0.852277\pi\)
\(972\) 0 0
\(973\) −9.82038 + 21.5036i −0.314827 + 0.689375i
\(974\) 0 0
\(975\) 7.87077 0.252067
\(976\) 0 0
\(977\) 1.10686 + 0.711337i 0.0354117 + 0.0227577i 0.558227 0.829688i \(-0.311482\pi\)
−0.522815 + 0.852446i \(0.675118\pi\)
\(978\) 0 0
\(979\) 6.55883 45.6176i 0.209621 1.45795i
\(980\) 0 0
\(981\) −0.780573 + 5.42901i −0.0249218 + 0.173335i
\(982\) 0 0
\(983\) −13.6681 + 29.9291i −0.435946 + 0.954589i 0.556379 + 0.830929i \(0.312190\pi\)
−0.992325 + 0.123660i \(0.960537\pi\)
\(984\) 0 0
\(985\) −7.68956 16.8378i −0.245010 0.536497i
\(986\) 0 0
\(987\) −1.99677 13.8878i −0.0635578 0.442054i
\(988\) 0 0
\(989\) −40.7918 + 11.9776i −1.29710 + 0.380864i
\(990\) 0 0
\(991\) −6.18705 43.0319i −0.196538 1.36695i −0.814234 0.580537i \(-0.802843\pi\)
0.617696 0.786417i \(-0.288066\pi\)
\(992\) 0 0
\(993\) −10.9911 + 7.06354i −0.348791 + 0.224155i
\(994\) 0 0
\(995\) 8.50550 18.6244i 0.269642 0.590435i
\(996\) 0 0
\(997\) 33.8242 + 21.7375i 1.07122 + 0.688434i 0.952514 0.304495i \(-0.0984876\pi\)
0.118710 + 0.992929i \(0.462124\pi\)
\(998\) 0 0
\(999\) −5.67678 1.66685i −0.179605 0.0527369i
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 804.2.q.b.397.2 yes 60
67.40 even 11 inner 804.2.q.b.241.2 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.q.b.241.2 60 67.40 even 11 inner
804.2.q.b.397.2 yes 60 1.1 even 1 trivial