Properties

Label 804.2.s.b.161.8
Level $804$
Weight $2$
Character 804.161
Analytic conductor $6.420$
Analytic rank $0$
Dimension $200$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(5,804)]
 
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, 11, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.s (of order \(22\), 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: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 161.8
Character \(\chi\) \(=\) 804.161
Dual form 804.2.s.b.5.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.786808 + 1.54303i) q^{3} +(0.966140 + 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-1.76187 - 2.42813i) q^{9} +O(q^{10})\) \(q+(-0.786808 + 1.54303i) q^{3} +(0.966140 + 0.283684i) q^{5} +(1.54930 - 1.34247i) q^{7} +(-1.76187 - 2.42813i) q^{9} +(2.68695 + 0.788959i) q^{11} +(0.303154 - 0.471717i) q^{13} +(-1.19790 + 1.26757i) q^{15} +(2.99315 - 0.430350i) q^{17} +(3.48728 - 4.02453i) q^{19} +(0.852473 + 3.44688i) q^{21} +(1.38260 + 0.631411i) q^{23} +(-3.35332 - 2.15505i) q^{25} +(5.13293 - 0.808130i) q^{27} +1.01679i q^{29} +(1.77218 + 2.75757i) q^{31} +(-3.33150 + 3.52527i) q^{33} +(1.87767 - 0.857505i) q^{35} +0.414150 q^{37} +(0.489348 + 0.838926i) q^{39} +(0.649850 + 4.51980i) q^{41} +(0.863281 - 0.124121i) q^{43} +(-1.01338 - 2.84573i) q^{45} +(1.67750 + 0.766089i) q^{47} +(-0.398118 + 2.76897i) q^{49} +(-1.69099 + 4.95712i) q^{51} +(-1.21708 + 8.46498i) q^{53} +(2.37215 + 1.52449i) q^{55} +(3.46614 + 8.54750i) q^{57} +(1.75024 + 2.72343i) q^{59} +(-0.230536 - 0.785133i) q^{61} +(-5.98935 - 1.39664i) q^{63} +(0.426708 - 0.369744i) q^{65} +(8.16532 + 0.572263i) q^{67} +(-2.06212 + 1.63659i) q^{69} +(2.98320 + 0.428919i) q^{71} +(-3.06133 + 0.898887i) q^{73} +(5.96371 - 3.47865i) q^{75} +(5.22203 - 2.38482i) q^{77} +(0.0461512 - 0.0718126i) q^{79} +(-2.79166 + 8.55609i) q^{81} +(3.01301 - 10.2614i) q^{83} +(3.01389 + 0.433331i) q^{85} +(-1.56894 - 0.800022i) q^{87} +(-8.74397 + 3.99324i) q^{89} +(-0.163592 - 1.13781i) q^{91} +(-5.64937 + 0.564846i) q^{93} +(4.51089 - 2.89897i) q^{95} -3.47150i q^{97} +(-2.81834 - 7.91431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{17}{22}\right)\) \(1\)

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
\(3\) −0.786808 + 1.54303i −0.454264 + 0.890867i
\(4\) 0 0
\(5\) 0.966140 + 0.283684i 0.432071 + 0.126867i 0.490534 0.871422i \(-0.336802\pi\)
−0.0584631 + 0.998290i \(0.518620\pi\)
\(6\) 0 0
\(7\) 1.54930 1.34247i 0.585579 0.507407i −0.310930 0.950433i \(-0.600640\pi\)
0.896509 + 0.443026i \(0.146095\pi\)
\(8\) 0 0
\(9\) −1.76187 2.42813i −0.587288 0.809378i
\(10\) 0 0
\(11\) 2.68695 + 0.788959i 0.810145 + 0.237880i 0.660467 0.750855i \(-0.270358\pi\)
0.149678 + 0.988735i \(0.452176\pi\)
\(12\) 0 0
\(13\) 0.303154 0.471717i 0.0840798 0.130831i −0.796666 0.604419i \(-0.793405\pi\)
0.880746 + 0.473588i \(0.157042\pi\)
\(14\) 0 0
\(15\) −1.19790 + 1.26757i −0.309296 + 0.327286i
\(16\) 0 0
\(17\) 2.99315 0.430350i 0.725946 0.104375i 0.230572 0.973055i \(-0.425940\pi\)
0.495374 + 0.868680i \(0.335031\pi\)
\(18\) 0 0
\(19\) 3.48728 4.02453i 0.800036 0.923291i −0.198347 0.980132i \(-0.563557\pi\)
0.998383 + 0.0568410i \(0.0181028\pi\)
\(20\) 0 0
\(21\) 0.852473 + 3.44688i 0.186025 + 0.752170i
\(22\) 0 0
\(23\) 1.38260 + 0.631411i 0.288292 + 0.131658i 0.554312 0.832309i \(-0.312982\pi\)
−0.266020 + 0.963967i \(0.585709\pi\)
\(24\) 0 0
\(25\) −3.35332 2.15505i −0.670664 0.431009i
\(26\) 0 0
\(27\) 5.13293 0.808130i 0.987832 0.155525i
\(28\) 0 0
\(29\) 1.01679i 0.188814i 0.995534 + 0.0944069i \(0.0300955\pi\)
−0.995534 + 0.0944069i \(0.969905\pi\)
\(30\) 0 0
\(31\) 1.77218 + 2.75757i 0.318293 + 0.495274i 0.963126 0.269049i \(-0.0867095\pi\)
−0.644833 + 0.764323i \(0.723073\pi\)
\(32\) 0 0
\(33\) −3.33150 + 3.52527i −0.579939 + 0.613671i
\(34\) 0 0
\(35\) 1.87767 0.857505i 0.317385 0.144945i
\(36\) 0 0
\(37\) 0.414150 0.0680858 0.0340429 0.999420i \(-0.489162\pi\)
0.0340429 + 0.999420i \(0.489162\pi\)
\(38\) 0 0
\(39\) 0.489348 + 0.838926i 0.0783584 + 0.134336i
\(40\) 0 0
\(41\) 0.649850 + 4.51980i 0.101489 + 0.705875i 0.975505 + 0.219977i \(0.0705982\pi\)
−0.874016 + 0.485898i \(0.838493\pi\)
\(42\) 0 0
\(43\) 0.863281 0.124121i 0.131649 0.0189283i −0.0761752 0.997094i \(-0.524271\pi\)
0.207824 + 0.978166i \(0.433362\pi\)
\(44\) 0 0
\(45\) −1.01338 2.84573i −0.151066 0.424216i
\(46\) 0 0
\(47\) 1.67750 + 0.766089i 0.244689 + 0.111746i 0.533985 0.845494i \(-0.320694\pi\)
−0.289296 + 0.957240i \(0.593421\pi\)
\(48\) 0 0
\(49\) −0.398118 + 2.76897i −0.0568740 + 0.395568i
\(50\) 0 0
\(51\) −1.69099 + 4.95712i −0.236787 + 0.694135i
\(52\) 0 0
\(53\) −1.21708 + 8.46498i −0.167179 + 1.16275i 0.717502 + 0.696557i \(0.245285\pi\)
−0.884681 + 0.466197i \(0.845624\pi\)
\(54\) 0 0
\(55\) 2.37215 + 1.52449i 0.319861 + 0.205562i
\(56\) 0 0
\(57\) 3.46614 + 8.54750i 0.459102 + 1.13214i
\(58\) 0 0
\(59\) 1.75024 + 2.72343i 0.227862 + 0.354560i 0.936293 0.351220i \(-0.114233\pi\)
−0.708431 + 0.705780i \(0.750597\pi\)
\(60\) 0 0
\(61\) −0.230536 0.785133i −0.0295171 0.100526i 0.943417 0.331609i \(-0.107591\pi\)
−0.972934 + 0.231083i \(0.925773\pi\)
\(62\) 0 0
\(63\) −5.98935 1.39664i −0.754588 0.175960i
\(64\) 0 0
\(65\) 0.426708 0.369744i 0.0529266 0.0458612i
\(66\) 0 0
\(67\) 8.16532 + 0.572263i 0.997553 + 0.0699131i
\(68\) 0 0
\(69\) −2.06212 + 1.63659i −0.248251 + 0.197022i
\(70\) 0 0
\(71\) 2.98320 + 0.428919i 0.354040 + 0.0509033i 0.317041 0.948412i \(-0.397311\pi\)
0.0369996 + 0.999315i \(0.488220\pi\)
\(72\) 0 0
\(73\) −3.06133 + 0.898887i −0.358301 + 0.105207i −0.455929 0.890016i \(-0.650693\pi\)
0.0976275 + 0.995223i \(0.468875\pi\)
\(74\) 0 0
\(75\) 5.96371 3.47865i 0.688630 0.401680i
\(76\) 0 0
\(77\) 5.22203 2.38482i 0.595106 0.271776i
\(78\) 0 0
\(79\) 0.0461512 0.0718126i 0.00519241 0.00807955i −0.838648 0.544674i \(-0.816653\pi\)
0.843840 + 0.536595i \(0.180290\pi\)
\(80\) 0 0
\(81\) −2.79166 + 8.55609i −0.310185 + 0.950676i
\(82\) 0 0
\(83\) 3.01301 10.2614i 0.330720 1.12633i −0.611474 0.791264i \(-0.709423\pi\)
0.942195 0.335066i \(-0.108759\pi\)
\(84\) 0 0
\(85\) 3.01389 + 0.433331i 0.326902 + 0.0470014i
\(86\) 0 0
\(87\) −1.56894 0.800022i −0.168208 0.0857713i
\(88\) 0 0
\(89\) −8.74397 + 3.99324i −0.926859 + 0.423282i −0.820890 0.571087i \(-0.806522\pi\)
−0.105970 + 0.994369i \(0.533795\pi\)
\(90\) 0 0
\(91\) −0.163592 1.13781i −0.0171491 0.119274i
\(92\) 0 0
\(93\) −5.64937 + 0.564846i −0.585812 + 0.0585718i
\(94\) 0 0
\(95\) 4.51089 2.89897i 0.462808 0.297428i
\(96\) 0 0
\(97\) 3.47150i 0.352477i −0.984347 0.176239i \(-0.943607\pi\)
0.984347 0.176239i \(-0.0563930\pi\)
\(98\) 0 0
\(99\) −2.81834 7.91431i −0.283254 0.795418i
\(100\) 0 0
\(101\) −2.21410 + 2.55520i −0.220311 + 0.254252i −0.855136 0.518403i \(-0.826527\pi\)
0.634825 + 0.772656i \(0.281072\pi\)
\(102\) 0 0
\(103\) 8.21404 5.27884i 0.809354 0.520140i −0.0693021 0.997596i \(-0.522077\pi\)
0.878656 + 0.477456i \(0.158441\pi\)
\(104\) 0 0
\(105\) −0.154216 + 3.57200i −0.0150500 + 0.348591i
\(106\) 0 0
\(107\) −1.90540 6.48919i −0.184202 0.627334i −0.998875 0.0474140i \(-0.984902\pi\)
0.814673 0.579920i \(-0.196916\pi\)
\(108\) 0 0
\(109\) 7.92724 12.3350i 0.759292 1.18148i −0.219297 0.975658i \(-0.570376\pi\)
0.978589 0.205824i \(-0.0659873\pi\)
\(110\) 0 0
\(111\) −0.325856 + 0.639044i −0.0309289 + 0.0606554i
\(112\) 0 0
\(113\) −12.4656 + 3.66022i −1.17266 + 0.344324i −0.809340 0.587340i \(-0.800175\pi\)
−0.363321 + 0.931664i \(0.618357\pi\)
\(114\) 0 0
\(115\) 1.15666 + 1.00225i 0.107859 + 0.0934606i
\(116\) 0 0
\(117\) −1.67951 + 0.0950032i −0.155271 + 0.00878305i
\(118\) 0 0
\(119\) 4.05954 4.68496i 0.372138 0.429470i
\(120\) 0 0
\(121\) −2.65656 1.70727i −0.241505 0.155206i
\(122\) 0 0
\(123\) −7.48549 2.55348i −0.674944 0.230240i
\(124\) 0 0
\(125\) −5.92541 6.83828i −0.529985 0.611635i
\(126\) 0 0
\(127\) −1.39668 1.61186i −0.123936 0.143029i 0.690391 0.723437i \(-0.257439\pi\)
−0.814326 + 0.580408i \(0.802893\pi\)
\(128\) 0 0
\(129\) −0.487714 + 1.42973i −0.0429409 + 0.125880i
\(130\) 0 0
\(131\) −7.30624 3.33665i −0.638349 0.291524i 0.0698282 0.997559i \(-0.477755\pi\)
−0.708177 + 0.706035i \(0.750482\pi\)
\(132\) 0 0
\(133\) 10.9168i 0.946604i
\(134\) 0 0
\(135\) 5.18838 + 0.675363i 0.446544 + 0.0581260i
\(136\) 0 0
\(137\) −6.97149 + 15.2654i −0.595615 + 1.30421i 0.336375 + 0.941728i \(0.390799\pi\)
−0.931989 + 0.362486i \(0.881928\pi\)
\(138\) 0 0
\(139\) −2.28442 + 7.78001i −0.193762 + 0.659892i 0.804098 + 0.594497i \(0.202649\pi\)
−0.997859 + 0.0653948i \(0.979169\pi\)
\(140\) 0 0
\(141\) −2.50197 + 1.98566i −0.210704 + 0.167223i
\(142\) 0 0
\(143\) 1.18672 1.02830i 0.0992389 0.0859910i
\(144\) 0 0
\(145\) −0.288448 + 0.982365i −0.0239543 + 0.0815809i
\(146\) 0 0
\(147\) −3.95936 2.79296i −0.326562 0.230359i
\(148\) 0 0
\(149\) −16.1494 13.9935i −1.32301 1.14640i −0.978187 0.207729i \(-0.933393\pi\)
−0.344825 0.938667i \(-0.612062\pi\)
\(150\) 0 0
\(151\) 0.189990 + 1.32141i 0.0154611 + 0.107535i 0.996091 0.0883374i \(-0.0281554\pi\)
−0.980629 + 0.195872i \(0.937246\pi\)
\(152\) 0 0
\(153\) −6.31848 6.50955i −0.510819 0.526266i
\(154\) 0 0
\(155\) 0.929896 + 3.16694i 0.0746911 + 0.254374i
\(156\) 0 0
\(157\) 8.86174 19.4045i 0.707244 1.54865i −0.123718 0.992317i \(-0.539482\pi\)
0.830961 0.556330i \(-0.187791\pi\)
\(158\) 0 0
\(159\) −12.1041 8.53830i −0.959916 0.677131i
\(160\) 0 0
\(161\) 2.98971 0.877857i 0.235622 0.0691848i
\(162\) 0 0
\(163\) −1.47744 −0.115722 −0.0578608 0.998325i \(-0.518428\pi\)
−0.0578608 + 0.998325i \(0.518428\pi\)
\(164\) 0 0
\(165\) −4.21876 + 2.46081i −0.328430 + 0.191574i
\(166\) 0 0
\(167\) 1.89688 + 1.64366i 0.146785 + 0.127190i 0.725158 0.688582i \(-0.241767\pi\)
−0.578373 + 0.815773i \(0.696312\pi\)
\(168\) 0 0
\(169\) 5.26978 + 11.5392i 0.405368 + 0.887632i
\(170\) 0 0
\(171\) −15.9162 1.37689i −1.21714 0.105293i
\(172\) 0 0
\(173\) −6.75608 10.5127i −0.513655 0.799263i 0.483444 0.875375i \(-0.339386\pi\)
−0.997099 + 0.0761122i \(0.975749\pi\)
\(174\) 0 0
\(175\) −8.08838 + 1.16293i −0.611424 + 0.0879095i
\(176\) 0 0
\(177\) −5.57943 + 0.557853i −0.419376 + 0.0419308i
\(178\) 0 0
\(179\) −4.58992 10.0505i −0.343067 0.751212i 0.656929 0.753952i \(-0.271855\pi\)
−0.999996 + 0.00274020i \(0.999128\pi\)
\(180\) 0 0
\(181\) 0.387326 0.848125i 0.0287897 0.0630406i −0.894691 0.446686i \(-0.852604\pi\)
0.923481 + 0.383645i \(0.125331\pi\)
\(182\) 0 0
\(183\) 1.39287 + 0.262026i 0.102964 + 0.0193695i
\(184\) 0 0
\(185\) 0.400126 + 0.117488i 0.0294179 + 0.00863787i
\(186\) 0 0
\(187\) 8.38197 + 1.20515i 0.612950 + 0.0881289i
\(188\) 0 0
\(189\) 6.86753 8.14285i 0.499539 0.592305i
\(190\) 0 0
\(191\) 3.97243 + 8.69841i 0.287435 + 0.629395i 0.997179 0.0750653i \(-0.0239165\pi\)
−0.709744 + 0.704460i \(0.751189\pi\)
\(192\) 0 0
\(193\) 20.1470 12.9477i 1.45021 0.931994i 0.450990 0.892529i \(-0.351071\pi\)
0.999221 0.0394647i \(-0.0125653\pi\)
\(194\) 0 0
\(195\) 0.234788 + 0.949340i 0.0168135 + 0.0679836i
\(196\) 0 0
\(197\) −1.49850 + 10.4223i −0.106764 + 0.742560i 0.864168 + 0.503204i \(0.167845\pi\)
−0.970932 + 0.239356i \(0.923064\pi\)
\(198\) 0 0
\(199\) −7.29446 8.41826i −0.517091 0.596755i 0.435809 0.900039i \(-0.356462\pi\)
−0.952900 + 0.303284i \(0.901917\pi\)
\(200\) 0 0
\(201\) −7.30756 + 12.1491i −0.515436 + 0.856928i
\(202\) 0 0
\(203\) 1.36502 + 1.57531i 0.0958055 + 0.110565i
\(204\) 0 0
\(205\) −0.654351 + 4.55111i −0.0457019 + 0.317864i
\(206\) 0 0
\(207\) −0.902801 4.46959i −0.0627490 0.310658i
\(208\) 0 0
\(209\) 12.5453 8.06239i 0.867778 0.557687i
\(210\) 0 0
\(211\) 5.67188 + 12.4197i 0.390468 + 0.855006i 0.998148 + 0.0608245i \(0.0193730\pi\)
−0.607680 + 0.794182i \(0.707900\pi\)
\(212\) 0 0
\(213\) −3.00904 + 4.26568i −0.206176 + 0.292279i
\(214\) 0 0
\(215\) 0.869261 + 0.124981i 0.0592831 + 0.00852362i
\(216\) 0 0
\(217\) 6.44760 + 1.89319i 0.437691 + 0.128518i
\(218\) 0 0
\(219\) 1.02167 5.43096i 0.0690381 0.366990i
\(220\) 0 0
\(221\) 0.704383 1.54238i 0.0473819 0.103752i
\(222\) 0 0
\(223\) 2.86676 + 6.27733i 0.191973 + 0.420361i 0.981003 0.193993i \(-0.0621439\pi\)
−0.789030 + 0.614354i \(0.789417\pi\)
\(224\) 0 0
\(225\) 0.675354 + 11.9392i 0.0450236 + 0.795947i
\(226\) 0 0
\(227\) −21.5035 + 3.09174i −1.42724 + 0.205206i −0.812240 0.583324i \(-0.801752\pi\)
−0.614997 + 0.788529i \(0.710843\pi\)
\(228\) 0 0
\(229\) 9.34315 + 14.5382i 0.617413 + 0.960713i 0.999333 + 0.0365175i \(0.0116265\pi\)
−0.381920 + 0.924195i \(0.624737\pi\)
\(230\) 0 0
\(231\) −0.428893 + 9.93414i −0.0282191 + 0.653618i
\(232\) 0 0
\(233\) −5.77365 12.6425i −0.378245 0.828240i −0.999020 0.0442520i \(-0.985910\pi\)
0.620776 0.783988i \(-0.286818\pi\)
\(234\) 0 0
\(235\) 1.40337 + 1.21603i 0.0915460 + 0.0793250i
\(236\) 0 0
\(237\) 0.0744967 + 0.127715i 0.00483908 + 0.00829600i
\(238\) 0 0
\(239\) −3.28691 −0.212613 −0.106306 0.994333i \(-0.533902\pi\)
−0.106306 + 0.994333i \(0.533902\pi\)
\(240\) 0 0
\(241\) −24.1310 + 7.08551i −1.55442 + 0.456418i −0.942417 0.334441i \(-0.891453\pi\)
−0.611999 + 0.790859i \(0.709634\pi\)
\(242\) 0 0
\(243\) −11.0058 11.0396i −0.706021 0.708191i
\(244\) 0 0
\(245\) −1.17015 + 2.56227i −0.0747583 + 0.163698i
\(246\) 0 0
\(247\) −0.841258 2.86506i −0.0535279 0.182299i
\(248\) 0 0
\(249\) 13.4629 + 12.7229i 0.853176 + 0.806279i
\(250\) 0 0
\(251\) −1.44108 10.0229i −0.0909599 0.632640i −0.983397 0.181468i \(-0.941915\pi\)
0.892437 0.451172i \(-0.148994\pi\)
\(252\) 0 0
\(253\) 3.21681 + 2.78738i 0.202239 + 0.175241i
\(254\) 0 0
\(255\) −3.03999 + 4.30956i −0.190372 + 0.269875i
\(256\) 0 0
\(257\) 3.00280 10.2266i 0.187310 0.637919i −0.811271 0.584670i \(-0.801224\pi\)
0.998581 0.0532489i \(-0.0169577\pi\)
\(258\) 0 0
\(259\) 0.641641 0.555985i 0.0398696 0.0345472i
\(260\) 0 0
\(261\) 2.46891 1.79145i 0.152822 0.110888i
\(262\) 0 0
\(263\) 5.74612 19.5695i 0.354321 1.20671i −0.568891 0.822413i \(-0.692627\pi\)
0.923211 0.384292i \(-0.125555\pi\)
\(264\) 0 0
\(265\) −3.57725 + 7.83308i −0.219749 + 0.481182i
\(266\) 0 0
\(267\) 0.718155 16.6341i 0.0439504 1.01799i
\(268\) 0 0
\(269\) 18.7758i 1.14478i 0.819980 + 0.572392i \(0.193984\pi\)
−0.819980 + 0.572392i \(0.806016\pi\)
\(270\) 0 0
\(271\) −10.3459 4.72482i −0.628470 0.287013i 0.0756055 0.997138i \(-0.475911\pi\)
−0.704075 + 0.710125i \(0.748638\pi\)
\(272\) 0 0
\(273\) 1.88438 + 0.642808i 0.114048 + 0.0389045i
\(274\) 0 0
\(275\) −7.30995 8.43613i −0.440806 0.508718i
\(276\) 0 0
\(277\) −7.83597 9.04319i −0.470818 0.543353i 0.469821 0.882762i \(-0.344318\pi\)
−0.940639 + 0.339409i \(0.889773\pi\)
\(278\) 0 0
\(279\) 3.57340 9.16156i 0.213934 0.548488i
\(280\) 0 0
\(281\) 3.01821 + 1.93968i 0.180051 + 0.115712i 0.627562 0.778567i \(-0.284053\pi\)
−0.447511 + 0.894279i \(0.647689\pi\)
\(282\) 0 0
\(283\) −7.46491 + 8.61497i −0.443743 + 0.512107i −0.932923 0.360076i \(-0.882751\pi\)
0.489180 + 0.872183i \(0.337296\pi\)
\(284\) 0 0
\(285\) 0.923988 + 9.24136i 0.0547323 + 0.547411i
\(286\) 0 0
\(287\) 7.07452 + 6.13011i 0.417596 + 0.361849i
\(288\) 0 0
\(289\) −7.53763 + 2.21325i −0.443390 + 0.130191i
\(290\) 0 0
\(291\) 5.35661 + 2.73140i 0.314010 + 0.160118i
\(292\) 0 0
\(293\) −5.35113 + 8.32652i −0.312616 + 0.486441i −0.961635 0.274332i \(-0.911543\pi\)
0.649019 + 0.760772i \(0.275180\pi\)
\(294\) 0 0
\(295\) 0.918384 + 3.12773i 0.0534704 + 0.182103i
\(296\) 0 0
\(297\) 14.4295 + 1.87826i 0.837284 + 0.108988i
\(298\) 0 0
\(299\) 0.716988 0.460780i 0.0414645 0.0266476i
\(300\) 0 0
\(301\) 1.17085 1.35123i 0.0674866 0.0778837i
\(302\) 0 0
\(303\) −2.20068 5.42687i −0.126426 0.311765i
\(304\) 0 0
\(305\) 0.823948i 0.0471791i
\(306\) 0 0
\(307\) 5.18062 3.32938i 0.295674 0.190018i −0.384390 0.923171i \(-0.625588\pi\)
0.680064 + 0.733153i \(0.261952\pi\)
\(308\) 0 0
\(309\) 1.68252 + 16.8279i 0.0957154 + 0.957308i
\(310\) 0 0
\(311\) 4.81843 + 33.5129i 0.273228 + 1.90034i 0.413957 + 0.910297i \(0.364147\pi\)
−0.140728 + 0.990048i \(0.544944\pi\)
\(312\) 0 0
\(313\) −21.8275 + 9.96830i −1.23377 + 0.563442i −0.922174 0.386775i \(-0.873589\pi\)
−0.311591 + 0.950216i \(0.600862\pi\)
\(314\) 0 0
\(315\) −5.39035 3.04844i −0.303712 0.171760i
\(316\) 0 0
\(317\) 19.5268 + 2.80753i 1.09673 + 0.157687i 0.666846 0.745195i \(-0.267644\pi\)
0.429888 + 0.902882i \(0.358553\pi\)
\(318\) 0 0
\(319\) −0.802209 + 2.73207i −0.0449151 + 0.152967i
\(320\) 0 0
\(321\) 11.5122 + 2.16567i 0.642547 + 0.120876i
\(322\) 0 0
\(323\) 8.70599 13.5468i 0.484414 0.753763i
\(324\) 0 0
\(325\) −2.03314 + 0.928506i −0.112779 + 0.0515042i
\(326\) 0 0
\(327\) 12.7961 + 21.9373i 0.707624 + 1.21313i
\(328\) 0 0
\(329\) 3.62740 1.06510i 0.199985 0.0587209i
\(330\) 0 0
\(331\) −8.36891 1.20327i −0.459997 0.0661375i −0.0915788 0.995798i \(-0.529191\pi\)
−0.368418 + 0.929660i \(0.620100\pi\)
\(332\) 0 0
\(333\) −0.729676 1.00561i −0.0399860 0.0551071i
\(334\) 0 0
\(335\) 7.72650 + 2.86926i 0.422144 + 0.156764i
\(336\) 0 0
\(337\) −2.94419 + 2.55116i −0.160380 + 0.138970i −0.731354 0.681998i \(-0.761111\pi\)
0.570974 + 0.820968i \(0.306566\pi\)
\(338\) 0 0
\(339\) 4.16019 22.1146i 0.225950 1.20110i
\(340\) 0 0
\(341\) 2.58615 + 8.80762i 0.140048 + 0.476959i
\(342\) 0 0
\(343\) 10.8587 + 16.8965i 0.586315 + 0.912325i
\(344\) 0 0
\(345\) −2.45657 + 0.996179i −0.132258 + 0.0536325i
\(346\) 0 0
\(347\) −9.66034 6.20832i −0.518594 0.333280i 0.255022 0.966935i \(-0.417917\pi\)
−0.773616 + 0.633655i \(0.781554\pi\)
\(348\) 0 0
\(349\) 4.77161 33.1873i 0.255418 1.77647i −0.309076 0.951037i \(-0.600020\pi\)
0.564494 0.825437i \(-0.309071\pi\)
\(350\) 0 0
\(351\) 1.17486 2.66628i 0.0627093 0.142315i
\(352\) 0 0
\(353\) −0.418454 + 2.91041i −0.0222721 + 0.154906i −0.997923 0.0644256i \(-0.979478\pi\)
0.975650 + 0.219331i \(0.0703876\pi\)
\(354\) 0 0
\(355\) 2.76051 + 1.26068i 0.146512 + 0.0669100i
\(356\) 0 0
\(357\) 4.03494 + 9.95016i 0.213552 + 0.526618i
\(358\) 0 0
\(359\) 36.2740 5.21541i 1.91447 0.275259i 0.921016 0.389524i \(-0.127360\pi\)
0.993450 + 0.114265i \(0.0364513\pi\)
\(360\) 0 0
\(361\) −1.33177 9.26270i −0.0700934 0.487510i
\(362\) 0 0
\(363\) 4.72456 2.75585i 0.247975 0.144645i
\(364\) 0 0
\(365\) −3.21267 −0.168159
\(366\) 0 0
\(367\) −15.0174 + 6.85821i −0.783901 + 0.357995i −0.766823 0.641859i \(-0.778164\pi\)
−0.0170778 + 0.999854i \(0.505436\pi\)
\(368\) 0 0
\(369\) 9.82974 9.54121i 0.511716 0.496695i
\(370\) 0 0
\(371\) 9.47838 + 14.7487i 0.492093 + 0.765712i
\(372\) 0 0
\(373\) 24.2146i 1.25378i −0.779106 0.626892i \(-0.784327\pi\)
0.779106 0.626892i \(-0.215673\pi\)
\(374\) 0 0
\(375\) 15.2138 3.76264i 0.785638 0.194302i
\(376\) 0 0
\(377\) 0.479639 + 0.308245i 0.0247027 + 0.0158754i
\(378\) 0 0
\(379\) 3.71132 + 1.69490i 0.190638 + 0.0870612i 0.508447 0.861093i \(-0.330220\pi\)
−0.317809 + 0.948155i \(0.602947\pi\)
\(380\) 0 0
\(381\) 3.58606 0.886896i 0.183720 0.0454371i
\(382\) 0 0
\(383\) 4.71606 5.44262i 0.240979 0.278105i −0.622357 0.782733i \(-0.713825\pi\)
0.863337 + 0.504628i \(0.168370\pi\)
\(384\) 0 0
\(385\) 5.72175 0.822664i 0.291607 0.0419268i
\(386\) 0 0
\(387\) −1.82237 1.87748i −0.0926361 0.0954375i
\(388\) 0 0
\(389\) −8.77788 + 13.6586i −0.445056 + 0.692521i −0.989217 0.146460i \(-0.953212\pi\)
0.544160 + 0.838981i \(0.316848\pi\)
\(390\) 0 0
\(391\) 4.41005 + 1.29491i 0.223026 + 0.0654863i
\(392\) 0 0
\(393\) 10.8971 8.64842i 0.549688 0.436255i
\(394\) 0 0
\(395\) 0.0649606 0.0562887i 0.00326852 0.00283219i
\(396\) 0 0
\(397\) −5.99947 1.76160i −0.301105 0.0884123i 0.127690 0.991814i \(-0.459244\pi\)
−0.428795 + 0.903402i \(0.641062\pi\)
\(398\) 0 0
\(399\) 16.8449 + 8.58940i 0.843298 + 0.430008i
\(400\) 0 0
\(401\) 20.2313 1.01030 0.505152 0.863030i \(-0.331436\pi\)
0.505152 + 0.863030i \(0.331436\pi\)
\(402\) 0 0
\(403\) 1.83804 0.0915591
\(404\) 0 0
\(405\) −5.12436 + 7.47442i −0.254632 + 0.371407i
\(406\) 0 0
\(407\) 1.11280 + 0.326747i 0.0551594 + 0.0161963i
\(408\) 0 0
\(409\) 0.00324140 0.00280869i 0.000160277 0.000138881i −0.654781 0.755819i \(-0.727239\pi\)
0.654941 + 0.755680i \(0.272694\pi\)
\(410\) 0 0
\(411\) −18.0698 22.7682i −0.891315 1.12307i
\(412\) 0 0
\(413\) 6.36777 + 1.86975i 0.313338 + 0.0920042i
\(414\) 0 0
\(415\) 5.82197 9.05916i 0.285789 0.444697i
\(416\) 0 0
\(417\) −10.2074 9.64630i −0.499857 0.472381i
\(418\) 0 0
\(419\) −22.8438 + 3.28445i −1.11600 + 0.160456i −0.675543 0.737320i \(-0.736091\pi\)
−0.440452 + 0.897776i \(0.645182\pi\)
\(420\) 0 0
\(421\) −3.60373 + 4.15892i −0.175635 + 0.202693i −0.836741 0.547599i \(-0.815542\pi\)
0.661106 + 0.750293i \(0.270087\pi\)
\(422\) 0 0
\(423\) −1.09536 5.42294i −0.0532584 0.263672i
\(424\) 0 0
\(425\) −10.9644 5.00728i −0.531852 0.242889i
\(426\) 0 0
\(427\) −1.41119 0.906916i −0.0682922 0.0438887i
\(428\) 0 0
\(429\) 0.652974 + 2.64023i 0.0315259 + 0.127471i
\(430\) 0 0
\(431\) 33.0153i 1.59029i 0.606418 + 0.795146i \(0.292606\pi\)
−0.606418 + 0.795146i \(0.707394\pi\)
\(432\) 0 0
\(433\) 5.71980 + 8.90018i 0.274876 + 0.427716i 0.951055 0.309022i \(-0.100002\pi\)
−0.676179 + 0.736738i \(0.736365\pi\)
\(434\) 0 0
\(435\) −1.28886 1.21802i −0.0617962 0.0583994i
\(436\) 0 0
\(437\) 7.36264 3.36240i 0.352203 0.160846i
\(438\) 0 0
\(439\) −28.9237 −1.38045 −0.690226 0.723593i \(-0.742489\pi\)
−0.690226 + 0.723593i \(0.742489\pi\)
\(440\) 0 0
\(441\) 7.42487 3.91187i 0.353565 0.186280i
\(442\) 0 0
\(443\) −2.62916 18.2862i −0.124915 0.868803i −0.951863 0.306524i \(-0.900834\pi\)
0.826948 0.562279i \(-0.190075\pi\)
\(444\) 0 0
\(445\) −9.58071 + 1.37750i −0.454169 + 0.0652997i
\(446\) 0 0
\(447\) 34.2989 13.9087i 1.62228 0.657861i
\(448\) 0 0
\(449\) 16.1989 + 7.39779i 0.764473 + 0.349123i 0.759195 0.650863i \(-0.225593\pi\)
0.00527804 + 0.999986i \(0.498320\pi\)
\(450\) 0 0
\(451\) −1.81983 + 12.6572i −0.0856924 + 0.596003i
\(452\) 0 0
\(453\) −2.18845 0.746535i −0.102822 0.0350753i
\(454\) 0 0
\(455\) 0.164725 1.14569i 0.00772243 0.0537107i
\(456\) 0 0
\(457\) −28.4659 18.2939i −1.33158 0.855754i −0.335315 0.942106i \(-0.608843\pi\)
−0.996265 + 0.0863520i \(0.972479\pi\)
\(458\) 0 0
\(459\) 15.0158 4.62781i 0.700879 0.216008i
\(460\) 0 0
\(461\) 2.94920 + 4.58905i 0.137358 + 0.213733i 0.903117 0.429394i \(-0.141273\pi\)
−0.765759 + 0.643128i \(0.777636\pi\)
\(462\) 0 0
\(463\) 5.34889 + 18.2166i 0.248584 + 0.846599i 0.985364 + 0.170466i \(0.0545274\pi\)
−0.736780 + 0.676133i \(0.763654\pi\)
\(464\) 0 0
\(465\) −5.61832 1.05692i −0.260543 0.0490133i
\(466\) 0 0
\(467\) −14.0193 + 12.1478i −0.648736 + 0.562133i −0.915844 0.401534i \(-0.868477\pi\)
0.267108 + 0.963667i \(0.413932\pi\)
\(468\) 0 0
\(469\) 13.4188 10.0751i 0.619621 0.465226i
\(470\) 0 0
\(471\) 22.9692 + 28.9415i 1.05836 + 1.33355i
\(472\) 0 0
\(473\) 2.41752 + 0.347586i 0.111158 + 0.0159820i
\(474\) 0 0
\(475\) −20.3670 + 5.98029i −0.934502 + 0.274395i
\(476\) 0 0
\(477\) 22.6984 11.9589i 1.03929 0.547561i
\(478\) 0 0
\(479\) −24.8352 + 11.3419i −1.13475 + 0.518222i −0.892076 0.451886i \(-0.850751\pi\)
−0.242673 + 0.970108i \(0.578024\pi\)
\(480\) 0 0
\(481\) 0.125551 0.195361i 0.00572464 0.00890771i
\(482\) 0 0
\(483\) −0.997769 + 5.30390i −0.0454001 + 0.241336i
\(484\) 0 0
\(485\) 0.984809 3.35395i 0.0447179 0.152295i
\(486\) 0 0
\(487\) 27.5010 + 3.95405i 1.24619 + 0.179175i 0.733673 0.679503i \(-0.237804\pi\)
0.512516 + 0.858678i \(0.328714\pi\)
\(488\) 0 0
\(489\) 1.16246 2.27972i 0.0525682 0.103093i
\(490\) 0 0
\(491\) 2.78595 1.27230i 0.125728 0.0574182i −0.351558 0.936166i \(-0.614348\pi\)
0.477286 + 0.878748i \(0.341621\pi\)
\(492\) 0 0
\(493\) 0.437577 + 3.04342i 0.0197075 + 0.137069i
\(494\) 0 0
\(495\) −0.477748 8.44584i −0.0214732 0.379612i
\(496\) 0 0
\(497\) 5.19767 3.34034i 0.233147 0.149835i
\(498\) 0 0
\(499\) 33.7775i 1.51209i 0.654521 + 0.756044i \(0.272870\pi\)
−0.654521 + 0.756044i \(0.727130\pi\)
\(500\) 0 0
\(501\) −4.02869 + 1.63370i −0.179989 + 0.0729882i
\(502\) 0 0
\(503\) 8.18125 9.44167i 0.364784 0.420983i −0.543453 0.839440i \(-0.682883\pi\)
0.908237 + 0.418456i \(0.137429\pi\)
\(504\) 0 0
\(505\) −2.86400 + 1.84058i −0.127446 + 0.0819047i
\(506\) 0 0
\(507\) −21.9516 0.947733i −0.974906 0.0420903i
\(508\) 0 0
\(509\) 7.15954 + 24.3831i 0.317341 + 1.08076i 0.951522 + 0.307580i \(0.0995191\pi\)
−0.634181 + 0.773184i \(0.718663\pi\)
\(510\) 0 0
\(511\) −3.53617 + 5.50239i −0.156431 + 0.243411i
\(512\) 0 0
\(513\) 14.6476 23.4758i 0.646707 1.03648i
\(514\) 0 0
\(515\) 9.43344 2.76991i 0.415687 0.122057i
\(516\) 0 0
\(517\) 3.90295 + 3.38192i 0.171651 + 0.148737i
\(518\) 0 0
\(519\) 21.5371 2.15336i 0.945372 0.0945221i
\(520\) 0 0
\(521\) 8.55265 9.87029i 0.374699 0.432425i −0.536812 0.843702i \(-0.680372\pi\)
0.911511 + 0.411277i \(0.134917\pi\)
\(522\) 0 0
\(523\) 19.5661 + 12.5744i 0.855567 + 0.549840i 0.893306 0.449448i \(-0.148379\pi\)
−0.0377395 + 0.999288i \(0.512016\pi\)
\(524\) 0 0
\(525\) 4.56957 13.3956i 0.199432 0.584631i
\(526\) 0 0
\(527\) 6.49113 + 7.49116i 0.282758 + 0.326320i
\(528\) 0 0
\(529\) −13.5489 15.6363i −0.589083 0.679838i
\(530\) 0 0
\(531\) 3.52916 9.04813i 0.153152 0.392656i
\(532\) 0 0
\(533\) 2.32907 + 1.06365i 0.100883 + 0.0460719i
\(534\) 0 0
\(535\) 6.81000i 0.294422i
\(536\) 0 0
\(537\) 19.1196 + 0.825465i 0.825073 + 0.0356215i
\(538\) 0 0
\(539\) −3.25433 + 7.12599i −0.140174 + 0.306938i
\(540\) 0 0
\(541\) −10.6811 + 36.3766i −0.459218 + 1.56395i 0.326393 + 0.945234i \(0.394167\pi\)
−0.785612 + 0.618720i \(0.787652\pi\)
\(542\) 0 0
\(543\) 1.00393 + 1.26497i 0.0430827 + 0.0542849i
\(544\) 0 0
\(545\) 11.1581 9.66853i 0.477960 0.414154i
\(546\) 0 0
\(547\) 6.93535 23.6196i 0.296534 1.00990i −0.667607 0.744514i \(-0.732681\pi\)
0.964141 0.265389i \(-0.0855005\pi\)
\(548\) 0 0
\(549\) −1.50023 + 1.94307i −0.0640284 + 0.0829282i
\(550\) 0 0
\(551\) 4.09212 + 3.54584i 0.174330 + 0.151058i
\(552\) 0 0
\(553\) −0.0249047 0.173216i −0.00105905 0.00736588i
\(554\) 0 0
\(555\) −0.496110 + 0.524966i −0.0210587 + 0.0222835i
\(556\) 0 0
\(557\) 0.197657 + 0.673158i 0.00837500 + 0.0285226i 0.963574 0.267440i \(-0.0861778\pi\)
−0.955199 + 0.295963i \(0.904360\pi\)
\(558\) 0 0
\(559\) 0.203157 0.444852i 0.00859263 0.0188152i
\(560\) 0 0
\(561\) −8.45457 + 11.9854i −0.356952 + 0.506023i
\(562\) 0 0
\(563\) −3.72548 + 1.09390i −0.157010 + 0.0461024i −0.359293 0.933225i \(-0.616982\pi\)
0.202283 + 0.979327i \(0.435164\pi\)
\(564\) 0 0
\(565\) −13.0818 −0.550356
\(566\) 0 0
\(567\) 7.16120 + 17.0036i 0.300742 + 0.714086i
\(568\) 0 0
\(569\) 10.8384 + 9.39154i 0.454370 + 0.393714i 0.851757 0.523937i \(-0.175537\pi\)
−0.397387 + 0.917651i \(0.630083\pi\)
\(570\) 0 0
\(571\) 10.9314 + 23.9364i 0.457464 + 1.00171i 0.988058 + 0.154081i \(0.0492416\pi\)
−0.530594 + 0.847626i \(0.678031\pi\)
\(572\) 0 0
\(573\) −16.5474 0.714413i −0.691278 0.0298450i
\(574\) 0 0
\(575\) −3.27557 5.09689i −0.136601 0.212555i
\(576\) 0 0
\(577\) −38.1561 + 5.48602i −1.58846 + 0.228386i −0.879162 0.476523i \(-0.841897\pi\)
−0.709297 + 0.704909i \(0.750988\pi\)
\(578\) 0 0
\(579\) 4.12680 + 41.2747i 0.171504 + 1.71532i
\(580\) 0 0
\(581\) −9.10755 19.9428i −0.377845 0.827365i
\(582\) 0 0
\(583\) −9.94875 + 21.7847i −0.412035 + 0.902231i
\(584\) 0 0
\(585\) −1.64959 0.384664i −0.0682022 0.0159039i
\(586\) 0 0
\(587\) −23.3634 6.86013i −0.964313 0.283148i −0.238579 0.971123i \(-0.576682\pi\)
−0.725734 + 0.687975i \(0.758500\pi\)
\(588\) 0 0
\(589\) 17.2780 + 2.48420i 0.711928 + 0.102360i
\(590\) 0 0
\(591\) −14.9029 10.5126i −0.613023 0.432431i
\(592\) 0 0
\(593\) −5.35922 11.7351i −0.220077 0.481901i 0.767101 0.641526i \(-0.221699\pi\)
−0.987178 + 0.159626i \(0.948971\pi\)
\(594\) 0 0
\(595\) 5.25114 3.37470i 0.215276 0.138349i
\(596\) 0 0
\(597\) 18.7290 4.63200i 0.766525 0.189575i
\(598\) 0 0
\(599\) −4.00325 + 27.8432i −0.163568 + 1.13764i 0.728271 + 0.685290i \(0.240324\pi\)
−0.891839 + 0.452353i \(0.850585\pi\)
\(600\) 0 0
\(601\) −16.3336 18.8499i −0.666260 0.768905i 0.317526 0.948249i \(-0.397148\pi\)
−0.983786 + 0.179345i \(0.942602\pi\)
\(602\) 0 0
\(603\) −12.9967 20.8347i −0.529265 0.848456i
\(604\) 0 0
\(605\) −2.08228 2.40308i −0.0846567 0.0976991i
\(606\) 0 0
\(607\) 0.952491 6.62472i 0.0386604 0.268889i −0.961318 0.275440i \(-0.911176\pi\)
0.999979 + 0.00655145i \(0.00208541\pi\)
\(608\) 0 0
\(609\) −3.50476 + 0.866789i −0.142020 + 0.0351241i
\(610\) 0 0
\(611\) 0.869919 0.559063i 0.0351931 0.0226173i
\(612\) 0 0
\(613\) 5.13198 + 11.2375i 0.207279 + 0.453877i 0.984508 0.175340i \(-0.0561026\pi\)
−0.777229 + 0.629218i \(0.783375\pi\)
\(614\) 0 0
\(615\) −6.50764 4.59054i −0.262413 0.185108i
\(616\) 0 0
\(617\) 5.84688 + 0.840654i 0.235386 + 0.0338435i 0.258998 0.965878i \(-0.416608\pi\)
−0.0236120 + 0.999721i \(0.507517\pi\)
\(618\) 0 0
\(619\) −39.7054 11.6586i −1.59590 0.468597i −0.641496 0.767127i \(-0.721686\pi\)
−0.954401 + 0.298529i \(0.903504\pi\)
\(620\) 0 0
\(621\) 7.60704 + 2.12367i 0.305260 + 0.0852199i
\(622\) 0 0
\(623\) −8.18619 + 17.9253i −0.327973 + 0.718160i
\(624\) 0 0
\(625\) 4.49457 + 9.84173i 0.179783 + 0.393669i
\(626\) 0 0
\(627\) 2.56972 + 25.7013i 0.102625 + 1.02641i
\(628\) 0 0
\(629\) 1.23961 0.178229i 0.0494266 0.00710647i
\(630\) 0 0
\(631\) 21.6056 + 33.6190i 0.860105 + 1.33835i 0.939869 + 0.341536i \(0.110947\pi\)
−0.0797638 + 0.996814i \(0.525417\pi\)
\(632\) 0 0
\(633\) −23.6266 1.02005i −0.939073 0.0405432i
\(634\) 0 0
\(635\) −0.892132 1.95350i −0.0354032 0.0775222i
\(636\) 0 0
\(637\) 1.18548 + 1.02722i 0.0469705 + 0.0407001i
\(638\) 0 0
\(639\) −4.21452 7.99929i −0.166724 0.316447i
\(640\) 0 0
\(641\) −21.3864 −0.844712 −0.422356 0.906430i \(-0.638797\pi\)
−0.422356 + 0.906430i \(0.638797\pi\)
\(642\) 0 0
\(643\) 16.2695 4.77715i 0.641606 0.188393i 0.0552841 0.998471i \(-0.482394\pi\)
0.586322 + 0.810078i \(0.300575\pi\)
\(644\) 0 0
\(645\) −0.876791 + 1.24296i −0.0345236 + 0.0489414i
\(646\) 0 0
\(647\) −4.74123 + 10.3819i −0.186397 + 0.408153i −0.979643 0.200749i \(-0.935662\pi\)
0.793246 + 0.608902i \(0.208390\pi\)
\(648\) 0 0
\(649\) 2.55413 + 8.69858i 0.100259 + 0.341449i
\(650\) 0 0
\(651\) −7.99426 + 8.45924i −0.313320 + 0.331544i
\(652\) 0 0
\(653\) −6.71761 46.7220i −0.262880 1.82837i −0.510925 0.859625i \(-0.670697\pi\)
0.248045 0.968749i \(-0.420212\pi\)
\(654\) 0 0
\(655\) −6.11229 5.29633i −0.238827 0.206945i
\(656\) 0 0
\(657\) 7.57626 + 5.84959i 0.295578 + 0.228214i
\(658\) 0 0
\(659\) 11.1587 38.0030i 0.434681 1.48039i −0.393185 0.919459i \(-0.628627\pi\)
0.827865 0.560927i \(-0.189555\pi\)
\(660\) 0 0
\(661\) 1.78336 1.54529i 0.0693648 0.0601049i −0.619488 0.785006i \(-0.712660\pi\)
0.688853 + 0.724901i \(0.258114\pi\)
\(662\) 0 0
\(663\) 1.82572 + 2.30044i 0.0709052 + 0.0893417i
\(664\) 0 0
\(665\) 3.09691 10.5471i 0.120093 0.409000i
\(666\) 0 0
\(667\) −0.642015 + 1.40582i −0.0248589 + 0.0544335i
\(668\) 0 0
\(669\) −11.9417 0.515567i −0.461692 0.0199330i
\(670\) 0 0
\(671\) 2.29149i 0.0884622i
\(672\) 0 0
\(673\) −36.5482 16.6910i −1.40883 0.643391i −0.441581 0.897221i \(-0.645582\pi\)
−0.967249 + 0.253830i \(0.918309\pi\)
\(674\) 0 0
\(675\) −18.9539 8.35178i −0.729536 0.321460i
\(676\) 0 0
\(677\) −9.77120 11.2766i −0.375538 0.433393i 0.536248 0.844061i \(-0.319841\pi\)
−0.911785 + 0.410667i \(0.865296\pi\)
\(678\) 0 0
\(679\) −4.66039 5.37838i −0.178849 0.206403i
\(680\) 0 0
\(681\) 12.1485 35.6131i 0.465531 1.36470i
\(682\) 0 0
\(683\) −29.6644 19.0642i −1.13508 0.729471i −0.168465 0.985708i \(-0.553881\pi\)
−0.966614 + 0.256237i \(0.917517\pi\)
\(684\) 0 0
\(685\) −11.0660 + 12.7708i −0.422810 + 0.487949i
\(686\) 0 0
\(687\) −29.7841 + 2.97794i −1.13634 + 0.113615i
\(688\) 0 0
\(689\) 3.62411 + 3.14031i 0.138068 + 0.119636i
\(690\) 0 0
\(691\) −1.16029 + 0.340691i −0.0441395 + 0.0129605i −0.303728 0.952759i \(-0.598231\pi\)
0.259588 + 0.965719i \(0.416413\pi\)
\(692\) 0 0
\(693\) −14.9912 8.47806i −0.569468 0.322055i
\(694\) 0 0
\(695\) −4.41413 + 6.86852i −0.167438 + 0.260538i
\(696\) 0 0
\(697\) 3.89020 + 13.2488i 0.147352 + 0.501834i
\(698\) 0 0
\(699\) 24.0505 + 1.03835i 0.909675 + 0.0392740i
\(700\) 0 0
\(701\) 22.7655 14.6305i 0.859840 0.552585i −0.0347895 0.999395i \(-0.511076\pi\)
0.894629 + 0.446809i \(0.147440\pi\)
\(702\) 0 0
\(703\) 1.44425 1.66676i 0.0544711 0.0628630i
\(704\) 0 0
\(705\) −2.98055 + 1.20866i −0.112254 + 0.0455208i
\(706\) 0 0
\(707\) 6.93114i 0.260672i
\(708\) 0 0
\(709\) −21.0873 + 13.5520i −0.791950 + 0.508956i −0.872980 0.487756i \(-0.837816\pi\)
0.0810296 + 0.996712i \(0.474179\pi\)
\(710\) 0 0
\(711\) −0.255683 + 0.0144630i −0.00958885 + 0.000542404i
\(712\) 0 0
\(713\) 0.709055 + 4.93159i 0.0265543 + 0.184689i
\(714\) 0 0
\(715\) 1.43826 0.656829i 0.0537877 0.0245640i
\(716\) 0 0
\(717\) 2.58617 5.07180i 0.0965824 0.189410i
\(718\) 0 0
\(719\) −36.2245 5.20830i −1.35095 0.194237i −0.571447 0.820639i \(-0.693618\pi\)
−0.779500 + 0.626402i \(0.784527\pi\)
\(720\) 0 0
\(721\) 5.63928 19.2056i 0.210018 0.715255i
\(722\) 0 0
\(723\) 8.05336 42.8098i 0.299508 1.59211i
\(724\) 0 0
\(725\) 2.19124 3.40963i 0.0813805 0.126631i
\(726\) 0 0
\(727\) 2.87291 1.31201i 0.106550 0.0486599i −0.361427 0.932401i \(-0.617710\pi\)
0.467977 + 0.883741i \(0.344983\pi\)
\(728\) 0 0
\(729\) 25.6939 8.29615i 0.951624 0.307265i
\(730\) 0 0
\(731\) 2.53051 0.743026i 0.0935945 0.0274818i
\(732\) 0 0
\(733\) 1.93442 + 0.278128i 0.0714494 + 0.0102729i 0.177947 0.984040i \(-0.443054\pi\)
−0.106497 + 0.994313i \(0.533964\pi\)
\(734\) 0 0
\(735\) −3.03297 3.82160i −0.111873 0.140962i
\(736\) 0 0
\(737\) 21.4883 + 7.97975i 0.791532 + 0.293938i
\(738\) 0 0
\(739\) −15.9300 + 13.8034i −0.585995 + 0.507768i −0.896641 0.442758i \(-0.854000\pi\)
0.310646 + 0.950526i \(0.399455\pi\)
\(740\) 0 0
\(741\) 5.08277 + 0.956170i 0.186720 + 0.0351258i
\(742\) 0 0
\(743\) −6.85255 23.3376i −0.251396 0.856175i −0.984399 0.175950i \(-0.943700\pi\)
0.733003 0.680225i \(-0.238118\pi\)
\(744\) 0 0
\(745\) −11.6328 18.1010i −0.426194 0.663171i
\(746\) 0 0
\(747\) −30.2245 + 10.7631i −1.10585 + 0.393803i
\(748\) 0 0
\(749\) −11.6636 7.49574i −0.426178 0.273888i
\(750\) 0 0
\(751\) 2.12290 14.7651i 0.0774656 0.538785i −0.913724 0.406335i \(-0.866807\pi\)
0.991190 0.132450i \(-0.0422844\pi\)
\(752\) 0 0
\(753\) 16.5995 + 5.66248i 0.604918 + 0.206352i
\(754\) 0 0
\(755\) −0.191306 + 1.33056i −0.00696233 + 0.0484241i
\(756\) 0 0
\(757\) 1.05419 + 0.481431i 0.0383150 + 0.0174979i 0.434480 0.900681i \(-0.356932\pi\)
−0.396165 + 0.918179i \(0.629659\pi\)
\(758\) 0 0
\(759\) −6.83202 + 2.77049i −0.247987 + 0.100562i
\(760\) 0 0
\(761\) −23.9508 + 3.44360i −0.868215 + 0.124830i −0.562005 0.827134i \(-0.689970\pi\)
−0.306209 + 0.951964i \(0.599061\pi\)
\(762\) 0 0
\(763\) −4.27780 29.7527i −0.154867 1.07712i
\(764\) 0 0
\(765\) −4.25787 8.08159i −0.153944 0.292190i
\(766\) 0 0
\(767\) 1.81528 0.0655460
\(768\) 0 0
\(769\) 15.4927 7.07527i 0.558680 0.255141i −0.116002 0.993249i \(-0.537008\pi\)
0.674682 + 0.738108i \(0.264281\pi\)
\(770\) 0 0
\(771\) 13.4173 + 12.6798i 0.483213 + 0.456652i
\(772\) 0 0
\(773\) −14.4824 22.5351i −0.520897 0.810531i 0.476754 0.879037i \(-0.341813\pi\)
−0.997651 + 0.0685055i \(0.978177\pi\)
\(774\) 0 0
\(775\) 13.0661i 0.469350i
\(776\) 0 0
\(777\) 0.353051 + 1.42752i 0.0126656 + 0.0512121i
\(778\) 0 0
\(779\) 20.4563 + 13.1465i 0.732923 + 0.471021i
\(780\) 0 0
\(781\) 7.67729 + 3.50610i 0.274715 + 0.125458i
\(782\) 0 0
\(783\) 0.821702 + 5.21913i 0.0293652 + 0.186516i
\(784\) 0 0
\(785\) 14.0664 16.2335i 0.502052 0.579399i
\(786\) 0 0
\(787\) −2.61100 + 0.375406i −0.0930723 + 0.0133818i −0.188694 0.982036i \(-0.560425\pi\)
0.0956213 + 0.995418i \(0.469516\pi\)
\(788\) 0 0
\(789\) 25.6751 + 24.2638i 0.914059 + 0.863816i
\(790\) 0 0
\(791\) −14.3991 + 22.4054i −0.511973 + 0.796646i
\(792\) 0 0
\(793\) −0.440249 0.129269i −0.0156337 0.00459046i
\(794\) 0 0
\(795\) −9.27205 11.6829i −0.328846 0.414351i
\(796\) 0 0
\(797\) 27.9982 24.2605i 0.991746 0.859352i 0.00168569 0.999999i \(-0.499463\pi\)
0.990060 + 0.140646i \(0.0449180\pi\)
\(798\) 0 0
\(799\) 5.35070 + 1.57111i 0.189294 + 0.0555818i
\(800\) 0 0
\(801\) 25.1018 + 14.1960i 0.886929 + 0.501590i
\(802\) 0 0
\(803\) −8.93481 −0.315303
\(804\) 0 0
\(805\) 3.13751 0.110583
\(806\) 0 0
\(807\) −28.9716 14.7730i −1.01985 0.520034i
\(808\) 0 0
\(809\) −16.0045 4.69934i −0.562688 0.165220i −0.0119949 0.999928i \(-0.503818\pi\)
−0.550693 + 0.834708i \(0.685636\pi\)
\(810\) 0 0
\(811\) 20.7879 18.0128i 0.729963 0.632517i −0.208450 0.978033i \(-0.566842\pi\)
0.938413 + 0.345516i \(0.112296\pi\)
\(812\) 0 0
\(813\) 15.4308 12.2465i 0.541181 0.429504i
\(814\) 0 0
\(815\) −1.42741 0.419125i −0.0499999 0.0146813i
\(816\) 0 0
\(817\) 2.51097 3.90715i 0.0878477 0.136694i
\(818\) 0 0
\(819\) −2.47452 + 2.40188i −0.0864666 + 0.0839286i
\(820\) 0 0
\(821\) −14.8405 + 2.13374i −0.517936 + 0.0744679i −0.396326 0.918110i \(-0.629715\pi\)
−0.121610 + 0.992578i \(0.538806\pi\)
\(822\) 0 0
\(823\) −8.65464 + 9.98799i −0.301682 + 0.348159i −0.886268 0.463172i \(-0.846711\pi\)
0.584587 + 0.811331i \(0.301257\pi\)
\(824\) 0 0
\(825\) 18.7687 4.64183i 0.653442 0.161608i
\(826\) 0 0
\(827\) −17.8256 8.14067i −0.619856 0.283079i 0.0806307 0.996744i \(-0.474307\pi\)
−0.700487 + 0.713665i \(0.747034\pi\)
\(828\) 0 0
\(829\) −6.02006 3.86886i −0.209085 0.134371i 0.431907 0.901918i \(-0.357841\pi\)
−0.640993 + 0.767547i \(0.721477\pi\)
\(830\) 0 0
\(831\) 20.1193 4.97585i 0.697930 0.172610i
\(832\) 0 0
\(833\) 8.45928i 0.293097i
\(834\) 0 0
\(835\) 1.36637 + 2.12612i 0.0472853 + 0.0735774i
\(836\) 0 0
\(837\) 11.3250 + 12.7222i 0.391448 + 0.439745i
\(838\) 0 0
\(839\) −7.63535 + 3.48695i −0.263601 + 0.120383i −0.542832 0.839841i \(-0.682648\pi\)
0.279230 + 0.960224i \(0.409921\pi\)
\(840\) 0 0
\(841\) 27.9661 0.964349
\(842\) 0 0
\(843\) −5.36774 + 3.13102i −0.184875 + 0.107838i
\(844\) 0 0
\(845\) 1.81785 + 12.6434i 0.0625360 + 0.434948i
\(846\) 0 0
\(847\) −6.40775 + 0.921296i −0.220173 + 0.0316561i
\(848\) 0 0
\(849\) −7.41967 18.2969i −0.254643 0.627948i
\(850\) 0 0
\(851\) 0.572603 + 0.261499i 0.0196286 + 0.00896406i
\(852\) 0 0
\(853\) 1.63189 11.3501i 0.0558749 0.388619i −0.942624 0.333855i \(-0.891650\pi\)
0.998499 0.0547635i \(-0.0174405\pi\)
\(854\) 0 0
\(855\) −14.9867 5.84544i −0.512534 0.199910i
\(856\) 0 0
\(857\) −1.83260 + 12.7460i −0.0626003 + 0.435395i 0.934285 + 0.356527i \(0.116039\pi\)
−0.996885 + 0.0788672i \(0.974870\pi\)
\(858\) 0 0
\(859\) −11.8921 7.64260i −0.405754 0.260762i 0.321807 0.946805i \(-0.395710\pi\)
−0.727561 + 0.686043i \(0.759346\pi\)
\(860\) 0 0
\(861\) −15.0252 + 6.09296i −0.512058 + 0.207648i
\(862\) 0 0
\(863\) −11.0327 17.1672i −0.375557 0.584378i 0.601102 0.799172i \(-0.294728\pi\)
−0.976659 + 0.214794i \(0.931092\pi\)
\(864\) 0 0
\(865\) −3.54504 12.0733i −0.120535 0.410504i
\(866\) 0 0
\(867\) 2.51557 13.3722i 0.0854332 0.454143i
\(868\) 0 0
\(869\) 0.180663 0.156545i 0.00612857 0.00531044i
\(870\) 0 0
\(871\) 2.74530 3.67824i 0.0930209 0.124632i
\(872\) 0 0
\(873\) −8.42925 + 6.11631i −0.285287 + 0.207006i
\(874\) 0 0
\(875\) −18.3604 2.63983i −0.620696 0.0892426i
\(876\) 0 0
\(877\) 10.6670 3.13210i 0.360197 0.105763i −0.0966264 0.995321i \(-0.530805\pi\)
0.456824 + 0.889557i \(0.348987\pi\)
\(878\) 0 0
\(879\) −8.63773 14.8083i −0.291344 0.499472i
\(880\) 0 0
\(881\) −14.6371 + 6.68455i −0.493137 + 0.225208i −0.646431 0.762973i \(-0.723739\pi\)
0.153294 + 0.988181i \(0.451012\pi\)
\(882\) 0 0
\(883\) 12.8188 19.9464i 0.431385 0.671249i −0.555711 0.831375i \(-0.687554\pi\)
0.987096 + 0.160127i \(0.0511903\pi\)
\(884\) 0 0
\(885\) −5.54876 1.04383i −0.186520 0.0350880i
\(886\) 0 0
\(887\) −11.8144 + 40.2361i −0.396688 + 1.35100i 0.483073 + 0.875580i \(0.339521\pi\)
−0.879761 + 0.475416i \(0.842297\pi\)
\(888\) 0 0
\(889\) −4.32775 0.622237i −0.145148 0.0208691i
\(890\) 0 0
\(891\) −14.2515 + 20.7873i −0.477442 + 0.696399i
\(892\) 0 0
\(893\) 8.93306 4.07959i 0.298933 0.136518i
\(894\) 0 0
\(895\) −1.58333 11.0123i −0.0529249 0.368101i
\(896\) 0 0
\(897\) 0.146864 + 1.46888i 0.00490365 + 0.0490444i
\(898\) 0 0
\(899\) −2.80388 + 1.80194i −0.0935146 + 0.0600982i
\(900\) 0 0
\(901\) 25.8607i 0.861546i
\(902\) 0 0
\(903\) 1.16375 + 2.86981i 0.0387273 + 0.0955014i
\(904\) 0 0
\(905\) 0.614810 0.709529i 0.0204370 0.0235855i
\(906\) 0 0
\(907\) −32.9158 + 21.1537i −1.09295 + 0.702396i −0.957513 0.288390i \(-0.906880\pi\)
−0.135437 + 0.990786i \(0.543244\pi\)
\(908\) 0 0
\(909\) 10.1053 + 0.874197i 0.335172 + 0.0289953i
\(910\) 0 0
\(911\) 9.40813 + 32.0411i 0.311705 + 1.06157i 0.955161 + 0.296087i \(0.0956818\pi\)
−0.643456 + 0.765483i \(0.722500\pi\)
\(912\) 0 0
\(913\) 16.1916 25.1946i 0.535863 0.833819i
\(914\) 0 0
\(915\) 1.27137 + 0.648289i 0.0420303 + 0.0214318i
\(916\) 0 0
\(917\) −15.7989 + 4.63897i −0.521725 + 0.153192i
\(918\) 0 0
\(919\) 13.5490 + 11.7403i 0.446940 + 0.387276i 0.849047 0.528317i \(-0.177177\pi\)
−0.402107 + 0.915593i \(0.631722\pi\)
\(920\) 0 0
\(921\) 1.06117 + 10.6134i 0.0349668 + 0.349724i
\(922\) 0 0
\(923\) 1.10670 1.27720i 0.0364274 0.0420394i
\(924\) 0 0
\(925\) −1.38878 0.892512i −0.0456627 0.0293456i
\(926\) 0 0
\(927\) −27.2898 10.6442i −0.896314 0.349601i
\(928\) 0 0
\(929\) −26.2500 30.2941i −0.861235 0.993918i −0.999994 0.00359196i \(-0.998857\pi\)
0.138759 0.990326i \(-0.455689\pi\)
\(930\) 0 0
\(931\) 9.75547 + 11.2584i 0.319723 + 0.368980i
\(932\) 0 0
\(933\) −55.5026 18.9333i −1.81707 0.619848i
\(934\) 0 0
\(935\) 7.75627 + 3.54217i 0.253657 + 0.115841i
\(936\) 0 0
\(937\) 16.6410i 0.543638i 0.962348 + 0.271819i \(0.0876253\pi\)
−0.962348 + 0.271819i \(0.912375\pi\)
\(938\) 0 0
\(939\) 1.79273 41.5236i 0.0585035 1.35507i
\(940\) 0 0
\(941\) −10.6549 + 23.3310i −0.347340 + 0.760568i 0.652656 + 0.757654i \(0.273655\pi\)
−0.999996 + 0.00291342i \(0.999073\pi\)
\(942\) 0 0
\(943\) −1.95537 + 6.65940i −0.0636758 + 0.216860i
\(944\) 0 0
\(945\) 8.94499 5.91892i 0.290981 0.192542i
\(946\) 0 0
\(947\) 25.8510 22.4001i 0.840046 0.727904i −0.124386 0.992234i \(-0.539696\pi\)
0.964432 + 0.264330i \(0.0851507\pi\)
\(948\) 0 0
\(949\) −0.504034 + 1.71658i −0.0163616 + 0.0557226i
\(950\) 0 0
\(951\) −19.6960 + 27.9214i −0.638685 + 0.905414i
\(952\) 0 0
\(953\) −32.3020 27.9898i −1.04636 0.906680i −0.0506091 0.998719i \(-0.516116\pi\)
−0.995755 + 0.0920385i \(0.970662\pi\)
\(954\) 0 0
\(955\) 1.37032 + 9.53079i 0.0443425 + 0.308409i
\(956\) 0 0
\(957\) −3.58448 3.38745i −0.115870 0.109501i
\(958\) 0 0
\(959\) 9.69253 + 33.0097i 0.312988 + 1.06594i
\(960\) 0 0
\(961\) 8.41431 18.4248i 0.271429 0.594347i
\(962\) 0 0
\(963\) −12.3996 + 16.0596i −0.399570 + 0.517515i
\(964\) 0 0
\(965\) 23.1378 6.79388i 0.744833 0.218703i
\(966\) 0 0
\(967\) 25.9422 0.834244 0.417122 0.908850i \(-0.363039\pi\)
0.417122 + 0.908850i \(0.363039\pi\)
\(968\) 0 0
\(969\) 14.0531 + 24.0923i 0.451451 + 0.773956i
\(970\) 0 0
\(971\) 30.7269 + 26.6250i 0.986072 + 0.854436i 0.989350 0.145558i \(-0.0464978\pi\)
−0.00327763 + 0.999995i \(0.501043\pi\)
\(972\) 0 0
\(973\) 6.90521 + 15.1203i 0.221371 + 0.484735i
\(974\) 0 0
\(975\) 0.166985 3.86775i 0.00534781 0.123867i
\(976\) 0 0
\(977\) 11.2919 + 17.5706i 0.361261 + 0.562133i 0.973542 0.228507i \(-0.0733844\pi\)
−0.612281 + 0.790640i \(0.709748\pi\)
\(978\) 0 0
\(979\) −26.6451 + 3.83099i −0.851581 + 0.122439i
\(980\) 0 0
\(981\) −43.9178 + 2.48426i −1.40219 + 0.0793163i
\(982\) 0 0
\(983\) −19.2208 42.0876i −0.613047 1.34239i −0.920470 0.390813i \(-0.872194\pi\)
0.307423 0.951573i \(-0.400533\pi\)
\(984\) 0 0
\(985\) −4.40441 + 9.64431i −0.140336 + 0.307293i
\(986\) 0 0
\(987\) −1.21059 + 6.43521i −0.0385335 + 0.204835i
\(988\) 0 0
\(989\) 1.27194 + 0.373476i 0.0404454 + 0.0118758i
\(990\) 0 0
\(991\) 34.8046 + 5.00415i 1.10560 + 0.158962i 0.670854 0.741589i \(-0.265928\pi\)
0.434750 + 0.900551i \(0.356837\pi\)
\(992\) 0 0
\(993\) 8.44140 11.9667i 0.267880 0.379752i
\(994\) 0 0
\(995\) −4.65934 10.2025i −0.147711 0.323442i
\(996\) 0 0
\(997\) 38.6314 24.8269i 1.22347 0.786275i 0.240606 0.970623i \(-0.422654\pi\)
0.982861 + 0.184348i \(0.0590173\pi\)
\(998\) 0 0
\(999\) 2.12580 0.334687i 0.0672573 0.0105890i
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.s.b.161.8 yes 200
3.2 odd 2 inner 804.2.s.b.161.15 yes 200
67.5 odd 22 inner 804.2.s.b.5.15 yes 200
201.5 even 22 inner 804.2.s.b.5.8 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.s.b.5.8 200 201.5 even 22 inner
804.2.s.b.5.15 yes 200 67.5 odd 22 inner
804.2.s.b.161.8 yes 200 1.1 even 1 trivial
804.2.s.b.161.15 yes 200 3.2 odd 2 inner