Properties

Label 92.2.e.a.29.1
Level $92$
Weight $2$
Character 92.29
Analytic conductor $0.735$
Analytic rank $0$
Dimension $20$
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] = [92,2,Mod(9,92)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(92, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([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("92.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 92.e (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: \(0.734623698596\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + 14788 x^{12} - 23925 x^{11} + 35080 x^{10} - 43945 x^{9} + 57269 x^{8} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 29.1
Root \(0.291382 - 2.02660i\) of defining polynomial
Character \(\chi\) \(=\) 92.29
Dual form 92.2.e.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.96451 - 0.576832i) q^{3} +(3.22799 - 2.07450i) q^{5} +(0.267813 - 1.86268i) q^{7} +(1.00280 + 0.644459i) q^{9} +O(q^{10})\) \(q+(-1.96451 - 0.576832i) q^{3} +(3.22799 - 2.07450i) q^{5} +(0.267813 - 1.86268i) q^{7} +(1.00280 + 0.644459i) q^{9} +(0.804680 + 1.76200i) q^{11} +(-0.112273 - 0.780878i) q^{13} +(-7.53806 + 2.21337i) q^{15} +(-4.90640 + 5.66229i) q^{17} +(3.96265 + 4.57314i) q^{19} +(-1.60057 + 3.50477i) q^{21} +(-1.77773 - 4.45418i) q^{23} +(4.03929 - 8.84481i) q^{25} +(2.42411 + 2.79757i) q^{27} +(-1.75966 + 2.03076i) q^{29} +(2.65784 - 0.780411i) q^{31} +(-0.564421 - 3.92564i) q^{33} +(-2.99964 - 6.56830i) q^{35} +(8.29737 + 5.33239i) q^{37} +(-0.229873 + 1.59881i) q^{39} +(-5.52765 + 3.55240i) q^{41} +(-7.72022 - 2.26686i) q^{43} +4.57396 q^{45} -1.75371 q^{47} +(3.31859 + 0.974427i) q^{49} +(12.9049 - 8.29345i) q^{51} +(0.516246 - 3.59057i) q^{53} +(6.25279 + 4.01842i) q^{55} +(-5.14673 - 11.2698i) q^{57} +(0.999647 + 6.95269i) q^{59} +(-1.86952 + 0.548941i) q^{61} +(1.46898 - 1.69530i) q^{63} +(-1.98235 - 2.28776i) q^{65} +(4.08243 - 8.93929i) q^{67} +(0.923056 + 9.77572i) q^{69} +(-2.88802 + 6.32387i) q^{71} +(-8.63107 - 9.96078i) q^{73} +(-13.0372 + 15.0457i) q^{75} +(3.49756 - 1.02698i) q^{77} +(0.0541763 + 0.376804i) q^{79} +(-4.63402 - 10.1471i) q^{81} +(2.75842 + 1.77273i) q^{83} +(-4.09138 + 28.4562i) q^{85} +(4.62828 - 2.97442i) q^{87} +(-4.66512 - 1.36980i) q^{89} -1.48460 q^{91} -5.67151 q^{93} +(22.2784 + 6.54153i) q^{95} +(-7.65402 + 4.91894i) q^{97} +(-0.328608 + 2.28552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37} + 30 q^{39} + 28 q^{41} + 44 q^{43} + 78 q^{45} + 26 q^{47} + 60 q^{49} + 62 q^{51} + 14 q^{53} + 26 q^{55} + 3 q^{57} - 10 q^{59} - 56 q^{61} - 27 q^{63} - 87 q^{65} - 44 q^{67} - 51 q^{69} - 37 q^{71} - 12 q^{73} - 53 q^{75} - 47 q^{77} - 6 q^{79} - 10 q^{81} - 25 q^{83} + 8 q^{85} + 48 q^{87} + 10 q^{89} + 26 q^{91} - 14 q^{93} + 29 q^{95} - q^{97} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(47\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(1\)

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
\(3\) −1.96451 0.576832i −1.13421 0.333034i −0.339849 0.940480i \(-0.610376\pi\)
−0.794361 + 0.607446i \(0.792194\pi\)
\(4\) 0 0
\(5\) 3.22799 2.07450i 1.44360 0.927747i 0.444107 0.895974i \(-0.353521\pi\)
0.999495 0.0317727i \(-0.0101153\pi\)
\(6\) 0 0
\(7\) 0.267813 1.86268i 0.101224 0.704027i −0.874500 0.485025i \(-0.838811\pi\)
0.975724 0.219003i \(-0.0702803\pi\)
\(8\) 0 0
\(9\) 1.00280 + 0.644459i 0.334266 + 0.214820i
\(10\) 0 0
\(11\) 0.804680 + 1.76200i 0.242620 + 0.531264i 0.991293 0.131676i \(-0.0420357\pi\)
−0.748673 + 0.662940i \(0.769308\pi\)
\(12\) 0 0
\(13\) −0.112273 0.780878i −0.0311390 0.216577i 0.968311 0.249749i \(-0.0803481\pi\)
−0.999450 + 0.0331723i \(0.989439\pi\)
\(14\) 0 0
\(15\) −7.53806 + 2.21337i −1.94632 + 0.571491i
\(16\) 0 0
\(17\) −4.90640 + 5.66229i −1.18998 + 1.37331i −0.279292 + 0.960206i \(0.590100\pi\)
−0.910685 + 0.413101i \(0.864446\pi\)
\(18\) 0 0
\(19\) 3.96265 + 4.57314i 0.909095 + 1.04915i 0.998586 + 0.0531635i \(0.0169304\pi\)
−0.0894912 + 0.995988i \(0.528524\pi\)
\(20\) 0 0
\(21\) −1.60057 + 3.50477i −0.349274 + 0.764804i
\(22\) 0 0
\(23\) −1.77773 4.45418i −0.370682 0.928760i
\(24\) 0 0
\(25\) 4.03929 8.84481i 0.807858 1.76896i
\(26\) 0 0
\(27\) 2.42411 + 2.79757i 0.466521 + 0.538394i
\(28\) 0 0
\(29\) −1.75966 + 2.03076i −0.326761 + 0.377103i −0.895232 0.445601i \(-0.852990\pi\)
0.568470 + 0.822704i \(0.307535\pi\)
\(30\) 0 0
\(31\) 2.65784 0.780411i 0.477361 0.140166i −0.0341959 0.999415i \(-0.510887\pi\)
0.511557 + 0.859249i \(0.329069\pi\)
\(32\) 0 0
\(33\) −0.564421 3.92564i −0.0982531 0.683366i
\(34\) 0 0
\(35\) −2.99964 6.56830i −0.507032 1.11025i
\(36\) 0 0
\(37\) 8.29737 + 5.33239i 1.36408 + 0.876640i 0.998533 0.0541530i \(-0.0172459\pi\)
0.365546 + 0.930793i \(0.380882\pi\)
\(38\) 0 0
\(39\) −0.229873 + 1.59881i −0.0368092 + 0.256014i
\(40\) 0 0
\(41\) −5.52765 + 3.55240i −0.863273 + 0.554792i −0.895688 0.444682i \(-0.853317\pi\)
0.0324150 + 0.999474i \(0.489680\pi\)
\(42\) 0 0
\(43\) −7.72022 2.26686i −1.17732 0.345693i −0.366181 0.930544i \(-0.619335\pi\)
−0.811141 + 0.584851i \(0.801153\pi\)
\(44\) 0 0
\(45\) 4.57396 0.681845
\(46\) 0 0
\(47\) −1.75371 −0.255805 −0.127903 0.991787i \(-0.540824\pi\)
−0.127903 + 0.991787i \(0.540824\pi\)
\(48\) 0 0
\(49\) 3.31859 + 0.974427i 0.474085 + 0.139204i
\(50\) 0 0
\(51\) 12.9049 8.29345i 1.80704 1.16131i
\(52\) 0 0
\(53\) 0.516246 3.59057i 0.0709118 0.493203i −0.923155 0.384429i \(-0.874398\pi\)
0.994067 0.108774i \(-0.0346925\pi\)
\(54\) 0 0
\(55\) 6.25279 + 4.01842i 0.843126 + 0.541844i
\(56\) 0 0
\(57\) −5.14673 11.2698i −0.681701 1.49272i
\(58\) 0 0
\(59\) 0.999647 + 6.95269i 0.130143 + 0.905164i 0.945365 + 0.326015i \(0.105706\pi\)
−0.815222 + 0.579149i \(0.803385\pi\)
\(60\) 0 0
\(61\) −1.86952 + 0.548941i −0.239368 + 0.0702847i −0.399216 0.916857i \(-0.630718\pi\)
0.159848 + 0.987142i \(0.448899\pi\)
\(62\) 0 0
\(63\) 1.46898 1.69530i 0.185075 0.213587i
\(64\) 0 0
\(65\) −1.98235 2.28776i −0.245881 0.283761i
\(66\) 0 0
\(67\) 4.08243 8.93929i 0.498749 1.09211i −0.478125 0.878292i \(-0.658683\pi\)
0.976874 0.213816i \(-0.0685892\pi\)
\(68\) 0 0
\(69\) 0.923056 + 9.77572i 0.111123 + 1.17686i
\(70\) 0 0
\(71\) −2.88802 + 6.32387i −0.342745 + 0.750506i −0.999995 0.00316639i \(-0.998992\pi\)
0.657250 + 0.753672i \(0.271719\pi\)
\(72\) 0 0
\(73\) −8.63107 9.96078i −1.01019 1.16582i −0.986107 0.166111i \(-0.946879\pi\)
−0.0240830 0.999710i \(-0.507667\pi\)
\(74\) 0 0
\(75\) −13.0372 + 15.0457i −1.50540 + 1.73733i
\(76\) 0 0
\(77\) 3.49756 1.02698i 0.398584 0.117035i
\(78\) 0 0
\(79\) 0.0541763 + 0.376804i 0.00609531 + 0.0423938i 0.992642 0.121085i \(-0.0386375\pi\)
−0.986547 + 0.163479i \(0.947728\pi\)
\(80\) 0 0
\(81\) −4.63402 10.1471i −0.514891 1.12745i
\(82\) 0 0
\(83\) 2.75842 + 1.77273i 0.302776 + 0.194582i 0.683203 0.730229i \(-0.260587\pi\)
−0.380427 + 0.924811i \(0.624223\pi\)
\(84\) 0 0
\(85\) −4.09138 + 28.4562i −0.443773 + 3.08651i
\(86\) 0 0
\(87\) 4.62828 2.97442i 0.496204 0.318891i
\(88\) 0 0
\(89\) −4.66512 1.36980i −0.494501 0.145199i 0.0249672 0.999688i \(-0.492052\pi\)
−0.519469 + 0.854490i \(0.673870\pi\)
\(90\) 0 0
\(91\) −1.48460 −0.155628
\(92\) 0 0
\(93\) −5.67151 −0.588108
\(94\) 0 0
\(95\) 22.2784 + 6.54153i 2.28572 + 0.671147i
\(96\) 0 0
\(97\) −7.65402 + 4.91894i −0.777148 + 0.499443i −0.868086 0.496414i \(-0.834650\pi\)
0.0909378 + 0.995857i \(0.471014\pi\)
\(98\) 0 0
\(99\) −0.328608 + 2.28552i −0.0330263 + 0.229703i
\(100\) 0 0
\(101\) −2.57015 1.65173i −0.255739 0.164353i 0.406489 0.913655i \(-0.366753\pi\)
−0.662228 + 0.749302i \(0.730389\pi\)
\(102\) 0 0
\(103\) −3.24333 7.10191i −0.319575 0.699772i 0.679861 0.733341i \(-0.262040\pi\)
−0.999436 + 0.0335688i \(0.989313\pi\)
\(104\) 0 0
\(105\) 2.10402 + 14.6338i 0.205331 + 1.42811i
\(106\) 0 0
\(107\) −1.69097 + 0.496515i −0.163473 + 0.0479999i −0.362445 0.932005i \(-0.618058\pi\)
0.198972 + 0.980005i \(0.436240\pi\)
\(108\) 0 0
\(109\) 5.60965 6.47388i 0.537307 0.620085i −0.420572 0.907259i \(-0.638170\pi\)
0.957878 + 0.287174i \(0.0927159\pi\)
\(110\) 0 0
\(111\) −13.2244 15.2617i −1.25520 1.44858i
\(112\) 0 0
\(113\) 0.270448 0.592199i 0.0254416 0.0557094i −0.896485 0.443075i \(-0.853888\pi\)
0.921926 + 0.387366i \(0.126615\pi\)
\(114\) 0 0
\(115\) −14.9787 10.6901i −1.39677 0.996860i
\(116\) 0 0
\(117\) 0.390657 0.855419i 0.0361162 0.0790835i
\(118\) 0 0
\(119\) 9.23304 + 10.6555i 0.846392 + 0.976788i
\(120\) 0 0
\(121\) 4.74632 5.47755i 0.431484 0.497959i
\(122\) 0 0
\(123\) 12.9082 3.79020i 1.16390 0.341751i
\(124\) 0 0
\(125\) −2.57941 17.9402i −0.230709 1.60462i
\(126\) 0 0
\(127\) −0.830695 1.81897i −0.0737122 0.161407i 0.869189 0.494480i \(-0.164642\pi\)
−0.942901 + 0.333073i \(0.891914\pi\)
\(128\) 0 0
\(129\) 13.8588 + 8.90653i 1.22020 + 0.784177i
\(130\) 0 0
\(131\) 1.34552 9.35830i 0.117559 0.817639i −0.842671 0.538428i \(-0.819018\pi\)
0.960230 0.279210i \(-0.0900726\pi\)
\(132\) 0 0
\(133\) 9.57956 6.15641i 0.830653 0.533828i
\(134\) 0 0
\(135\) 13.6286 + 4.00172i 1.17296 + 0.344413i
\(136\) 0 0
\(137\) −2.06670 −0.176570 −0.0882850 0.996095i \(-0.528139\pi\)
−0.0882850 + 0.996095i \(0.528139\pi\)
\(138\) 0 0
\(139\) 1.69986 0.144180 0.0720900 0.997398i \(-0.477033\pi\)
0.0720900 + 0.997398i \(0.477033\pi\)
\(140\) 0 0
\(141\) 3.44518 + 1.01160i 0.290137 + 0.0851918i
\(142\) 0 0
\(143\) 1.28557 0.826184i 0.107504 0.0690889i
\(144\) 0 0
\(145\) −1.46736 + 10.2057i −0.121858 + 0.847538i
\(146\) 0 0
\(147\) −5.95732 3.82854i −0.491352 0.315773i
\(148\) 0 0
\(149\) −7.27513 15.9303i −0.596002 1.30506i −0.931747 0.363109i \(-0.881715\pi\)
0.335745 0.941953i \(-0.391012\pi\)
\(150\) 0 0
\(151\) 1.18599 + 8.24877i 0.0965149 + 0.671276i 0.979436 + 0.201755i \(0.0646643\pi\)
−0.882921 + 0.469521i \(0.844427\pi\)
\(152\) 0 0
\(153\) −8.56924 + 2.51616i −0.692782 + 0.203419i
\(154\) 0 0
\(155\) 6.96051 8.03285i 0.559081 0.645214i
\(156\) 0 0
\(157\) 4.40887 + 5.08810i 0.351866 + 0.406075i 0.903898 0.427748i \(-0.140693\pi\)
−0.552032 + 0.833823i \(0.686147\pi\)
\(158\) 0 0
\(159\) −3.08532 + 6.75592i −0.244682 + 0.535779i
\(160\) 0 0
\(161\) −8.77281 + 2.11846i −0.691394 + 0.166958i
\(162\) 0 0
\(163\) −6.50265 + 14.2388i −0.509327 + 1.11527i 0.463997 + 0.885837i \(0.346415\pi\)
−0.973324 + 0.229434i \(0.926313\pi\)
\(164\) 0 0
\(165\) −9.96570 11.5010i −0.775829 0.895354i
\(166\) 0 0
\(167\) −12.5986 + 14.5396i −0.974908 + 1.12510i 0.0172165 + 0.999852i \(0.494520\pi\)
−0.992125 + 0.125252i \(0.960026\pi\)
\(168\) 0 0
\(169\) 11.8762 3.48718i 0.913557 0.268245i
\(170\) 0 0
\(171\) 1.02653 + 7.13970i 0.0785010 + 0.545987i
\(172\) 0 0
\(173\) 3.59270 + 7.86692i 0.273148 + 0.598111i 0.995641 0.0932675i \(-0.0297312\pi\)
−0.722493 + 0.691378i \(0.757004\pi\)
\(174\) 0 0
\(175\) −15.3933 9.89266i −1.16362 0.747815i
\(176\) 0 0
\(177\) 2.04672 14.2353i 0.153841 1.06999i
\(178\) 0 0
\(179\) −5.83152 + 3.74769i −0.435868 + 0.280115i −0.740118 0.672477i \(-0.765230\pi\)
0.304250 + 0.952592i \(0.401594\pi\)
\(180\) 0 0
\(181\) 4.88561 + 1.43455i 0.363145 + 0.106629i 0.458214 0.888842i \(-0.348489\pi\)
−0.0950696 + 0.995471i \(0.530307\pi\)
\(182\) 0 0
\(183\) 3.98934 0.294900
\(184\) 0 0
\(185\) 37.8459 2.78249
\(186\) 0 0
\(187\) −13.9251 4.08877i −1.01830 0.299000i
\(188\) 0 0
\(189\) 5.86020 3.76612i 0.426267 0.273945i
\(190\) 0 0
\(191\) 3.45452 24.0267i 0.249960 1.73851i −0.348453 0.937326i \(-0.613293\pi\)
0.598414 0.801187i \(-0.295798\pi\)
\(192\) 0 0
\(193\) 10.8361 + 6.96394i 0.779999 + 0.501275i 0.869033 0.494753i \(-0.164742\pi\)
−0.0890340 + 0.996029i \(0.528378\pi\)
\(194\) 0 0
\(195\) 2.57470 + 5.63780i 0.184378 + 0.403731i
\(196\) 0 0
\(197\) 0.304917 + 2.12074i 0.0217244 + 0.151097i 0.997796 0.0663514i \(-0.0211358\pi\)
−0.976072 + 0.217448i \(0.930227\pi\)
\(198\) 0 0
\(199\) −23.2441 + 6.82508i −1.64773 + 0.483817i −0.968272 0.249899i \(-0.919603\pi\)
−0.679457 + 0.733716i \(0.737784\pi\)
\(200\) 0 0
\(201\) −13.1764 + 15.2064i −0.929394 + 1.07258i
\(202\) 0 0
\(203\) 3.31140 + 3.82156i 0.232415 + 0.268221i
\(204\) 0 0
\(205\) −10.4737 + 22.9343i −0.731516 + 1.60180i
\(206\) 0 0
\(207\) 1.08783 5.61231i 0.0756094 0.390083i
\(208\) 0 0
\(209\) −4.86923 + 10.6621i −0.336812 + 0.737515i
\(210\) 0 0
\(211\) −14.3395 16.5486i −0.987169 1.13925i −0.990256 0.139258i \(-0.955528\pi\)
0.00308717 0.999995i \(-0.499017\pi\)
\(212\) 0 0
\(213\) 9.32134 10.7574i 0.638688 0.737085i
\(214\) 0 0
\(215\) −29.6234 + 8.69822i −2.02030 + 0.593214i
\(216\) 0 0
\(217\) −0.741854 5.15971i −0.0503603 0.350264i
\(218\) 0 0
\(219\) 11.2101 + 24.5467i 0.757509 + 1.65871i
\(220\) 0 0
\(221\) 4.97242 + 3.19558i 0.334481 + 0.214958i
\(222\) 0 0
\(223\) −0.738261 + 5.13472i −0.0494376 + 0.343846i 0.950058 + 0.312075i \(0.101024\pi\)
−0.999495 + 0.0317713i \(0.989885\pi\)
\(224\) 0 0
\(225\) 9.75070 6.26640i 0.650047 0.417760i
\(226\) 0 0
\(227\) 6.22585 + 1.82807i 0.413224 + 0.121334i 0.481735 0.876317i \(-0.340007\pi\)
−0.0685112 + 0.997650i \(0.521825\pi\)
\(228\) 0 0
\(229\) −18.1325 −1.19823 −0.599116 0.800662i \(-0.704481\pi\)
−0.599116 + 0.800662i \(0.704481\pi\)
\(230\) 0 0
\(231\) −7.46337 −0.491054
\(232\) 0 0
\(233\) −14.1559 4.15654i −0.927383 0.272304i −0.217042 0.976162i \(-0.569641\pi\)
−0.710341 + 0.703858i \(0.751459\pi\)
\(234\) 0 0
\(235\) −5.66097 + 3.63808i −0.369281 + 0.237322i
\(236\) 0 0
\(237\) 0.110923 0.771486i 0.00720522 0.0501134i
\(238\) 0 0
\(239\) 13.9897 + 8.99062i 0.904917 + 0.581555i 0.908245 0.418440i \(-0.137423\pi\)
−0.00332787 + 0.999994i \(0.501059\pi\)
\(240\) 0 0
\(241\) 6.08552 + 13.3254i 0.392003 + 0.858366i 0.998019 + 0.0629140i \(0.0200394\pi\)
−0.606016 + 0.795452i \(0.707233\pi\)
\(242\) 0 0
\(243\) 1.66998 + 11.6149i 0.107129 + 0.745099i
\(244\) 0 0
\(245\) 12.7338 3.73899i 0.813535 0.238876i
\(246\) 0 0
\(247\) 3.12617 3.60779i 0.198913 0.229558i
\(248\) 0 0
\(249\) −4.39637 5.07368i −0.278609 0.321531i
\(250\) 0 0
\(251\) 7.88046 17.2558i 0.497410 1.08918i −0.479892 0.877327i \(-0.659324\pi\)
0.977302 0.211849i \(-0.0679484\pi\)
\(252\) 0 0
\(253\) 6.41777 6.71655i 0.403482 0.422266i
\(254\) 0 0
\(255\) 24.4520 53.5424i 1.53124 3.35295i
\(256\) 0 0
\(257\) 12.8045 + 14.7771i 0.798720 + 0.921772i 0.998310 0.0581072i \(-0.0185065\pi\)
−0.199590 + 0.979879i \(0.563961\pi\)
\(258\) 0 0
\(259\) 12.1547 14.0273i 0.755256 0.871612i
\(260\) 0 0
\(261\) −3.07333 + 0.902410i −0.190234 + 0.0558578i
\(262\) 0 0
\(263\) −0.718442 4.99688i −0.0443010 0.308121i −0.999909 0.0134798i \(-0.995709\pi\)
0.955608 0.294641i \(-0.0952000\pi\)
\(264\) 0 0
\(265\) −5.78221 12.6613i −0.355199 0.777776i
\(266\) 0 0
\(267\) 8.37452 + 5.38197i 0.512512 + 0.329372i
\(268\) 0 0
\(269\) 2.21563 15.4101i 0.135090 0.939568i −0.803690 0.595049i \(-0.797133\pi\)
0.938779 0.344520i \(-0.111958\pi\)
\(270\) 0 0
\(271\) −14.8244 + 9.52705i −0.900517 + 0.578727i −0.906943 0.421252i \(-0.861591\pi\)
0.00642675 + 0.999979i \(0.497954\pi\)
\(272\) 0 0
\(273\) 2.91650 + 0.856362i 0.176515 + 0.0518294i
\(274\) 0 0
\(275\) 18.8349 1.13579
\(276\) 0 0
\(277\) −2.75886 −0.165764 −0.0828820 0.996559i \(-0.526412\pi\)
−0.0828820 + 0.996559i \(0.526412\pi\)
\(278\) 0 0
\(279\) 3.16821 + 0.930272i 0.189676 + 0.0556939i
\(280\) 0 0
\(281\) −1.04029 + 0.668553i −0.0620584 + 0.0398825i −0.571302 0.820740i \(-0.693562\pi\)
0.509244 + 0.860622i \(0.329925\pi\)
\(282\) 0 0
\(283\) −0.120397 + 0.837378i −0.00715685 + 0.0497770i −0.993087 0.117381i \(-0.962550\pi\)
0.985930 + 0.167158i \(0.0534591\pi\)
\(284\) 0 0
\(285\) −39.9928 25.7018i −2.36897 1.52244i
\(286\) 0 0
\(287\) 5.13662 + 11.2476i 0.303205 + 0.663926i
\(288\) 0 0
\(289\) −5.56939 38.7360i −0.327611 2.27859i
\(290\) 0 0
\(291\) 17.8738 5.24822i 1.04778 0.307656i
\(292\) 0 0
\(293\) −9.29563 + 10.7277i −0.543057 + 0.626721i −0.959251 0.282555i \(-0.908818\pi\)
0.416195 + 0.909276i \(0.363364\pi\)
\(294\) 0 0
\(295\) 17.6502 + 20.3695i 1.02764 + 1.18596i
\(296\) 0 0
\(297\) −2.97870 + 6.52245i −0.172842 + 0.378471i
\(298\) 0 0
\(299\) −3.27858 + 1.88828i −0.189605 + 0.109202i
\(300\) 0 0
\(301\) −6.29002 + 13.7732i −0.362550 + 0.793875i
\(302\) 0 0
\(303\) 4.09630 + 4.72738i 0.235326 + 0.271581i
\(304\) 0 0
\(305\) −4.89602 + 5.65031i −0.280345 + 0.323536i
\(306\) 0 0
\(307\) 15.0430 4.41703i 0.858551 0.252093i 0.177312 0.984155i \(-0.443260\pi\)
0.681239 + 0.732061i \(0.261442\pi\)
\(308\) 0 0
\(309\) 2.27495 + 15.8226i 0.129417 + 0.900117i
\(310\) 0 0
\(311\) 6.30890 + 13.8146i 0.357745 + 0.783352i 0.999860 + 0.0167438i \(0.00532996\pi\)
−0.642115 + 0.766608i \(0.721943\pi\)
\(312\) 0 0
\(313\) 0.201698 + 0.129623i 0.0114006 + 0.00732674i 0.546329 0.837571i \(-0.316025\pi\)
−0.534928 + 0.844898i \(0.679661\pi\)
\(314\) 0 0
\(315\) 1.22497 8.51982i 0.0690190 0.480038i
\(316\) 0 0
\(317\) −1.79447 + 1.15324i −0.100788 + 0.0647723i −0.590064 0.807357i \(-0.700897\pi\)
0.489276 + 0.872129i \(0.337261\pi\)
\(318\) 0 0
\(319\) −4.99417 1.46642i −0.279620 0.0821039i
\(320\) 0 0
\(321\) 3.60834 0.201398
\(322\) 0 0
\(323\) −45.3368 −2.52261
\(324\) 0 0
\(325\) −7.36022 2.16116i −0.408272 0.119879i
\(326\) 0 0
\(327\) −14.7545 + 9.48216i −0.815928 + 0.524365i
\(328\) 0 0
\(329\) −0.469667 + 3.26661i −0.0258936 + 0.180094i
\(330\) 0 0
\(331\) 19.5337 + 12.5535i 1.07367 + 0.690005i 0.953086 0.302698i \(-0.0978875\pi\)
0.120582 + 0.992703i \(0.461524\pi\)
\(332\) 0 0
\(333\) 4.88407 + 10.6946i 0.267645 + 0.586062i
\(334\) 0 0
\(335\) −5.36652 37.3250i −0.293204 2.03928i
\(336\) 0 0
\(337\) 9.46693 2.77974i 0.515697 0.151422i −0.0135206 0.999909i \(-0.504304\pi\)
0.529217 + 0.848486i \(0.322486\pi\)
\(338\) 0 0
\(339\) −0.872896 + 1.00738i −0.0474092 + 0.0547132i
\(340\) 0 0
\(341\) 3.51380 + 4.05514i 0.190283 + 0.219598i
\(342\) 0 0
\(343\) 8.17601 17.9030i 0.441463 0.966669i
\(344\) 0 0
\(345\) 23.2594 + 29.6410i 1.25224 + 1.59582i
\(346\) 0 0
\(347\) −6.24758 + 13.6803i −0.335388 + 0.734397i −0.999917 0.0128652i \(-0.995905\pi\)
0.664529 + 0.747262i \(0.268632\pi\)
\(348\) 0 0
\(349\) 17.4702 + 20.1617i 0.935158 + 1.07923i 0.996704 + 0.0811261i \(0.0258516\pi\)
−0.0615454 + 0.998104i \(0.519603\pi\)
\(350\) 0 0
\(351\) 1.91240 2.20703i 0.102077 0.117803i
\(352\) 0 0
\(353\) −10.0682 + 2.95629i −0.535877 + 0.157348i −0.538463 0.842649i \(-0.680995\pi\)
0.00258650 + 0.999997i \(0.499177\pi\)
\(354\) 0 0
\(355\) 3.79641 + 26.4046i 0.201493 + 1.40141i
\(356\) 0 0
\(357\) −11.9920 26.2587i −0.634682 1.38976i
\(358\) 0 0
\(359\) −25.2421 16.2221i −1.33223 0.856170i −0.335908 0.941895i \(-0.609043\pi\)
−0.996319 + 0.0857246i \(0.972679\pi\)
\(360\) 0 0
\(361\) −2.50705 + 17.4369i −0.131950 + 0.917734i
\(362\) 0 0
\(363\) −12.4838 + 8.02286i −0.655230 + 0.421091i
\(364\) 0 0
\(365\) −48.5247 14.2481i −2.53990 0.745782i
\(366\) 0 0
\(367\) −4.42878 −0.231181 −0.115590 0.993297i \(-0.536876\pi\)
−0.115590 + 0.993297i \(0.536876\pi\)
\(368\) 0 0
\(369\) −7.83249 −0.407743
\(370\) 0 0
\(371\) −6.54983 1.92320i −0.340050 0.0998477i
\(372\) 0 0
\(373\) 11.9565 7.68400i 0.619086 0.397863i −0.193168 0.981166i \(-0.561876\pi\)
0.812255 + 0.583303i \(0.198240\pi\)
\(374\) 0 0
\(375\) −5.28119 + 36.7315i −0.272720 + 1.89681i
\(376\) 0 0
\(377\) 1.78334 + 1.14608i 0.0918467 + 0.0590263i
\(378\) 0 0
\(379\) −9.26397 20.2853i −0.475858 1.04198i −0.983582 0.180464i \(-0.942240\pi\)
0.507723 0.861520i \(-0.330487\pi\)
\(380\) 0 0
\(381\) 0.582668 + 4.05255i 0.0298510 + 0.207618i
\(382\) 0 0
\(383\) 32.9588 9.67757i 1.68412 0.494501i 0.707001 0.707213i \(-0.250048\pi\)
0.977115 + 0.212712i \(0.0682296\pi\)
\(384\) 0 0
\(385\) 9.15962 10.5708i 0.466817 0.538736i
\(386\) 0 0
\(387\) −6.28092 7.24857i −0.319277 0.368465i
\(388\) 0 0
\(389\) 3.70219 8.10666i 0.187708 0.411024i −0.792258 0.610186i \(-0.791095\pi\)
0.979967 + 0.199162i \(0.0638220\pi\)
\(390\) 0 0
\(391\) 33.9431 + 11.7880i 1.71658 + 0.596142i
\(392\) 0 0
\(393\) −8.04145 + 17.6083i −0.405638 + 0.888222i
\(394\) 0 0
\(395\) 0.956563 + 1.10393i 0.0481299 + 0.0555449i
\(396\) 0 0
\(397\) 22.7369 26.2398i 1.14113 1.31694i 0.199653 0.979867i \(-0.436019\pi\)
0.941480 0.337070i \(-0.109436\pi\)
\(398\) 0 0
\(399\) −22.3703 + 6.56852i −1.11992 + 0.328837i
\(400\) 0 0
\(401\) 0.0741208 + 0.515522i 0.00370142 + 0.0257439i 0.991588 0.129431i \(-0.0413150\pi\)
−0.987887 + 0.155175i \(0.950406\pi\)
\(402\) 0 0
\(403\) −0.907810 1.98783i −0.0452212 0.0990207i
\(404\) 0 0
\(405\) −36.0087 23.1414i −1.78929 1.14991i
\(406\) 0 0
\(407\) −2.71897 + 18.9109i −0.134774 + 0.937377i
\(408\) 0 0
\(409\) 5.70238 3.66470i 0.281965 0.181208i −0.392012 0.919960i \(-0.628221\pi\)
0.673977 + 0.738752i \(0.264585\pi\)
\(410\) 0 0
\(411\) 4.06005 + 1.19214i 0.200267 + 0.0588038i
\(412\) 0 0
\(413\) 13.2184 0.650434
\(414\) 0 0
\(415\) 12.5817 0.617610
\(416\) 0 0
\(417\) −3.33938 0.980532i −0.163530 0.0480168i
\(418\) 0 0
\(419\) 5.04672 3.24333i 0.246548 0.158447i −0.411531 0.911396i \(-0.635006\pi\)
0.658079 + 0.752949i \(0.271369\pi\)
\(420\) 0 0
\(421\) −1.38237 + 9.61457i −0.0673724 + 0.468585i 0.928007 + 0.372563i \(0.121521\pi\)
−0.995379 + 0.0960221i \(0.969388\pi\)
\(422\) 0 0
\(423\) −1.75862 1.13020i −0.0855070 0.0549520i
\(424\) 0 0
\(425\) 30.2635 + 66.2678i 1.46800 + 3.21446i
\(426\) 0 0
\(427\) 0.521820 + 3.62934i 0.0252526 + 0.175636i
\(428\) 0 0
\(429\) −3.00208 + 0.881489i −0.144942 + 0.0425587i
\(430\) 0 0
\(431\) 8.73778 10.0839i 0.420884 0.485726i −0.505222 0.862989i \(-0.668589\pi\)
0.926106 + 0.377263i \(0.123135\pi\)
\(432\) 0 0
\(433\) −10.8888 12.5664i −0.523283 0.603900i 0.431167 0.902272i \(-0.358102\pi\)
−0.954450 + 0.298372i \(0.903556\pi\)
\(434\) 0 0
\(435\) 8.76961 19.2028i 0.420471 0.920703i
\(436\) 0 0
\(437\) 13.3251 25.7802i 0.637424 1.23323i
\(438\) 0 0
\(439\) 15.0542 32.9642i 0.718499 1.57329i −0.0974963 0.995236i \(-0.531083\pi\)
0.815996 0.578058i \(-0.196189\pi\)
\(440\) 0 0
\(441\) 2.69990 + 3.11585i 0.128567 + 0.148374i
\(442\) 0 0
\(443\) −6.00878 + 6.93450i −0.285486 + 0.329468i −0.880320 0.474380i \(-0.842672\pi\)
0.594834 + 0.803848i \(0.297218\pi\)
\(444\) 0 0
\(445\) −17.9006 + 5.25610i −0.848571 + 0.249163i
\(446\) 0 0
\(447\) 5.10294 + 35.4918i 0.241361 + 1.67870i
\(448\) 0 0
\(449\) −8.66462 18.9729i −0.408909 0.895385i −0.996289 0.0860740i \(-0.972568\pi\)
0.587380 0.809311i \(-0.300159\pi\)
\(450\) 0 0
\(451\) −10.7073 6.88119i −0.504189 0.324022i
\(452\) 0 0
\(453\) 2.42826 16.8889i 0.114090 0.793510i
\(454\) 0 0
\(455\) −4.79226 + 3.07980i −0.224665 + 0.144383i
\(456\) 0 0
\(457\) 7.71162 + 2.26434i 0.360734 + 0.105921i 0.457077 0.889427i \(-0.348896\pi\)
−0.0963428 + 0.995348i \(0.530714\pi\)
\(458\) 0 0
\(459\) −27.7344 −1.29453
\(460\) 0 0
\(461\) −3.23977 −0.150891 −0.0754455 0.997150i \(-0.524038\pi\)
−0.0754455 + 0.997150i \(0.524038\pi\)
\(462\) 0 0
\(463\) 8.62234 + 2.53175i 0.400714 + 0.117660i 0.475879 0.879511i \(-0.342130\pi\)
−0.0751646 + 0.997171i \(0.523948\pi\)
\(464\) 0 0
\(465\) −18.3076 + 11.7656i −0.848994 + 0.545615i
\(466\) 0 0
\(467\) 3.24689 22.5826i 0.150248 1.04500i −0.765555 0.643370i \(-0.777536\pi\)
0.915803 0.401627i \(-0.131555\pi\)
\(468\) 0 0
\(469\) −15.5577 9.99833i −0.718388 0.461680i
\(470\) 0 0
\(471\) −5.72628 12.5388i −0.263853 0.577757i
\(472\) 0 0
\(473\) −2.21809 15.4272i −0.101988 0.709341i
\(474\) 0 0
\(475\) 56.4549 16.5766i 2.59033 0.760589i
\(476\) 0 0
\(477\) 2.83166 3.26792i 0.129653 0.149628i
\(478\) 0 0
\(479\) −0.320654 0.370054i −0.0146511 0.0169082i 0.748377 0.663274i \(-0.230834\pi\)
−0.763028 + 0.646366i \(0.776288\pi\)
\(480\) 0 0
\(481\) 3.23238 7.07792i 0.147384 0.322725i
\(482\) 0 0
\(483\) 18.4563 + 0.898706i 0.839788 + 0.0408925i
\(484\) 0 0
\(485\) −14.5028 + 31.7566i −0.658536 + 1.44199i
\(486\) 0 0
\(487\) 8.88989 + 10.2595i 0.402839 + 0.464901i 0.920533 0.390665i \(-0.127755\pi\)
−0.517694 + 0.855566i \(0.673209\pi\)
\(488\) 0 0
\(489\) 20.9879 24.2213i 0.949106 1.09533i
\(490\) 0 0
\(491\) 10.3852 3.04937i 0.468677 0.137616i −0.0388622 0.999245i \(-0.512373\pi\)
0.507539 + 0.861629i \(0.330555\pi\)
\(492\) 0 0
\(493\) −2.86513 19.9275i −0.129039 0.897487i
\(494\) 0 0
\(495\) 3.68057 + 8.05933i 0.165429 + 0.362240i
\(496\) 0 0
\(497\) 11.0059 + 7.07307i 0.493683 + 0.317271i
\(498\) 0 0
\(499\) 5.04370 35.0797i 0.225787 1.57038i −0.489784 0.871844i \(-0.662925\pi\)
0.715571 0.698540i \(-0.246166\pi\)
\(500\) 0 0
\(501\) 33.1369 21.2958i 1.48045 0.951426i
\(502\) 0 0
\(503\) 21.3170 + 6.25923i 0.950478 + 0.279085i 0.719986 0.693989i \(-0.244148\pi\)
0.230492 + 0.973074i \(0.425966\pi\)
\(504\) 0 0
\(505\) −11.7229 −0.521664
\(506\) 0 0
\(507\) −25.3425 −1.12550
\(508\) 0 0
\(509\) 30.5783 + 8.97860i 1.35536 + 0.397970i 0.877125 0.480262i \(-0.159459\pi\)
0.478235 + 0.878232i \(0.341277\pi\)
\(510\) 0 0
\(511\) −20.8653 + 13.4093i −0.923026 + 0.593193i
\(512\) 0 0
\(513\) −3.18780 + 22.1716i −0.140745 + 0.978901i
\(514\) 0 0
\(515\) −25.2024 16.1966i −1.11055 0.713707i
\(516\) 0 0
\(517\) −1.41118 3.09005i −0.0620635 0.135900i
\(518\) 0 0
\(519\) −2.52000 17.5270i −0.110616 0.769350i
\(520\) 0 0
\(521\) −23.2469 + 6.82590i −1.01846 + 0.299048i −0.748012 0.663685i \(-0.768992\pi\)
−0.270453 + 0.962733i \(0.587173\pi\)
\(522\) 0 0
\(523\) −27.0894 + 31.2628i −1.18454 + 1.36703i −0.269831 + 0.962908i \(0.586968\pi\)
−0.914706 + 0.404121i \(0.867578\pi\)
\(524\) 0 0
\(525\) 24.5338 + 28.3136i 1.07074 + 1.23570i
\(526\) 0 0
\(527\) −8.62150 + 18.8784i −0.375558 + 0.822358i
\(528\) 0 0
\(529\) −16.6794 + 15.8366i −0.725189 + 0.688550i
\(530\) 0 0
\(531\) −3.47828 + 7.61638i −0.150945 + 0.330523i
\(532\) 0 0
\(533\) 3.39460 + 3.91758i 0.147037 + 0.169689i
\(534\) 0 0
\(535\) −4.42843 + 5.11068i −0.191458 + 0.220954i
\(536\) 0 0
\(537\) 13.6178 3.99856i 0.587654 0.172551i
\(538\) 0 0
\(539\) 0.953462 + 6.63148i 0.0410685 + 0.285638i
\(540\) 0 0
\(541\) 16.5874 + 36.3214i 0.713149 + 1.56158i 0.823264 + 0.567659i \(0.192151\pi\)
−0.110116 + 0.993919i \(0.535122\pi\)
\(542\) 0 0
\(543\) −8.77034 5.63635i −0.376371 0.241879i
\(544\) 0 0
\(545\) 4.67781 32.5349i 0.200375 1.39364i
\(546\) 0 0
\(547\) −29.5547 + 18.9937i −1.26367 + 0.812111i −0.988782 0.149366i \(-0.952277\pi\)
−0.274887 + 0.961477i \(0.588640\pi\)
\(548\) 0 0
\(549\) −2.22852 0.654353i −0.0951110 0.0279271i
\(550\) 0 0
\(551\) −16.2599 −0.692695
\(552\) 0 0
\(553\) 0.716375 0.0304634
\(554\) 0 0
\(555\) −74.3486 21.8307i −3.15592 0.926662i
\(556\) 0 0
\(557\) −32.8275 + 21.0970i −1.39095 + 0.893907i −0.999653 0.0263580i \(-0.991609\pi\)
−0.391295 + 0.920265i \(0.627973\pi\)
\(558\) 0 0
\(559\) −0.903368 + 6.28306i −0.0382084 + 0.265745i
\(560\) 0 0
\(561\) 24.9974 + 16.0648i 1.05539 + 0.678258i
\(562\) 0 0
\(563\) 15.0969 + 33.0575i 0.636257 + 1.39321i 0.903084 + 0.429463i \(0.141297\pi\)
−0.266828 + 0.963744i \(0.585976\pi\)
\(564\) 0 0
\(565\) −0.355515 2.47266i −0.0149566 0.104025i
\(566\) 0 0
\(567\) −20.1418 + 5.91418i −0.845878 + 0.248372i
\(568\) 0 0
\(569\) 24.1240 27.8406i 1.01133 1.16714i 0.0254519 0.999676i \(-0.491898\pi\)
0.985879 0.167462i \(-0.0535570\pi\)
\(570\) 0 0
\(571\) 4.36811 + 5.04106i 0.182800 + 0.210962i 0.839752 0.542970i \(-0.182700\pi\)
−0.656953 + 0.753932i \(0.728155\pi\)
\(572\) 0 0
\(573\) −20.6458 + 45.2080i −0.862491 + 1.88859i
\(574\) 0 0
\(575\) −46.5771 2.26802i −1.94240 0.0945829i
\(576\) 0 0
\(577\) 2.74466 6.00998i 0.114262 0.250199i −0.843858 0.536567i \(-0.819721\pi\)
0.958120 + 0.286368i \(0.0924481\pi\)
\(578\) 0 0
\(579\) −17.2706 19.9313i −0.717741 0.828317i
\(580\) 0 0
\(581\) 4.04077 4.66329i 0.167639 0.193466i
\(582\) 0 0
\(583\) 6.74201 1.97963i 0.279226 0.0819880i
\(584\) 0 0
\(585\) −0.513533 3.57170i −0.0212320 0.147672i
\(586\) 0 0
\(587\) 15.6309 + 34.2268i 0.645155 + 1.41269i 0.895731 + 0.444596i \(0.146653\pi\)
−0.250576 + 0.968097i \(0.580620\pi\)
\(588\) 0 0
\(589\) 14.1010 + 9.06217i 0.581022 + 0.373400i
\(590\) 0 0
\(591\) 0.624300 4.34210i 0.0256803 0.178610i
\(592\) 0 0
\(593\) 18.3734 11.8079i 0.754507 0.484892i −0.105978 0.994369i \(-0.533797\pi\)
0.860485 + 0.509476i \(0.170161\pi\)
\(594\) 0 0
\(595\) 51.9091 + 15.2419i 2.12806 + 0.624856i
\(596\) 0 0
\(597\) 49.6001 2.03000
\(598\) 0 0
\(599\) 24.6893 1.00878 0.504389 0.863477i \(-0.331718\pi\)
0.504389 + 0.863477i \(0.331718\pi\)
\(600\) 0 0
\(601\) −28.3417 8.32189i −1.15608 0.339457i −0.353174 0.935558i \(-0.614898\pi\)
−0.802910 + 0.596101i \(0.796716\pi\)
\(602\) 0 0
\(603\) 9.85486 6.33333i 0.401321 0.257913i
\(604\) 0 0
\(605\) 3.95789 27.5277i 0.160911 1.11916i
\(606\) 0 0
\(607\) −19.0056 12.2142i −0.771414 0.495757i 0.0947603 0.995500i \(-0.469792\pi\)
−0.866174 + 0.499743i \(0.833428\pi\)
\(608\) 0 0
\(609\) −4.30087 9.41760i −0.174280 0.381620i
\(610\) 0 0
\(611\) 0.196895 + 1.36944i 0.00796553 + 0.0554014i
\(612\) 0 0
\(613\) 26.2691 7.71331i 1.06100 0.311538i 0.295746 0.955266i \(-0.404432\pi\)
0.765254 + 0.643729i \(0.222613\pi\)
\(614\) 0 0
\(615\) 33.8049 39.0130i 1.36315 1.57315i
\(616\) 0 0
\(617\) −23.5656 27.1961i −0.948714 1.09487i −0.995385 0.0959635i \(-0.969407\pi\)
0.0466713 0.998910i \(-0.485139\pi\)
\(618\) 0 0
\(619\) −8.77016 + 19.2040i −0.352503 + 0.771873i 0.647450 + 0.762108i \(0.275836\pi\)
−0.999952 + 0.00976497i \(0.996892\pi\)
\(620\) 0 0
\(621\) 8.15147 15.7708i 0.327107 0.632859i
\(622\) 0 0
\(623\) −3.80088 + 8.32278i −0.152279 + 0.333445i
\(624\) 0 0
\(625\) −13.7056 15.8171i −0.548222 0.632682i
\(626\) 0 0
\(627\) 15.7159 18.1371i 0.627632 0.724326i
\(628\) 0 0
\(629\) −70.9038 + 20.8192i −2.82712 + 0.830117i
\(630\) 0 0
\(631\) −2.20429 15.3312i −0.0877514 0.610324i −0.985482 0.169780i \(-0.945694\pi\)
0.897731 0.440545i \(-0.145215\pi\)
\(632\) 0 0
\(633\) 18.6242 + 40.7813i 0.740246 + 1.62091i
\(634\) 0 0
\(635\) −6.45493 4.14833i −0.256156 0.164622i
\(636\) 0 0
\(637\) 0.388319 2.70082i 0.0153858 0.107010i
\(638\) 0 0
\(639\) −6.97157 + 4.48036i −0.275791 + 0.177240i
\(640\) 0 0
\(641\) −14.9918 4.40200i −0.592142 0.173869i −0.0280867 0.999605i \(-0.508941\pi\)
−0.564056 + 0.825737i \(0.690760\pi\)
\(642\) 0 0
\(643\) −10.4115 −0.410590 −0.205295 0.978700i \(-0.565815\pi\)
−0.205295 + 0.978700i \(0.565815\pi\)
\(644\) 0 0
\(645\) 63.2129 2.48900
\(646\) 0 0
\(647\) 5.31858 + 1.56168i 0.209095 + 0.0613958i 0.384603 0.923082i \(-0.374338\pi\)
−0.175508 + 0.984478i \(0.556157\pi\)
\(648\) 0 0
\(649\) −11.4463 + 7.35608i −0.449306 + 0.288751i
\(650\) 0 0
\(651\) −1.51890 + 10.5642i −0.0595305 + 0.414044i
\(652\) 0 0
\(653\) 22.1268 + 14.2200i 0.865889 + 0.556473i 0.896493 0.443058i \(-0.146107\pi\)
−0.0306034 + 0.999532i \(0.509743\pi\)
\(654\) 0 0
\(655\) −15.0705 32.9998i −0.588853 1.28941i
\(656\) 0 0
\(657\) −2.23590 15.5510i −0.0872307 0.606703i
\(658\) 0 0
\(659\) −35.3457 + 10.3784i −1.37687 + 0.404287i −0.884680 0.466198i \(-0.845623\pi\)
−0.492194 + 0.870485i \(0.663805\pi\)
\(660\) 0 0
\(661\) −27.1782 + 31.3653i −1.05711 + 1.21997i −0.0823732 + 0.996602i \(0.526250\pi\)
−0.974735 + 0.223366i \(0.928295\pi\)
\(662\) 0 0
\(663\) −7.92505 9.14599i −0.307783 0.355201i
\(664\) 0 0
\(665\) 18.1512 39.7457i 0.703875 1.54127i
\(666\) 0 0
\(667\) 12.1736 + 4.22771i 0.471362 + 0.163697i
\(668\) 0 0
\(669\) 4.41219 9.66134i 0.170585 0.373529i
\(670\) 0 0
\(671\) −2.47160 2.85238i −0.0954152 0.110115i
\(672\) 0 0
\(673\) −13.6694 + 15.7753i −0.526917 + 0.608095i −0.955349 0.295479i \(-0.904521\pi\)
0.428432 + 0.903574i \(0.359066\pi\)
\(674\) 0 0
\(675\) 34.5357 10.1406i 1.32928 0.390312i
\(676\) 0 0
\(677\) 1.72691 + 12.0109i 0.0663707 + 0.461618i 0.995720 + 0.0924175i \(0.0294594\pi\)
−0.929350 + 0.369201i \(0.879631\pi\)
\(678\) 0 0
\(679\) 7.11257 + 15.5744i 0.272956 + 0.597689i
\(680\) 0 0
\(681\) −11.1762 7.18253i −0.428274 0.275235i
\(682\) 0 0
\(683\) 0.172392 1.19902i 0.00659641 0.0458791i −0.986257 0.165216i \(-0.947168\pi\)
0.992854 + 0.119337i \(0.0380769\pi\)
\(684\) 0 0
\(685\) −6.67128 + 4.28737i −0.254897 + 0.163812i
\(686\) 0 0
\(687\) 35.6215 + 10.4594i 1.35905 + 0.399052i
\(688\) 0 0
\(689\) −2.86176 −0.109024
\(690\) 0 0
\(691\) 8.65337 0.329190 0.164595 0.986361i \(-0.447368\pi\)
0.164595 + 0.986361i \(0.447368\pi\)
\(692\) 0 0
\(693\) 4.16918 + 1.22418i 0.158374 + 0.0465029i
\(694\) 0 0
\(695\) 5.48713 3.52636i 0.208139 0.133763i
\(696\) 0 0
\(697\) 7.00612 48.7287i 0.265376 1.84573i
\(698\) 0 0
\(699\) 25.4117 + 16.3311i 0.961160 + 0.617700i
\(700\) 0 0
\(701\) −0.323088 0.707464i −0.0122029 0.0267205i 0.903432 0.428730i \(-0.141039\pi\)
−0.915635 + 0.402010i \(0.868312\pi\)
\(702\) 0 0
\(703\) 8.49377 + 59.0755i 0.320349 + 2.22807i
\(704\) 0 0
\(705\) 13.2196 3.88162i 0.497878 0.146190i
\(706\) 0 0
\(707\) −3.76497 + 4.34501i −0.141596 + 0.163411i
\(708\) 0 0
\(709\) −13.7169 15.8302i −0.515151 0.594516i 0.437259 0.899335i \(-0.355949\pi\)
−0.952410 + 0.304820i \(0.901404\pi\)
\(710\) 0 0
\(711\) −0.188507 + 0.412773i −0.00706957 + 0.0154802i
\(712\) 0 0
\(713\) −8.20100 10.4511i −0.307130 0.391397i
\(714\) 0 0
\(715\) 2.43588 5.33383i 0.0910967 0.199474i
\(716\) 0 0
\(717\) −22.2968 25.7318i −0.832688 0.960973i
\(718\) 0 0
\(719\) 30.7857 35.5286i 1.14811 1.32499i 0.210385 0.977619i \(-0.432528\pi\)
0.937727 0.347373i \(-0.112926\pi\)
\(720\) 0 0
\(721\) −14.0972 + 4.13931i −0.525007 + 0.154156i
\(722\) 0 0
\(723\) −4.26852 29.6882i −0.158748 1.10412i
\(724\) 0 0
\(725\) 10.8539 + 23.7667i 0.403103 + 0.882673i
\(726\) 0 0
\(727\) −18.6601 11.9921i −0.692064 0.444763i 0.146755 0.989173i \(-0.453117\pi\)
−0.838819 + 0.544410i \(0.816754\pi\)
\(728\) 0 0
\(729\) −1.34345 + 9.34387i −0.0497572 + 0.346069i
\(730\) 0 0
\(731\) 50.7141 32.5920i 1.87573 1.20546i
\(732\) 0 0
\(733\) 28.6349 + 8.40795i 1.05765 + 0.310555i 0.763905 0.645328i \(-0.223279\pi\)
0.293747 + 0.955883i \(0.405098\pi\)
\(734\) 0 0
\(735\) −27.1725 −1.00227
\(736\) 0 0
\(737\) 19.0361 0.701204
\(738\) 0 0
\(739\) 39.1921 + 11.5079i 1.44171 + 0.423323i 0.906790 0.421582i \(-0.138525\pi\)
0.534916 + 0.844905i \(0.320343\pi\)
\(740\) 0 0
\(741\) −8.22247 + 5.28426i −0.302060 + 0.194122i
\(742\) 0 0
\(743\) 1.51739 10.5537i 0.0556678 0.387178i −0.942872 0.333155i \(-0.891887\pi\)
0.998540 0.0540226i \(-0.0172043\pi\)
\(744\) 0 0
\(745\) −56.5316 36.3306i −2.07116 1.33105i
\(746\) 0 0
\(747\) 1.62368 + 3.55537i 0.0594075 + 0.130084i
\(748\) 0 0
\(749\) 0.471984 + 3.28272i 0.0172459 + 0.119948i
\(750\) 0 0
\(751\) −8.48857 + 2.49247i −0.309752 + 0.0909514i −0.432914 0.901435i \(-0.642515\pi\)
0.123162 + 0.992387i \(0.460697\pi\)
\(752\) 0 0
\(753\) −25.4349 + 29.3535i −0.926900 + 1.06970i
\(754\) 0 0
\(755\) 20.9405 + 24.1666i 0.762103 + 0.879514i
\(756\) 0 0
\(757\) −8.58531 + 18.7992i −0.312038 + 0.683269i −0.999059 0.0433692i \(-0.986191\pi\)
0.687021 + 0.726638i \(0.258918\pi\)
\(758\) 0 0
\(759\) −16.4821 + 9.49275i −0.598262 + 0.344565i
\(760\) 0 0
\(761\) −1.44451 + 3.16303i −0.0523634 + 0.114660i −0.934005 0.357259i \(-0.883711\pi\)
0.881642 + 0.471919i \(0.156439\pi\)
\(762\) 0 0
\(763\) −10.5564 12.1828i −0.382169 0.441046i
\(764\) 0 0
\(765\) −22.4417 + 25.8991i −0.811380 + 0.936383i
\(766\) 0 0
\(767\) 5.31698 1.56120i 0.191985 0.0563718i
\(768\) 0 0
\(769\) −2.06897 14.3900i −0.0746090 0.518917i −0.992515 0.122120i \(-0.961031\pi\)
0.917906 0.396797i \(-0.129878\pi\)
\(770\) 0 0
\(771\) −16.6305 36.4158i −0.598935 1.31148i
\(772\) 0 0
\(773\) 32.3451 + 20.7870i 1.16337 + 0.747655i 0.972258 0.233912i \(-0.0751529\pi\)
0.191116 + 0.981567i \(0.438789\pi\)
\(774\) 0 0
\(775\) 3.83318 26.6604i 0.137692 0.957668i
\(776\) 0 0
\(777\) −31.9694 + 20.5455i −1.14689 + 0.737065i
\(778\) 0 0
\(779\) −38.1498 11.2018i −1.36686 0.401346i
\(780\) 0 0
\(781\) −13.4666 −0.481874
\(782\) 0 0
\(783\) −9.94683 −0.355471
\(784\) 0 0
\(785\) 24.7871 + 7.27814i 0.884689 + 0.259768i
\(786\) 0 0
\(787\) −0.556296 + 0.357510i −0.0198298 + 0.0127438i −0.550518 0.834823i \(-0.685570\pi\)
0.530688 + 0.847567i \(0.321933\pi\)
\(788\) 0 0
\(789\) −1.47097 + 10.2308i −0.0523679 + 0.364227i
\(790\) 0 0
\(791\) −1.03065 0.662357i −0.0366456 0.0235507i
\(792\) 0 0
\(793\) 0.638554 + 1.39824i 0.0226757 + 0.0496529i
\(794\) 0 0
\(795\) 4.05578 + 28.2086i 0.143844 + 1.00045i
\(796\) 0 0
\(797\) 8.55630 2.51236i 0.303080 0.0889923i −0.126657 0.991947i \(-0.540425\pi\)
0.429736 + 0.902954i \(0.358606\pi\)
\(798\) 0 0
\(799\) 8.60442 9.93003i 0.304402 0.351299i
\(800\) 0 0
\(801\) −3.79539 4.38011i −0.134103 0.154764i
\(802\) 0 0
\(803\) 10.6057 23.2232i 0.374267 0.819530i
\(804\) 0 0
\(805\) −23.9238 + 25.0376i −0.843203 + 0.882459i
\(806\) 0 0
\(807\) −13.2416 + 28.9952i −0.466128 + 1.02068i
\(808\) 0 0
\(809\) 25.2724 + 29.1659i 0.888531 + 1.02542i 0.999501 + 0.0315959i \(0.0100590\pi\)
−0.110970 + 0.993824i \(0.535396\pi\)
\(810\) 0 0
\(811\) −17.7831 + 20.5228i −0.624449 + 0.720653i −0.976546 0.215311i \(-0.930923\pi\)
0.352096 + 0.935964i \(0.385469\pi\)
\(812\) 0 0
\(813\) 34.6181 10.1648i 1.21411 0.356495i
\(814\) 0 0
\(815\) 8.54799 + 59.4526i 0.299423 + 2.08253i
\(816\) 0 0
\(817\) −20.2259 44.2884i −0.707613 1.54946i
\(818\) 0 0
\(819\) −1.48875 0.956761i −0.0520211 0.0334319i
\(820\) 0 0
\(821\) −1.23523 + 8.59123i −0.0431099 + 0.299836i 0.956847 + 0.290591i \(0.0938519\pi\)
−0.999957 + 0.00924507i \(0.997057\pi\)
\(822\) 0 0
\(823\) −5.68274 + 3.65208i −0.198088 + 0.127303i −0.635925 0.771751i \(-0.719381\pi\)
0.437837 + 0.899054i \(0.355745\pi\)
\(824\) 0 0
\(825\) −37.0014 10.8646i −1.28822 0.378256i
\(826\) 0 0
\(827\) 54.2431 1.88622 0.943109 0.332484i \(-0.107887\pi\)
0.943109 + 0.332484i \(0.107887\pi\)
\(828\) 0 0
\(829\) −52.3288 −1.81745 −0.908727 0.417392i \(-0.862944\pi\)
−0.908727 + 0.417392i \(0.862944\pi\)
\(830\) 0 0
\(831\) 5.41981 + 1.59140i 0.188011 + 0.0552050i
\(832\) 0 0
\(833\) −21.7998 + 14.0099i −0.755320 + 0.485414i
\(834\) 0 0
\(835\) −10.5058 + 73.0694i −0.363568 + 2.52867i
\(836\) 0 0
\(837\) 8.62615 + 5.54369i 0.298163 + 0.191618i
\(838\) 0 0
\(839\) −7.41634 16.2395i −0.256041 0.560651i 0.737340 0.675522i \(-0.236082\pi\)
−0.993380 + 0.114871i \(0.963354\pi\)
\(840\) 0 0
\(841\) 3.09956 + 21.5579i 0.106881 + 0.743376i
\(842\) 0 0
\(843\) 2.42930 0.713306i 0.0836694 0.0245676i
\(844\) 0 0
\(845\) 31.1022 35.8939i 1.06995 1.23479i
\(846\) 0 0
\(847\) −8.93180 10.3078i −0.306900 0.354182i
\(848\) 0 0
\(849\) 0.719547 1.57559i 0.0246948 0.0540740i
\(850\) 0 0
\(851\) 9.00094 46.4375i 0.308548 1.59186i
\(852\) 0 0
\(853\) −3.14859 + 6.89446i −0.107806 + 0.236062i −0.955845 0.293872i \(-0.905056\pi\)
0.848039 + 0.529934i \(0.177783\pi\)
\(854\) 0 0
\(855\) 18.1250 + 20.9174i 0.619862 + 0.715358i
\(856\) 0 0
\(857\) −32.9446 + 38.0201i −1.12537 + 1.29874i −0.176062 + 0.984379i \(0.556336\pi\)
−0.949303 + 0.314362i \(0.898210\pi\)
\(858\) 0 0
\(859\) 30.3209 8.90301i 1.03453 0.303767i 0.279981 0.960005i \(-0.409672\pi\)
0.754553 + 0.656239i \(0.227853\pi\)
\(860\) 0 0
\(861\) −3.60294 25.0590i −0.122788 0.854009i
\(862\) 0 0
\(863\) −13.6266 29.8382i −0.463856 1.01570i −0.986592 0.163208i \(-0.947816\pi\)
0.522736 0.852495i \(-0.324912\pi\)
\(864\) 0 0
\(865\) 27.9172 + 17.9413i 0.949212 + 0.610022i
\(866\) 0 0
\(867\) −11.4030 + 79.3098i −0.387267 + 2.69350i
\(868\) 0 0
\(869\) −0.620336 + 0.398666i −0.0210435 + 0.0135238i
\(870\) 0 0
\(871\) −7.43884 2.18424i −0.252056 0.0740102i
\(872\) 0 0
\(873\) −10.8455 −0.367064
\(874\) 0 0
\(875\) −34.1076 −1.15305
\(876\) 0 0
\(877\) −22.5735 6.62818i −0.762253 0.223818i −0.122574 0.992459i \(-0.539115\pi\)
−0.639679 + 0.768642i \(0.720933\pi\)
\(878\) 0 0
\(879\) 24.4494 15.7127i 0.824659 0.529976i
\(880\) 0 0
\(881\) −1.33403 + 9.27840i −0.0449447 + 0.312597i 0.954931 + 0.296828i \(0.0959288\pi\)
−0.999876 + 0.0157693i \(0.994980\pi\)
\(882\) 0 0
\(883\) 12.9552 + 8.32577i 0.435976 + 0.280185i 0.740163 0.672428i \(-0.234748\pi\)
−0.304187 + 0.952612i \(0.598385\pi\)
\(884\) 0 0
\(885\) −22.9243 50.1972i −0.770592 1.68736i
\(886\) 0 0
\(887\) −5.45902 37.9683i −0.183296 1.27485i −0.848903 0.528549i \(-0.822736\pi\)
0.665607 0.746302i \(-0.268173\pi\)
\(888\) 0 0
\(889\) −3.61063 + 1.06018i −0.121097 + 0.0355572i
\(890\) 0 0
\(891\) 14.1503 16.3303i 0.474053 0.547086i
\(892\) 0 0
\(893\) −6.94935 8.01998i −0.232551 0.268378i
\(894\) 0 0
\(895\) −11.0495 + 24.1950i −0.369344 + 0.808750i
\(896\) 0 0
\(897\) 7.53001 1.81835i 0.251420 0.0607128i
\(898\) 0 0
\(899\) −3.09207 + 6.77069i −0.103126 + 0.225815i
\(900\) 0 0
\(901\) 17.7979 + 20.5399i 0.592935 + 0.684284i
\(902\) 0 0
\(903\) 20.3016 23.4293i 0.675595 0.779679i
\(904\) 0 0
\(905\) 18.7467 5.50453i 0.623161 0.182977i
\(906\) 0 0
\(907\) −3.19434 22.2171i −0.106066 0.737708i −0.971561 0.236790i \(-0.923905\pi\)
0.865494 0.500918i \(-0.167004\pi\)
\(908\) 0 0
\(909\) −1.51286 3.31271i −0.0501785 0.109876i
\(910\) 0 0
\(911\) 23.9713 + 15.4054i 0.794204 + 0.510404i 0.873720 0.486430i \(-0.161701\pi\)
−0.0795160 + 0.996834i \(0.525337\pi\)
\(912\) 0 0
\(913\) −0.903908 + 6.28682i −0.0299150 + 0.208063i
\(914\) 0 0
\(915\) 12.8775 8.27590i 0.425718 0.273593i
\(916\) 0 0
\(917\) −17.0712 5.01255i −0.563740 0.165529i
\(918\) 0 0
\(919\) −32.9290 −1.08623 −0.543113 0.839660i \(-0.682755\pi\)
−0.543113 + 0.839660i \(0.682755\pi\)
\(920\) 0 0
\(921\) −32.1000 −1.05773
\(922\) 0 0
\(923\) 5.26242 + 1.54519i 0.173215 + 0.0508605i
\(924\) 0 0
\(925\) 80.6795 51.8495i 2.65272 1.70480i
\(926\) 0 0
\(927\) 1.32448 9.21197i 0.0435017 0.302561i
\(928\) 0 0
\(929\) 35.5977 + 22.8773i 1.16792 + 0.750578i 0.973128 0.230266i \(-0.0739595\pi\)
0.194795 + 0.980844i \(0.437596\pi\)
\(930\) 0 0
\(931\) 8.69423 + 19.0377i 0.284942 + 0.623936i
\(932\) 0 0
\(933\) −4.42521 30.7780i −0.144875 1.00763i
\(934\) 0 0
\(935\) −53.4322 + 15.6891i −1.74742 + 0.513088i
\(936\) 0 0
\(937\) 13.9629 16.1140i 0.456147 0.526421i −0.480360 0.877072i \(-0.659494\pi\)
0.936507 + 0.350650i \(0.114039\pi\)
\(938\) 0 0
\(939\) −0.321466 0.370992i −0.0104907 0.0121069i
\(940\) 0 0
\(941\) 15.8083 34.6153i 0.515336 1.12843i −0.455840 0.890062i \(-0.650661\pi\)
0.971175 0.238366i \(-0.0766117\pi\)
\(942\) 0 0
\(943\) 25.6497 + 18.3059i 0.835269 + 0.596122i
\(944\) 0 0
\(945\) 11.1038 24.3140i 0.361208 0.790935i
\(946\) 0 0
\(947\) −6.34168 7.31869i −0.206077 0.237826i 0.643297 0.765616i \(-0.277566\pi\)
−0.849374 + 0.527791i \(0.823020\pi\)
\(948\) 0 0
\(949\) −6.80912 + 7.85814i −0.221033 + 0.255086i
\(950\) 0 0
\(951\) 4.19048 1.23044i 0.135886 0.0398997i
\(952\) 0 0
\(953\) −7.74379 53.8593i −0.250846 1.74467i −0.593157 0.805086i \(-0.702119\pi\)
0.342311 0.939587i \(-0.388790\pi\)
\(954\) 0 0
\(955\) −38.6924 84.7245i −1.25206 2.74162i
\(956\) 0 0
\(957\) 8.96522 + 5.76160i 0.289804 + 0.186246i
\(958\) 0 0
\(959\) −0.553489 + 3.84960i −0.0178731 + 0.124310i
\(960\) 0 0
\(961\) −19.6238 + 12.6115i −0.633026 + 0.406821i
\(962\) 0 0
\(963\) −2.01569 0.591859i −0.0649546 0.0190724i
\(964\) 0 0
\(965\) 49.4256 1.59106
\(966\) 0 0
\(967\) 43.2998 1.39243 0.696214 0.717834i \(-0.254866\pi\)
0.696214 + 0.717834i \(0.254866\pi\)
\(968\) 0 0
\(969\) 89.0646 + 26.1517i 2.86117 + 0.840114i
\(970\) 0 0
\(971\) 14.2880 9.18234i 0.458524 0.294675i −0.290915 0.956749i \(-0.593960\pi\)
0.749439 + 0.662073i \(0.230323\pi\)
\(972\) 0 0
\(973\) 0.455244 3.16629i 0.0145945 0.101507i
\(974\) 0 0
\(975\) 13.2126 + 8.49122i 0.423142 + 0.271937i
\(976\) 0 0
\(977\) −0.236343 0.517520i −0.00756130 0.0165569i 0.905814 0.423676i \(-0.139261\pi\)
−0.913375 + 0.407119i \(0.866533\pi\)
\(978\) 0 0
\(979\) −1.34033 9.32221i −0.0428372 0.297939i
\(980\) 0 0
\(981\) 9.79749 2.87680i 0.312810 0.0918492i
\(982\) 0 0
\(983\) −7.31141 + 8.43782i −0.233198 + 0.269125i −0.860272 0.509835i \(-0.829707\pi\)
0.627075 + 0.778959i \(0.284252\pi\)
\(984\) 0 0
\(985\) 5.38376 + 6.21319i 0.171541 + 0.197969i
\(986\) 0 0
\(987\) 2.80695 6.14636i 0.0893461 0.195641i
\(988\) 0 0
\(989\) 3.62747 + 38.4171i 0.115347 + 1.22159i
\(990\) 0 0
\(991\) 5.73064 12.5483i 0.182040 0.398611i −0.796509 0.604627i \(-0.793322\pi\)
0.978549 + 0.206015i \(0.0660496\pi\)
\(992\) 0 0
\(993\) −31.1328 35.9292i −0.987970 1.14018i
\(994\) 0 0
\(995\) −60.8730 + 70.2512i −1.92980 + 2.22711i
\(996\) 0 0
\(997\) −6.84252 + 2.00914i −0.216705 + 0.0636302i −0.388283 0.921540i \(-0.626932\pi\)
0.171578 + 0.985171i \(0.445113\pi\)
\(998\) 0 0
\(999\) 5.19598 + 36.1388i 0.164394 + 1.14338i
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 92.2.e.a.29.1 20
3.2 odd 2 828.2.q.a.397.1 20
4.3 odd 2 368.2.m.d.305.2 20
23.2 even 11 2116.2.a.j.1.7 10
23.4 even 11 inner 92.2.e.a.73.1 yes 20
23.21 odd 22 2116.2.a.i.1.7 10
69.50 odd 22 828.2.q.a.73.1 20
92.27 odd 22 368.2.m.d.257.2 20
92.67 even 22 8464.2.a.cd.1.4 10
92.71 odd 22 8464.2.a.ce.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
92.2.e.a.29.1 20 1.1 even 1 trivial
92.2.e.a.73.1 yes 20 23.4 even 11 inner
368.2.m.d.257.2 20 92.27 odd 22
368.2.m.d.305.2 20 4.3 odd 2
828.2.q.a.73.1 20 69.50 odd 22
828.2.q.a.397.1 20 3.2 odd 2
2116.2.a.i.1.7 10 23.21 odd 22
2116.2.a.j.1.7 10 23.2 even 11
8464.2.a.cd.1.4 10 92.67 even 22
8464.2.a.ce.1.4 10 92.71 odd 22