Properties

Label 1638.2.x.a.811.3
Level $1638$
Weight $2$
Character 1638.811
Analytic conductor $13.079$
Analytic rank $0$
Dimension $8$
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] = [1638,2,Mod(307,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.x (of order \(4\), degree \(2\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.836829184.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 811.3
Root \(2.06644i\) of defining polynomial
Character \(\chi\) \(=\) 1638.811
Dual form 1638.2.x.a.307.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(-0.292893 + 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(-0.292893 + 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} -3.06644 q^{10} +(-0.516075 - 0.516075i) q^{11} +(-3.60525 + 0.0469777i) q^{13} +(1.65222 + 2.06644i) q^{14} -1.00000 q^{16} -2.57461 q^{17} +(3.82052 + 3.82052i) q^{19} +(-2.16830 + 2.16830i) q^{20} -0.729840 q^{22} +6.97248i q^{23} +4.40303i q^{25} +(-2.51608 + 2.58251i) q^{26} +(2.62949 + 0.292893i) q^{28} +6.32541 q^{29} +(4.33660 + 4.33660i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.82052 + 1.82052i) q^{34} +(6.33660 - 5.06644i) q^{35} +(-3.58251 - 3.58251i) q^{37} +5.40303 q^{38} +3.06644i q^{40} +(-0.176204 - 0.176204i) q^{41} +7.89486i q^{43} +(-0.516075 + 0.516075i) q^{44} +(4.93029 + 4.93029i) q^{46} +(1.41421 - 1.41421i) q^{47} +(-6.82843 - 1.54032i) q^{49} +(3.11341 + 3.11341i) q^{50} +(0.0469777 + 3.60525i) q^{52} +0.514936 q^{53} +2.23801i q^{55} +(2.06644 - 1.65222i) q^{56} +(4.47274 - 4.47274i) q^{58} +(-3.17834 + 3.17834i) q^{59} -6.41208i q^{61} +6.13287 q^{62} +1.00000i q^{64} +(7.91911 + 7.71538i) q^{65} +(-3.96130 + 3.96130i) q^{67} +2.57461i q^{68} +(0.898138 - 8.06316i) q^{70} +(-8.12169 + 8.12169i) q^{71} +(-11.6056 + 11.6056i) q^{73} -5.06644 q^{74} +(3.82052 - 3.82052i) q^{76} +(1.50817 - 1.20586i) q^{77} +10.9455 q^{79} +(2.16830 + 2.16830i) q^{80} -0.249190 q^{82} +(1.01118 + 1.01118i) q^{83} +(5.58251 + 5.58251i) q^{85} +(5.58251 + 5.58251i) q^{86} +0.729840i q^{88} +(1.10977 - 1.10977i) q^{89} +(0.932425 - 9.49371i) q^{91} +6.97248 q^{92} -2.00000i q^{94} -16.5681i q^{95} +(9.34336 + 9.34336i) q^{97} +(-5.91760 + 3.73926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{13} + 4 q^{14} - 8 q^{16} + 4 q^{17} + 8 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{26} - 12 q^{29} + 8 q^{31} + 8 q^{34} + 24 q^{35} - 4 q^{37} - 4 q^{38} + 12 q^{41} + 24 q^{46} - 32 q^{49} + 8 q^{50} + 4 q^{52} - 40 q^{53} - 4 q^{56} + 4 q^{58} - 8 q^{59} + 8 q^{62} + 12 q^{65} + 32 q^{67} + 12 q^{71} - 20 q^{73} - 20 q^{74} + 8 q^{76} + 8 q^{77} + 24 q^{79} + 4 q^{80} - 40 q^{82} + 44 q^{83} + 20 q^{85} + 20 q^{86} + 16 q^{89} - 12 q^{91} + 28 q^{92} + 8 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) −2.16830 2.16830i −0.969692 0.969692i 0.0298617 0.999554i \(-0.490493\pi\)
−0.999554 + 0.0298617i \(0.990493\pi\)
\(6\) 0 0
\(7\) −0.292893 + 2.62949i −0.110703 + 0.993854i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) −3.06644 −0.969692
\(11\) −0.516075 0.516075i −0.155603 0.155603i 0.625012 0.780615i \(-0.285094\pi\)
−0.780615 + 0.625012i \(0.785094\pi\)
\(12\) 0 0
\(13\) −3.60525 + 0.0469777i −0.999915 + 0.0130293i
\(14\) 1.65222 + 2.06644i 0.441575 + 0.552278i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −2.57461 −0.624434 −0.312217 0.950011i \(-0.601072\pi\)
−0.312217 + 0.950011i \(0.601072\pi\)
\(18\) 0 0
\(19\) 3.82052 + 3.82052i 0.876488 + 0.876488i 0.993169 0.116682i \(-0.0372258\pi\)
−0.116682 + 0.993169i \(0.537226\pi\)
\(20\) −2.16830 + 2.16830i −0.484846 + 0.484846i
\(21\) 0 0
\(22\) −0.729840 −0.155603
\(23\) 6.97248i 1.45386i 0.686710 + 0.726931i \(0.259054\pi\)
−0.686710 + 0.726931i \(0.740946\pi\)
\(24\) 0 0
\(25\) 4.40303i 0.880606i
\(26\) −2.51608 + 2.58251i −0.493443 + 0.506472i
\(27\) 0 0
\(28\) 2.62949 + 0.292893i 0.496927 + 0.0553516i
\(29\) 6.32541 1.17460 0.587300 0.809369i \(-0.300191\pi\)
0.587300 + 0.809369i \(0.300191\pi\)
\(30\) 0 0
\(31\) 4.33660 + 4.33660i 0.778876 + 0.778876i 0.979640 0.200764i \(-0.0643424\pi\)
−0.200764 + 0.979640i \(0.564342\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0 0
\(34\) −1.82052 + 1.82052i −0.312217 + 0.312217i
\(35\) 6.33660 5.06644i 1.07108 0.856384i
\(36\) 0 0
\(37\) −3.58251 3.58251i −0.588961 0.588961i 0.348389 0.937350i \(-0.386729\pi\)
−0.937350 + 0.348389i \(0.886729\pi\)
\(38\) 5.40303 0.876488
\(39\) 0 0
\(40\) 3.06644i 0.484846i
\(41\) −0.176204 0.176204i −0.0275185 0.0275185i 0.693214 0.720732i \(-0.256194\pi\)
−0.720732 + 0.693214i \(0.756194\pi\)
\(42\) 0 0
\(43\) 7.89486i 1.20396i 0.798513 + 0.601978i \(0.205620\pi\)
−0.798513 + 0.601978i \(0.794380\pi\)
\(44\) −0.516075 + 0.516075i −0.0778013 + 0.0778013i
\(45\) 0 0
\(46\) 4.93029 + 4.93029i 0.726931 + 0.726931i
\(47\) 1.41421 1.41421i 0.206284 0.206284i −0.596402 0.802686i \(-0.703403\pi\)
0.802686 + 0.596402i \(0.203403\pi\)
\(48\) 0 0
\(49\) −6.82843 1.54032i −0.975490 0.220046i
\(50\) 3.11341 + 3.11341i 0.440303 + 0.440303i
\(51\) 0 0
\(52\) 0.0469777 + 3.60525i 0.00651463 + 0.499958i
\(53\) 0.514936 0.0707319 0.0353660 0.999374i \(-0.488740\pi\)
0.0353660 + 0.999374i \(0.488740\pi\)
\(54\) 0 0
\(55\) 2.23801i 0.301773i
\(56\) 2.06644 1.65222i 0.276139 0.220788i
\(57\) 0 0
\(58\) 4.47274 4.47274i 0.587300 0.587300i
\(59\) −3.17834 + 3.17834i −0.413785 + 0.413785i −0.883055 0.469270i \(-0.844517\pi\)
0.469270 + 0.883055i \(0.344517\pi\)
\(60\) 0 0
\(61\) 6.41208i 0.820982i −0.911865 0.410491i \(-0.865357\pi\)
0.911865 0.410491i \(-0.134643\pi\)
\(62\) 6.13287 0.778876
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 7.91911 + 7.71538i 0.982244 + 0.956976i
\(66\) 0 0
\(67\) −3.96130 + 3.96130i −0.483950 + 0.483950i −0.906391 0.422441i \(-0.861173\pi\)
0.422441 + 0.906391i \(0.361173\pi\)
\(68\) 2.57461i 0.312217i
\(69\) 0 0
\(70\) 0.898138 8.06316i 0.107348 0.963732i
\(71\) −8.12169 + 8.12169i −0.963867 + 0.963867i −0.999370 0.0355021i \(-0.988697\pi\)
0.0355021 + 0.999370i \(0.488697\pi\)
\(72\) 0 0
\(73\) −11.6056 + 11.6056i −1.35833 + 1.35833i −0.482364 + 0.875971i \(0.660222\pi\)
−0.875971 + 0.482364i \(0.839778\pi\)
\(74\) −5.06644 −0.588961
\(75\) 0 0
\(76\) 3.82052 3.82052i 0.438244 0.438244i
\(77\) 1.50817 1.20586i 0.171872 0.137420i
\(78\) 0 0
\(79\) 10.9455 1.23146 0.615732 0.787956i \(-0.288860\pi\)
0.615732 + 0.787956i \(0.288860\pi\)
\(80\) 2.16830 + 2.16830i 0.242423 + 0.242423i
\(81\) 0 0
\(82\) −0.249190 −0.0275185
\(83\) 1.01118 + 1.01118i 0.110992 + 0.110992i 0.760421 0.649430i \(-0.224992\pi\)
−0.649430 + 0.760421i \(0.724992\pi\)
\(84\) 0 0
\(85\) 5.58251 + 5.58251i 0.605508 + 0.605508i
\(86\) 5.58251 + 5.58251i 0.601978 + 0.601978i
\(87\) 0 0
\(88\) 0.729840i 0.0778013i
\(89\) 1.10977 1.10977i 0.117635 0.117635i −0.645839 0.763474i \(-0.723492\pi\)
0.763474 + 0.645839i \(0.223492\pi\)
\(90\) 0 0
\(91\) 0.932425 9.49371i 0.0977447 0.995212i
\(92\) 6.97248 0.726931
\(93\) 0 0
\(94\) 2.00000i 0.206284i
\(95\) 16.5681i 1.69985i
\(96\) 0 0
\(97\) 9.34336 + 9.34336i 0.948675 + 0.948675i 0.998746 0.0500709i \(-0.0159447\pi\)
−0.0500709 + 0.998746i \(0.515945\pi\)
\(98\) −5.91760 + 3.73926i −0.597768 + 0.377722i
\(99\) 0 0
\(100\) 4.40303 0.440303
\(101\) −5.86058 −0.583149 −0.291575 0.956548i \(-0.594179\pi\)
−0.291575 + 0.956548i \(0.594179\pi\)
\(102\) 0 0
\(103\) 9.16965 0.903513 0.451756 0.892141i \(-0.350798\pi\)
0.451756 + 0.892141i \(0.350798\pi\)
\(104\) 2.58251 + 2.51608i 0.253236 + 0.246721i
\(105\) 0 0
\(106\) 0.364115 0.364115i 0.0353660 0.0353660i
\(107\) −7.91334 −0.765011 −0.382506 0.923953i \(-0.624939\pi\)
−0.382506 + 0.923953i \(0.624939\pi\)
\(108\) 0 0
\(109\) 9.90330 9.90330i 0.948564 0.948564i −0.0501767 0.998740i \(-0.515978\pi\)
0.998740 + 0.0501767i \(0.0159785\pi\)
\(110\) 1.58251 + 1.58251i 0.150887 + 0.150887i
\(111\) 0 0
\(112\) 0.292893 2.62949i 0.0276758 0.248463i
\(113\) −11.9450 −1.12369 −0.561844 0.827243i \(-0.689908\pi\)
−0.561844 + 0.827243i \(0.689908\pi\)
\(114\) 0 0
\(115\) 15.1184 15.1184i 1.40980 1.40980i
\(116\) 6.32541i 0.587300i
\(117\) 0 0
\(118\) 4.49485i 0.413785i
\(119\) 0.754084 6.76990i 0.0691268 0.620595i
\(120\) 0 0
\(121\) 10.4673i 0.951576i
\(122\) −4.53402 4.53402i −0.410491 0.410491i
\(123\) 0 0
\(124\) 4.33660 4.33660i 0.389438 0.389438i
\(125\) −1.29440 + 1.29440i −0.115775 + 0.115775i
\(126\) 0 0
\(127\) 19.2112i 1.70472i 0.522954 + 0.852361i \(0.324830\pi\)
−0.522954 + 0.852361i \(0.675170\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 11.0553 0.144054i 0.969610 0.0126344i
\(131\) 9.83056i 0.858900i 0.903091 + 0.429450i \(0.141293\pi\)
−0.903091 + 0.429450i \(0.858707\pi\)
\(132\) 0 0
\(133\) −11.1650 + 8.92701i −0.968130 + 0.774070i
\(134\) 5.60212i 0.483950i
\(135\) 0 0
\(136\) 1.82052 + 1.82052i 0.156108 + 0.156108i
\(137\) −3.88019 3.88019i −0.331507 0.331507i 0.521652 0.853159i \(-0.325316\pi\)
−0.853159 + 0.521652i \(0.825316\pi\)
\(138\) 0 0
\(139\) 3.32681i 0.282176i 0.989997 + 0.141088i \(0.0450601\pi\)
−0.989997 + 0.141088i \(0.954940\pi\)
\(140\) −5.06644 6.33660i −0.428192 0.535540i
\(141\) 0 0
\(142\) 11.4858i 0.963867i
\(143\) 1.88482 + 1.83633i 0.157617 + 0.153562i
\(144\) 0 0
\(145\) −13.7154 13.7154i −1.13900 1.13900i
\(146\) 16.4128i 1.35833i
\(147\) 0 0
\(148\) −3.58251 + 3.58251i −0.294481 + 0.294481i
\(149\) −8.02774 + 8.02774i −0.657658 + 0.657658i −0.954825 0.297168i \(-0.903958\pi\)
0.297168 + 0.954825i \(0.403958\pi\)
\(150\) 0 0
\(151\) 13.5417 + 13.5417i 1.10201 + 1.10201i 0.994169 + 0.107837i \(0.0343926\pi\)
0.107837 + 0.994169i \(0.465607\pi\)
\(152\) 5.40303i 0.438244i
\(153\) 0 0
\(154\) 0.213765 1.91911i 0.0172257 0.154646i
\(155\) 18.8061i 1.51054i
\(156\) 0 0
\(157\) 3.14458i 0.250965i −0.992096 0.125482i \(-0.959952\pi\)
0.992096 0.125482i \(-0.0400479\pi\)
\(158\) 7.73963 7.73963i 0.615732 0.615732i
\(159\) 0 0
\(160\) 3.06644 0.242423
\(161\) −18.3341 2.04219i −1.44493 0.160947i
\(162\) 0 0
\(163\) −15.2816 15.2816i −1.19694 1.19694i −0.975077 0.221867i \(-0.928785\pi\)
−0.221867 0.975077i \(-0.571215\pi\)
\(164\) −0.176204 + 0.176204i −0.0137592 + 0.0137592i
\(165\) 0 0
\(166\) 1.43003 0.110992
\(167\) −9.21892 + 9.21892i −0.713382 + 0.713382i −0.967241 0.253860i \(-0.918300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(168\) 0 0
\(169\) 12.9956 0.338732i 0.999660 0.0260563i
\(170\) 7.89486 0.605508
\(171\) 0 0
\(172\) 7.89486 0.601978
\(173\) 17.4793 1.32892 0.664462 0.747322i \(-0.268661\pi\)
0.664462 + 0.747322i \(0.268661\pi\)
\(174\) 0 0
\(175\) −11.5777 1.28962i −0.875194 0.0974860i
\(176\) 0.516075 + 0.516075i 0.0389006 + 0.0389006i
\(177\) 0 0
\(178\) 1.56945i 0.117635i
\(179\) 18.3235i 1.36956i −0.728749 0.684781i \(-0.759898\pi\)
0.728749 0.684781i \(-0.240102\pi\)
\(180\) 0 0
\(181\) −4.96432 −0.368995 −0.184498 0.982833i \(-0.559066\pi\)
−0.184498 + 0.982833i \(0.559066\pi\)
\(182\) −6.05374 7.37239i −0.448733 0.546478i
\(183\) 0 0
\(184\) 4.93029 4.93029i 0.363466 0.363466i
\(185\) 15.5359i 1.14222i
\(186\) 0 0
\(187\) 1.32869 + 1.32869i 0.0971634 + 0.0971634i
\(188\) −1.41421 1.41421i −0.103142 0.103142i
\(189\) 0 0
\(190\) −11.7154 11.7154i −0.849923 0.849923i
\(191\) −10.5427 −0.762841 −0.381421 0.924402i \(-0.624565\pi\)
−0.381421 + 0.924402i \(0.624565\pi\)
\(192\) 0 0
\(193\) −13.6366 13.6366i −0.981586 0.981586i 0.0182475 0.999833i \(-0.494191\pi\)
−0.999833 + 0.0182475i \(0.994191\pi\)
\(194\) 13.2135 0.948675
\(195\) 0 0
\(196\) −1.54032 + 6.82843i −0.110023 + 0.487745i
\(197\) −13.4673 + 13.4673i −0.959508 + 0.959508i −0.999211 0.0397038i \(-0.987359\pi\)
0.0397038 + 0.999211i \(0.487359\pi\)
\(198\) 0 0
\(199\) −5.92452 −0.419978 −0.209989 0.977704i \(-0.567343\pi\)
−0.209989 + 0.977704i \(0.567343\pi\)
\(200\) 3.11341 3.11341i 0.220152 0.220152i
\(201\) 0 0
\(202\) −4.14405 + 4.14405i −0.291575 + 0.291575i
\(203\) −1.85267 + 16.6326i −0.130032 + 1.16738i
\(204\) 0 0
\(205\) 0.764127i 0.0533689i
\(206\) 6.48392 6.48392i 0.451756 0.451756i
\(207\) 0 0
\(208\) 3.60525 0.0469777i 0.249979 0.00325731i
\(209\) 3.94335i 0.272767i
\(210\) 0 0
\(211\) −7.04407 −0.484934 −0.242467 0.970160i \(-0.577957\pi\)
−0.242467 + 0.970160i \(0.577957\pi\)
\(212\) 0.514936i 0.0353660i
\(213\) 0 0
\(214\) −5.59557 + 5.59557i −0.382506 + 0.382506i
\(215\) 17.1184 17.1184i 1.16747 1.16747i
\(216\) 0 0
\(217\) −12.6732 + 10.1329i −0.860312 + 0.687864i
\(218\) 14.0054i 0.948564i
\(219\) 0 0
\(220\) 2.23801 0.150887
\(221\) 9.28208 0.120949i 0.624381 0.00813591i
\(222\) 0 0
\(223\) −9.71425 9.71425i −0.650514 0.650514i 0.302603 0.953117i \(-0.402144\pi\)
−0.953117 + 0.302603i \(0.902144\pi\)
\(224\) −1.65222 2.06644i −0.110394 0.138070i
\(225\) 0 0
\(226\) −8.44636 + 8.44636i −0.561844 + 0.561844i
\(227\) −13.9000 13.9000i −0.922577 0.922577i 0.0746342 0.997211i \(-0.476221\pi\)
−0.997211 + 0.0746342i \(0.976221\pi\)
\(228\) 0 0
\(229\) 5.97035 5.97035i 0.394532 0.394532i −0.481768 0.876299i \(-0.660005\pi\)
0.876299 + 0.481768i \(0.160005\pi\)
\(230\) 21.3807i 1.40980i
\(231\) 0 0
\(232\) −4.47274 4.47274i −0.293650 0.293650i
\(233\) 1.35293i 0.0886336i 0.999018 + 0.0443168i \(0.0141111\pi\)
−0.999018 + 0.0443168i \(0.985889\pi\)
\(234\) 0 0
\(235\) −6.13287 −0.400065
\(236\) 3.17834 + 3.17834i 0.206892 + 0.206892i
\(237\) 0 0
\(238\) −4.25382 5.32026i −0.275734 0.344861i
\(239\) −20.8904 + 20.8904i −1.35129 + 1.35129i −0.467071 + 0.884220i \(0.654691\pi\)
−0.884220 + 0.467071i \(0.845309\pi\)
\(240\) 0 0
\(241\) −11.1816 + 11.1816i −0.720269 + 0.720269i −0.968660 0.248391i \(-0.920098\pi\)
0.248391 + 0.968660i \(0.420098\pi\)
\(242\) −7.40152 7.40152i −0.475788 0.475788i
\(243\) 0 0
\(244\) −6.41208 −0.410491
\(245\) 11.4662 + 18.1459i 0.732548 + 1.15930i
\(246\) 0 0
\(247\) −13.9534 13.5944i −0.887833 0.864993i
\(248\) 6.13287i 0.389438i
\(249\) 0 0
\(250\) 1.83056i 0.115775i
\(251\) 20.6366 1.30257 0.651286 0.758832i \(-0.274230\pi\)
0.651286 + 0.758832i \(0.274230\pi\)
\(252\) 0 0
\(253\) 3.59832 3.59832i 0.226225 0.226225i
\(254\) 13.5844 + 13.5844i 0.852361 + 0.852361i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −9.21351 −0.574723 −0.287362 0.957822i \(-0.592778\pi\)
−0.287362 + 0.957822i \(0.592778\pi\)
\(258\) 0 0
\(259\) 10.4695 8.37088i 0.650541 0.520141i
\(260\) 7.71538 7.91911i 0.478488 0.491122i
\(261\) 0 0
\(262\) 6.95126 + 6.95126i 0.429450 + 0.429450i
\(263\) −9.50464 −0.586081 −0.293041 0.956100i \(-0.594667\pi\)
−0.293041 + 0.956100i \(0.594667\pi\)
\(264\) 0 0
\(265\) −1.11654 1.11654i −0.0685882 0.0685882i
\(266\) −1.58251 + 14.2072i −0.0970300 + 0.871100i
\(267\) 0 0
\(268\) 3.96130 + 3.96130i 0.241975 + 0.241975i
\(269\) 15.7423i 0.959824i −0.877317 0.479912i \(-0.840669\pi\)
0.877317 0.479912i \(-0.159331\pi\)
\(270\) 0 0
\(271\) 17.4746 17.4746i 1.06151 1.06151i 0.0635278 0.997980i \(-0.479765\pi\)
0.997980 0.0635278i \(-0.0202352\pi\)
\(272\) 2.57461 0.156108
\(273\) 0 0
\(274\) −5.48742 −0.331507
\(275\) 2.27230 2.27230i 0.137025 0.137025i
\(276\) 0 0
\(277\) 21.3991i 1.28575i 0.765971 + 0.642875i \(0.222259\pi\)
−0.765971 + 0.642875i \(0.777741\pi\)
\(278\) 2.35241 + 2.35241i 0.141088 + 0.141088i
\(279\) 0 0
\(280\) −8.06316 0.898138i −0.481866 0.0536740i
\(281\) −0.634274 0.634274i −0.0378376 0.0378376i 0.687935 0.725772i \(-0.258517\pi\)
−0.725772 + 0.687935i \(0.758517\pi\)
\(282\) 0 0
\(283\) 11.6503 0.692539 0.346269 0.938135i \(-0.387448\pi\)
0.346269 + 0.938135i \(0.387448\pi\)
\(284\) 8.12169 + 8.12169i 0.481934 + 0.481934i
\(285\) 0 0
\(286\) 2.63125 0.0342862i 0.155589 0.00202739i
\(287\) 0.514936 0.411718i 0.0303957 0.0243030i
\(288\) 0 0
\(289\) −10.3714 −0.610083
\(290\) −19.3965 −1.13900
\(291\) 0 0
\(292\) 11.6056 + 11.6056i 0.679167 + 0.679167i
\(293\) 16.3755 16.3755i 0.956668 0.956668i −0.0424317 0.999099i \(-0.513510\pi\)
0.999099 + 0.0424317i \(0.0135105\pi\)
\(294\) 0 0
\(295\) 13.7832 0.802488
\(296\) 5.06644i 0.294481i
\(297\) 0 0
\(298\) 11.3529i 0.657658i
\(299\) −0.327551 25.1375i −0.0189428 1.45374i
\(300\) 0 0
\(301\) −20.7595 2.31235i −1.19656 0.133282i
\(302\) 19.1508 1.10201
\(303\) 0 0
\(304\) −3.82052 3.82052i −0.219122 0.219122i
\(305\) −13.9033 + 13.9033i −0.796100 + 0.796100i
\(306\) 0 0
\(307\) −14.8704 + 14.8704i −0.848697 + 0.848697i −0.989971 0.141274i \(-0.954880\pi\)
0.141274 + 0.989971i \(0.454880\pi\)
\(308\) −1.20586 1.50817i −0.0687102 0.0859359i
\(309\) 0 0
\(310\) −13.2979 13.2979i −0.755270 0.755270i
\(311\) 26.0489 1.47710 0.738549 0.674199i \(-0.235511\pi\)
0.738549 + 0.674199i \(0.235511\pi\)
\(312\) 0 0
\(313\) 13.1007i 0.740497i −0.928933 0.370248i \(-0.879273\pi\)
0.928933 0.370248i \(-0.120727\pi\)
\(314\) −2.22355 2.22355i −0.125482 0.125482i
\(315\) 0 0
\(316\) 10.9455i 0.615732i
\(317\) 15.6157 15.6157i 0.877063 0.877063i −0.116167 0.993230i \(-0.537061\pi\)
0.993230 + 0.116167i \(0.0370608\pi\)
\(318\) 0 0
\(319\) −3.26439 3.26439i −0.182771 0.182771i
\(320\) 2.16830 2.16830i 0.121212 0.121212i
\(321\) 0 0
\(322\) −14.4082 + 11.5201i −0.802937 + 0.641990i
\(323\) −9.83633 9.83633i −0.547308 0.547308i
\(324\) 0 0
\(325\) −0.206844 15.8740i −0.0114736 0.880532i
\(326\) −21.6114 −1.19694
\(327\) 0 0
\(328\) 0.249190i 0.0137592i
\(329\) 3.30445 + 4.13287i 0.182180 + 0.227853i
\(330\) 0 0
\(331\) −6.01634 + 6.01634i −0.330688 + 0.330688i −0.852848 0.522160i \(-0.825126\pi\)
0.522160 + 0.852848i \(0.325126\pi\)
\(332\) 1.01118 1.01118i 0.0554958 0.0554958i
\(333\) 0 0
\(334\) 13.0375i 0.713382i
\(335\) 17.1786 0.938565
\(336\) 0 0
\(337\) 1.23748i 0.0674101i −0.999432 0.0337050i \(-0.989269\pi\)
0.999432 0.0337050i \(-0.0107307\pi\)
\(338\) 8.94975 9.42879i 0.486802 0.512858i
\(339\) 0 0
\(340\) 5.58251 5.58251i 0.302754 0.302754i
\(341\) 4.47602i 0.242390i
\(342\) 0 0
\(343\) 6.05025 17.5041i 0.326683 0.945134i
\(344\) 5.58251 5.58251i 0.300989 0.300989i
\(345\) 0 0
\(346\) 12.3597 12.3597i 0.664462 0.664462i
\(347\) 12.1613 0.652852 0.326426 0.945223i \(-0.394156\pi\)
0.326426 + 0.945223i \(0.394156\pi\)
\(348\) 0 0
\(349\) −17.9622 + 17.9622i −0.961494 + 0.961494i −0.999286 0.0377919i \(-0.987968\pi\)
0.0377919 + 0.999286i \(0.487968\pi\)
\(350\) −9.09859 + 7.27479i −0.486340 + 0.388854i
\(351\) 0 0
\(352\) 0.729840 0.0389006
\(353\) 21.2045 + 21.2045i 1.12860 + 1.12860i 0.990405 + 0.138195i \(0.0441300\pi\)
0.138195 + 0.990405i \(0.455870\pi\)
\(354\) 0 0
\(355\) 35.2205 1.86931
\(356\) −1.10977 1.10977i −0.0588176 0.0588176i
\(357\) 0 0
\(358\) −12.9567 12.9567i −0.684781 0.684781i
\(359\) −20.4359 20.4359i −1.07857 1.07857i −0.996638 0.0819287i \(-0.973892\pi\)
−0.0819287 0.996638i \(-0.526108\pi\)
\(360\) 0 0
\(361\) 10.1928i 0.536461i
\(362\) −3.51030 + 3.51030i −0.184498 + 0.184498i
\(363\) 0 0
\(364\) −9.49371 0.932425i −0.497606 0.0488723i
\(365\) 50.3289 2.63433
\(366\) 0 0
\(367\) 1.09998i 0.0574185i −0.999588 0.0287092i \(-0.990860\pi\)
0.999588 0.0287092i \(-0.00913969\pi\)
\(368\) 6.97248i 0.363466i
\(369\) 0 0
\(370\) 10.9855 + 10.9855i 0.571111 + 0.571111i
\(371\) −0.150821 + 1.35402i −0.00783025 + 0.0702972i
\(372\) 0 0
\(373\) 20.6382 1.06861 0.534304 0.845293i \(-0.320574\pi\)
0.534304 + 0.845293i \(0.320574\pi\)
\(374\) 1.87905 0.0971634
\(375\) 0 0
\(376\) −2.00000 −0.103142
\(377\) −22.8047 + 0.297153i −1.17450 + 0.0153042i
\(378\) 0 0
\(379\) −5.82027 + 5.82027i −0.298967 + 0.298967i −0.840609 0.541642i \(-0.817803\pi\)
0.541642 + 0.840609i \(0.317803\pi\)
\(380\) −16.5681 −0.849923
\(381\) 0 0
\(382\) −7.45480 + 7.45480i −0.381421 + 0.381421i
\(383\) −9.25710 9.25710i −0.473016 0.473016i 0.429874 0.902889i \(-0.358558\pi\)
−0.902889 + 0.429874i \(0.858558\pi\)
\(384\) 0 0
\(385\) −5.88482 0.655498i −0.299918 0.0334073i
\(386\) −19.2851 −0.981586
\(387\) 0 0
\(388\) 9.34336 9.34336i 0.474337 0.474337i
\(389\) 33.6641i 1.70684i 0.521224 + 0.853420i \(0.325476\pi\)
−0.521224 + 0.853420i \(0.674524\pi\)
\(390\) 0 0
\(391\) 17.9514i 0.907841i
\(392\) 3.73926 + 5.91760i 0.188861 + 0.298884i
\(393\) 0 0
\(394\) 19.0457i 0.959508i
\(395\) −23.7331 23.7331i −1.19414 1.19414i
\(396\) 0 0
\(397\) 24.1629 24.1629i 1.21270 1.21270i 0.242566 0.970135i \(-0.422011\pi\)
0.970135 0.242566i \(-0.0779889\pi\)
\(398\) −4.18927 + 4.18927i −0.209989 + 0.209989i
\(399\) 0 0
\(400\) 4.40303i 0.220152i
\(401\) 8.28885 + 8.28885i 0.413925 + 0.413925i 0.883104 0.469178i \(-0.155450\pi\)
−0.469178 + 0.883104i \(0.655450\pi\)
\(402\) 0 0
\(403\) −15.8382 15.4308i −0.788958 0.768661i
\(404\) 5.86058i 0.291575i
\(405\) 0 0
\(406\) 10.4510 + 13.0711i 0.518674 + 0.648706i
\(407\) 3.69769i 0.183288i
\(408\) 0 0
\(409\) −7.74077 7.74077i −0.382756 0.382756i 0.489338 0.872094i \(-0.337238\pi\)
−0.872094 + 0.489338i \(0.837238\pi\)
\(410\) 0.540319 + 0.540319i 0.0266845 + 0.0266845i
\(411\) 0 0
\(412\) 9.16965i 0.451756i
\(413\) −7.42650 9.28833i −0.365434 0.457049i
\(414\) 0 0
\(415\) 4.38508i 0.215255i
\(416\) 2.51608 2.58251i 0.123361 0.126618i
\(417\) 0 0
\(418\) −2.78837 2.78837i −0.136384 0.136384i
\(419\) 37.2548i 1.82002i 0.414592 + 0.910008i \(0.363924\pi\)
−0.414592 + 0.910008i \(0.636076\pi\)
\(420\) 0 0
\(421\) 26.1725 26.1725i 1.27557 1.27557i 0.332451 0.943121i \(-0.392125\pi\)
0.943121 0.332451i \(-0.107875\pi\)
\(422\) −4.98091 + 4.98091i −0.242467 + 0.242467i
\(423\) 0 0
\(424\) −0.364115 0.364115i −0.0176830 0.0176830i
\(425\) 11.3361i 0.549880i
\(426\) 0 0
\(427\) 16.8605 + 1.87805i 0.815936 + 0.0908854i
\(428\) 7.91334i 0.382506i
\(429\) 0 0
\(430\) 24.2091i 1.16747i
\(431\) −2.05151 + 2.05151i −0.0988177 + 0.0988177i −0.754787 0.655970i \(-0.772260\pi\)
0.655970 + 0.754787i \(0.272260\pi\)
\(432\) 0 0
\(433\) 15.7613 0.757441 0.378720 0.925511i \(-0.376364\pi\)
0.378720 + 0.925511i \(0.376364\pi\)
\(434\) −1.79628 + 16.1263i −0.0862240 + 0.774088i
\(435\) 0 0
\(436\) −9.90330 9.90330i −0.474282 0.474282i
\(437\) −26.6385 + 26.6385i −1.27429 + 1.27429i
\(438\) 0 0
\(439\) 10.8489 0.517788 0.258894 0.965906i \(-0.416642\pi\)
0.258894 + 0.965906i \(0.416642\pi\)
\(440\) 1.58251 1.58251i 0.0754433 0.0754433i
\(441\) 0 0
\(442\) 6.47790 6.64895i 0.308122 0.316258i
\(443\) 9.19115 0.436685 0.218342 0.975872i \(-0.429935\pi\)
0.218342 + 0.975872i \(0.429935\pi\)
\(444\) 0 0
\(445\) −4.81261 −0.228140
\(446\) −13.7380 −0.650514
\(447\) 0 0
\(448\) −2.62949 0.292893i −0.124232 0.0138379i
\(449\) −15.6122 15.6122i −0.736784 0.736784i 0.235170 0.971954i \(-0.424435\pi\)
−0.971954 + 0.235170i \(0.924435\pi\)
\(450\) 0 0
\(451\) 0.181869i 0.00856389i
\(452\) 11.9450i 0.561844i
\(453\) 0 0
\(454\) −19.6576 −0.922577
\(455\) −22.6070 + 18.5634i −1.05983 + 0.870267i
\(456\) 0 0
\(457\) −26.7396 + 26.7396i −1.25083 + 1.25083i −0.295477 + 0.955350i \(0.595479\pi\)
−0.955350 + 0.295477i \(0.904521\pi\)
\(458\) 8.44334i 0.394532i
\(459\) 0 0
\(460\) −15.1184 15.1184i −0.704900 0.704900i
\(461\) 17.1846 + 17.1846i 0.800368 + 0.800368i 0.983153 0.182785i \(-0.0585111\pi\)
−0.182785 + 0.983153i \(0.558511\pi\)
\(462\) 0 0
\(463\) −16.9948 16.9948i −0.789816 0.789816i 0.191648 0.981464i \(-0.438617\pi\)
−0.981464 + 0.191648i \(0.938617\pi\)
\(464\) −6.32541 −0.293650
\(465\) 0 0
\(466\) 0.956669 + 0.956669i 0.0443168 + 0.0443168i
\(467\) −7.72653 −0.357541 −0.178771 0.983891i \(-0.557212\pi\)
−0.178771 + 0.983891i \(0.557212\pi\)
\(468\) 0 0
\(469\) −9.25596 11.5764i −0.427400 0.534550i
\(470\) −4.33660 + 4.33660i −0.200032 + 0.200032i
\(471\) 0 0
\(472\) 4.49485 0.206892
\(473\) 4.07434 4.07434i 0.187338 0.187338i
\(474\) 0 0
\(475\) −16.8219 + 16.8219i −0.771841 + 0.771841i
\(476\) −6.76990 0.754084i −0.310298 0.0345634i
\(477\) 0 0
\(478\) 29.5436i 1.35129i
\(479\) −26.0081 + 26.0081i −1.18834 + 1.18834i −0.210816 + 0.977526i \(0.567612\pi\)
−0.977526 + 0.210816i \(0.932388\pi\)
\(480\) 0 0
\(481\) 13.0841 + 12.7475i 0.596585 + 0.581238i
\(482\) 15.8131i 0.720269i
\(483\) 0 0
\(484\) −10.4673 −0.475788
\(485\) 40.5184i 1.83985i
\(486\) 0 0
\(487\) −12.7641 + 12.7641i −0.578398 + 0.578398i −0.934462 0.356064i \(-0.884119\pi\)
0.356064 + 0.934462i \(0.384119\pi\)
\(488\) −4.53402 + 4.53402i −0.205246 + 0.205246i
\(489\) 0 0
\(490\) 20.9389 + 4.72329i 0.945925 + 0.213377i
\(491\) 43.7292i 1.97347i −0.162337 0.986735i \(-0.551903\pi\)
0.162337 0.986735i \(-0.448097\pi\)
\(492\) 0 0
\(493\) −16.2854 −0.733460
\(494\) −19.4793 + 0.253822i −0.876413 + 0.0114200i
\(495\) 0 0
\(496\) −4.33660 4.33660i −0.194719 0.194719i
\(497\) −18.9771 23.7347i −0.851240 1.06465i
\(498\) 0 0
\(499\) 6.31100 6.31100i 0.282519 0.282519i −0.551594 0.834113i \(-0.685980\pi\)
0.834113 + 0.551594i \(0.185980\pi\)
\(500\) 1.29440 + 1.29440i 0.0578875 + 0.0578875i
\(501\) 0 0
\(502\) 14.5923 14.5923i 0.651286 0.651286i
\(503\) 23.4423i 1.04524i 0.852565 + 0.522620i \(0.175046\pi\)
−0.852565 + 0.522620i \(0.824954\pi\)
\(504\) 0 0
\(505\) 12.7075 + 12.7075i 0.565475 + 0.565475i
\(506\) 5.08880i 0.226225i
\(507\) 0 0
\(508\) 19.2112 0.852361
\(509\) 16.5795 + 16.5795i 0.734874 + 0.734874i 0.971581 0.236707i \(-0.0760682\pi\)
−0.236707 + 0.971581i \(0.576068\pi\)
\(510\) 0 0
\(511\) −27.1176 33.9161i −1.19961 1.50036i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −6.51494 + 6.51494i −0.287362 + 0.287362i
\(515\) −19.8825 19.8825i −0.876130 0.876130i
\(516\) 0 0
\(517\) −1.45968 −0.0641967
\(518\) 1.48392 13.3221i 0.0651999 0.585341i
\(519\) 0 0
\(520\) −0.144054 11.0553i −0.00631719 0.484805i
\(521\) 32.3153i 1.41576i −0.706332 0.707880i \(-0.749652\pi\)
0.706332 0.707880i \(-0.250348\pi\)
\(522\) 0 0
\(523\) 11.3376i 0.495757i 0.968791 + 0.247878i \(0.0797333\pi\)
−0.968791 + 0.247878i \(0.920267\pi\)
\(524\) 9.83056 0.429450
\(525\) 0 0
\(526\) −6.72080 + 6.72080i −0.293041 + 0.293041i
\(527\) −11.1650 11.1650i −0.486356 0.486356i
\(528\) 0 0
\(529\) −25.6155 −1.11372
\(530\) −1.57902 −0.0685882
\(531\) 0 0
\(532\) 8.92701 + 11.1650i 0.387035 + 0.484065i
\(533\) 0.643537 + 0.626982i 0.0278747 + 0.0271576i
\(534\) 0 0
\(535\) 17.1585 + 17.1585i 0.741825 + 0.741825i
\(536\) 5.60212 0.241975
\(537\) 0 0
\(538\) −11.1315 11.1315i −0.479912 0.479912i
\(539\) 2.72906 + 4.31890i 0.117549 + 0.186028i
\(540\) 0 0
\(541\) 17.1266 + 17.1266i 0.736329 + 0.736329i 0.971866 0.235536i \(-0.0756847\pi\)
−0.235536 + 0.971866i \(0.575685\pi\)
\(542\) 24.7129i 1.06151i
\(543\) 0 0
\(544\) 1.82052 1.82052i 0.0780542 0.0780542i
\(545\) −42.9466 −1.83963
\(546\) 0 0
\(547\) 0.145972 0.00624133 0.00312066 0.999995i \(-0.499007\pi\)
0.00312066 + 0.999995i \(0.499007\pi\)
\(548\) −3.88019 + 3.88019i −0.165754 + 0.165754i
\(549\) 0 0
\(550\) 3.21351i 0.137025i
\(551\) 24.1664 + 24.1664i 1.02952 + 1.02952i
\(552\) 0 0
\(553\) −3.20586 + 28.7810i −0.136327 + 1.22389i
\(554\) 15.1315 + 15.1315i 0.642875 + 0.642875i
\(555\) 0 0
\(556\) 3.32681 0.141088
\(557\) 18.1533 + 18.1533i 0.769181 + 0.769181i 0.977962 0.208782i \(-0.0669498\pi\)
−0.208782 + 0.977962i \(0.566950\pi\)
\(558\) 0 0
\(559\) −0.370882 28.4629i −0.0156866 1.20385i
\(560\) −6.33660 + 5.06644i −0.267770 + 0.214096i
\(561\) 0 0
\(562\) −0.897000 −0.0378376
\(563\) 21.4249 0.902951 0.451476 0.892283i \(-0.350898\pi\)
0.451476 + 0.892283i \(0.350898\pi\)
\(564\) 0 0
\(565\) 25.9002 + 25.9002i 1.08963 + 1.08963i
\(566\) 8.23801 8.23801i 0.346269 0.346269i
\(567\) 0 0
\(568\) 11.4858 0.481934
\(569\) 26.3627i 1.10518i 0.833452 + 0.552591i \(0.186361\pi\)
−0.833452 + 0.552591i \(0.813639\pi\)
\(570\) 0 0
\(571\) 21.5077i 0.900068i −0.893012 0.450034i \(-0.851412\pi\)
0.893012 0.450034i \(-0.148588\pi\)
\(572\) 1.83633 1.88482i 0.0767810 0.0788083i
\(573\) 0 0
\(574\) 0.0729862 0.655244i 0.00304638 0.0273493i
\(575\) −30.7001 −1.28028
\(576\) 0 0
\(577\) 11.5787 + 11.5787i 0.482028 + 0.482028i 0.905779 0.423751i \(-0.139287\pi\)
−0.423751 + 0.905779i \(0.639287\pi\)
\(578\) −7.33369 + 7.33369i −0.305041 + 0.305041i
\(579\) 0 0
\(580\) −13.7154 + 13.7154i −0.569500 + 0.569500i
\(581\) −2.95506 + 2.36272i −0.122596 + 0.0980222i
\(582\) 0 0
\(583\) −0.265746 0.265746i −0.0110061 0.0110061i
\(584\) 16.4128 0.679167
\(585\) 0 0
\(586\) 23.1585i 0.956668i
\(587\) −27.3890 27.3890i −1.13047 1.13047i −0.990099 0.140368i \(-0.955172\pi\)
−0.140368 0.990099i \(-0.544828\pi\)
\(588\) 0 0
\(589\) 33.1361i 1.36535i
\(590\) 9.74618 9.74618i 0.401244 0.401244i
\(591\) 0 0
\(592\) 3.58251 + 3.58251i 0.147240 + 0.147240i
\(593\) 12.3499 12.3499i 0.507150 0.507150i −0.406500 0.913651i \(-0.633251\pi\)
0.913651 + 0.406500i \(0.133251\pi\)
\(594\) 0 0
\(595\) −16.3142 + 13.0441i −0.668818 + 0.534755i
\(596\) 8.02774 + 8.02774i 0.328829 + 0.328829i
\(597\) 0 0
\(598\) −18.0065 17.5433i −0.736341 0.717398i
\(599\) 29.0798 1.18817 0.594084 0.804403i \(-0.297515\pi\)
0.594084 + 0.804403i \(0.297515\pi\)
\(600\) 0 0
\(601\) 28.7194i 1.17149i 0.810496 + 0.585744i \(0.199198\pi\)
−0.810496 + 0.585744i \(0.800802\pi\)
\(602\) −16.3142 + 13.0441i −0.664919 + 0.531637i
\(603\) 0 0
\(604\) 13.5417 13.5417i 0.551003 0.551003i
\(605\) −22.6963 + 22.6963i −0.922736 + 0.922736i
\(606\) 0 0
\(607\) 22.9366i 0.930967i −0.885056 0.465484i \(-0.845880\pi\)
0.885056 0.465484i \(-0.154120\pi\)
\(608\) −5.40303 −0.219122
\(609\) 0 0
\(610\) 19.6622i 0.796100i
\(611\) −5.03215 + 5.16502i −0.203579 + 0.208954i
\(612\) 0 0
\(613\) −5.54006 + 5.54006i −0.223761 + 0.223761i −0.810080 0.586319i \(-0.800576\pi\)
0.586319 + 0.810080i \(0.300576\pi\)
\(614\) 21.0299i 0.848697i
\(615\) 0 0
\(616\) −1.91911 0.213765i −0.0773230 0.00861285i
\(617\) 3.86438 3.86438i 0.155574 0.155574i −0.625028 0.780602i \(-0.714913\pi\)
0.780602 + 0.625028i \(0.214913\pi\)
\(618\) 0 0
\(619\) −25.0182 + 25.0182i −1.00557 + 1.00557i −0.00558273 + 0.999984i \(0.501777\pi\)
−0.999984 + 0.00558273i \(0.998223\pi\)
\(620\) −18.8061 −0.755270
\(621\) 0 0
\(622\) 18.4194 18.4194i 0.738549 0.738549i
\(623\) 2.59308 + 3.24317i 0.103890 + 0.129935i
\(624\) 0 0
\(625\) 27.6285 1.10514
\(626\) −9.26361 9.26361i −0.370248 0.370248i
\(627\) 0 0
\(628\) −3.14458 −0.125482
\(629\) 9.22355 + 9.22355i 0.367767 + 0.367767i
\(630\) 0 0
\(631\) −8.12549 8.12549i −0.323471 0.323471i 0.526626 0.850097i \(-0.323457\pi\)
−0.850097 + 0.526626i \(0.823457\pi\)
\(632\) −7.73963 7.73963i −0.307866 0.307866i
\(633\) 0 0
\(634\) 22.0839i 0.877063i
\(635\) 41.6557 41.6557i 1.65306 1.65306i
\(636\) 0 0
\(637\) 24.6905 + 5.23244i 0.978274 + 0.207317i
\(638\) −4.61654 −0.182771
\(639\) 0 0
\(640\) 3.06644i 0.121212i
\(641\) 42.7580i 1.68884i 0.535682 + 0.844420i \(0.320055\pi\)
−0.535682 + 0.844420i \(0.679945\pi\)
\(642\) 0 0
\(643\) −7.37341 7.37341i −0.290779 0.290779i 0.546609 0.837388i \(-0.315918\pi\)
−0.837388 + 0.546609i \(0.815918\pi\)
\(644\) −2.04219 + 18.3341i −0.0804737 + 0.722463i
\(645\) 0 0
\(646\) −13.9107 −0.547308
\(647\) 22.7445 0.894178 0.447089 0.894490i \(-0.352461\pi\)
0.447089 + 0.894490i \(0.352461\pi\)
\(648\) 0 0
\(649\) 3.28052 0.128772
\(650\) −11.3709 11.0784i −0.446003 0.434529i
\(651\) 0 0
\(652\) −15.2816 + 15.2816i −0.598472 + 0.598472i
\(653\) 28.5645 1.11782 0.558908 0.829230i \(-0.311220\pi\)
0.558908 + 0.829230i \(0.311220\pi\)
\(654\) 0 0
\(655\) 21.3156 21.3156i 0.832869 0.832869i
\(656\) 0.176204 + 0.176204i 0.00687962 + 0.00687962i
\(657\) 0 0
\(658\) 5.25898 + 0.585786i 0.205016 + 0.0228363i
\(659\) 24.6149 0.958862 0.479431 0.877580i \(-0.340843\pi\)
0.479431 + 0.877580i \(0.340843\pi\)
\(660\) 0 0
\(661\) 14.7668 14.7668i 0.574363 0.574363i −0.358981 0.933345i \(-0.616876\pi\)
0.933345 + 0.358981i \(0.116876\pi\)
\(662\) 8.50839i 0.330688i
\(663\) 0 0
\(664\) 1.43003i 0.0554958i
\(665\) 43.5655 + 4.85267i 1.68940 + 0.188179i
\(666\) 0 0
\(667\) 44.1038i 1.70771i
\(668\) 9.21892 + 9.21892i 0.356691 + 0.356691i
\(669\) 0 0
\(670\) 12.1471 12.1471i 0.469282 0.469282i
\(671\) −3.30911 + 3.30911i −0.127747 + 0.127747i
\(672\) 0 0
\(673\) 50.9335i 1.96334i −0.190584 0.981671i \(-0.561038\pi\)
0.190584 0.981671i \(-0.438962\pi\)
\(674\) −0.875033 0.875033i −0.0337050 0.0337050i
\(675\) 0 0
\(676\) −0.338732 12.9956i −0.0130282 0.499830i
\(677\) 4.02891i 0.154844i −0.996998 0.0774218i \(-0.975331\pi\)
0.996998 0.0774218i \(-0.0246688\pi\)
\(678\) 0 0
\(679\) −27.3049 + 21.8317i −1.04787 + 0.837822i
\(680\) 7.89486i 0.302754i
\(681\) 0 0
\(682\) −3.16502 3.16502i −0.121195 0.121195i
\(683\) 17.3021 + 17.3021i 0.662045 + 0.662045i 0.955862 0.293817i \(-0.0949256\pi\)
−0.293817 + 0.955862i \(0.594926\pi\)
\(684\) 0 0
\(685\) 16.8268i 0.642920i
\(686\) −8.09911 16.6555i −0.309226 0.635908i
\(687\) 0 0
\(688\) 7.89486i 0.300989i
\(689\) −1.85647 + 0.0241905i −0.0707259 + 0.000921585i
\(690\) 0 0
\(691\) −2.49183 2.49183i −0.0947937 0.0947937i 0.658120 0.752913i \(-0.271352\pi\)
−0.752913 + 0.658120i \(0.771352\pi\)
\(692\) 17.4793i 0.664462i
\(693\) 0 0
\(694\) 8.59932 8.59932i 0.326426 0.326426i
\(695\) 7.21351 7.21351i 0.273624 0.273624i
\(696\) 0 0
\(697\) 0.453656 + 0.453656i 0.0171835 + 0.0171835i
\(698\) 25.4024i 0.961494i
\(699\) 0 0
\(700\) −1.28962 + 11.5777i −0.0487430 + 0.437597i
\(701\) 0.236091i 0.00891703i −0.999990 0.00445852i \(-0.998581\pi\)
0.999990 0.00445852i \(-0.00141919\pi\)
\(702\) 0 0
\(703\) 27.3741i 1.03243i
\(704\) 0.516075 0.516075i 0.0194503 0.0194503i
\(705\) 0 0
\(706\) 29.9876 1.12860
\(707\) 1.71652 15.4103i 0.0645565 0.579565i
\(708\) 0 0
\(709\) 9.68526 + 9.68526i 0.363737 + 0.363737i 0.865187 0.501449i \(-0.167200\pi\)
−0.501449 + 0.865187i \(0.667200\pi\)
\(710\) 24.9047 24.9047i 0.934655 0.934655i
\(711\) 0 0
\(712\) −1.56945 −0.0588176
\(713\) −30.2368 + 30.2368i −1.13238 + 1.13238i
\(714\) 0 0
\(715\) −0.105136 8.06857i −0.00393188 0.301747i
\(716\) −18.3235 −0.684781
\(717\) 0 0
\(718\) −28.9008 −1.07857
\(719\) 47.6518 1.77711 0.888556 0.458768i \(-0.151709\pi\)
0.888556 + 0.458768i \(0.151709\pi\)
\(720\) 0 0
\(721\) −2.68573 + 24.1115i −0.100022 + 0.897959i
\(722\) 7.20737 + 7.20737i 0.268231 + 0.268231i
\(723\) 0 0
\(724\) 4.96432i 0.184498i
\(725\) 27.8510i 1.03436i
\(726\) 0 0
\(727\) 10.6947 0.396644 0.198322 0.980137i \(-0.436451\pi\)
0.198322 + 0.980137i \(0.436451\pi\)
\(728\) −7.37239 + 6.05374i −0.273239 + 0.224367i
\(729\) 0 0
\(730\) 35.5879 35.5879i 1.31717 1.31717i
\(731\) 20.3262i 0.751790i
\(732\) 0 0
\(733\) −1.22630 1.22630i −0.0452945 0.0452945i 0.684097 0.729391i \(-0.260197\pi\)
−0.729391 + 0.684097i \(0.760197\pi\)
\(734\) −0.777803 0.777803i −0.0287092 0.0287092i
\(735\) 0 0
\(736\) −4.93029 4.93029i −0.181733 0.181733i
\(737\) 4.08866 0.150608
\(738\) 0 0
\(739\) 10.0141 + 10.0141i 0.368373 + 0.368373i 0.866884 0.498511i \(-0.166119\pi\)
−0.498511 + 0.866884i \(0.666119\pi\)
\(740\) 15.5359 0.571111
\(741\) 0 0
\(742\) 0.850789 + 1.06408i 0.0312335 + 0.0390637i
\(743\) 17.3229 17.3229i 0.635516 0.635516i −0.313930 0.949446i \(-0.601646\pi\)
0.949446 + 0.313930i \(0.101646\pi\)
\(744\) 0 0
\(745\) 34.8130 1.27545
\(746\) 14.5934 14.5934i 0.534304 0.534304i
\(747\) 0 0
\(748\) 1.32869 1.32869i 0.0485817 0.0485817i
\(749\) 2.31776 20.8080i 0.0846892 0.760309i
\(750\) 0 0
\(751\) 38.8207i 1.41659i −0.705919 0.708293i \(-0.749466\pi\)
0.705919 0.708293i \(-0.250534\pi\)
\(752\) −1.41421 + 1.41421i −0.0515711 + 0.0515711i
\(753\) 0 0
\(754\) −15.9152 + 16.3355i −0.579598 + 0.594902i
\(755\) 58.7248i 2.13721i
\(756\) 0 0
\(757\) −12.6121 −0.458395 −0.229198 0.973380i \(-0.573610\pi\)
−0.229198 + 0.973380i \(0.573610\pi\)
\(758\) 8.23110i 0.298967i
\(759\) 0 0
\(760\) −11.7154 + 11.7154i −0.424962 + 0.424962i
\(761\) −30.3727 + 30.3727i −1.10101 + 1.10101i −0.106721 + 0.994289i \(0.534035\pi\)
−0.994289 + 0.106721i \(0.965965\pi\)
\(762\) 0 0
\(763\) 23.1400 + 28.9412i 0.837724 + 1.04774i
\(764\) 10.5427i 0.381421i
\(765\) 0 0
\(766\) −13.0915 −0.473016
\(767\) 11.3094 11.6080i 0.408358 0.419141i
\(768\) 0 0
\(769\) −0.566917 0.566917i −0.0204435 0.0204435i 0.696811 0.717255i \(-0.254602\pi\)
−0.717255 + 0.696811i \(0.754602\pi\)
\(770\) −4.62470 + 3.69769i −0.166663 + 0.133256i
\(771\) 0 0
\(772\) −13.6366 + 13.6366i −0.490793 + 0.490793i
\(773\) 23.9977 + 23.9977i 0.863137 + 0.863137i 0.991701 0.128564i \(-0.0410369\pi\)
−0.128564 + 0.991701i \(0.541037\pi\)
\(774\) 0 0
\(775\) −19.0942 + 19.0942i −0.685883 + 0.685883i
\(776\) 13.2135i 0.474337i
\(777\) 0 0
\(778\) 23.8041 + 23.8041i 0.853420 + 0.853420i
\(779\) 1.34638i 0.0482392i
\(780\) 0 0
\(781\) 8.38281 0.299960
\(782\) −12.6935 12.6935i −0.453920 0.453920i
\(783\) 0 0
\(784\) 6.82843 + 1.54032i 0.243872 + 0.0550114i
\(785\) −6.81838 + 6.81838i −0.243359 + 0.243359i
\(786\) 0 0
\(787\) −32.7888 + 32.7888i −1.16879 + 1.16879i −0.186302 + 0.982492i \(0.559650\pi\)
−0.982492 + 0.186302i \(0.940350\pi\)
\(788\) 13.4673 + 13.4673i 0.479754 + 0.479754i
\(789\) 0 0
\(790\) −33.5636 −1.19414
\(791\) 3.49860 31.4091i 0.124396 1.11678i
\(792\) 0 0
\(793\) 0.301224 + 23.1171i 0.0106968 + 0.820913i
\(794\) 34.1715i 1.21270i
\(795\) 0 0
\(796\) 5.92452i 0.209989i
\(797\) 0.606614 0.0214874 0.0107437 0.999942i \(-0.496580\pi\)
0.0107437 + 0.999942i \(0.496580\pi\)
\(798\) 0 0
\(799\) −3.64104 + 3.64104i −0.128811 + 0.128811i
\(800\) −3.11341 3.11341i −0.110076 0.110076i
\(801\) 0 0
\(802\) 11.7222 0.413925
\(803\) 11.9787 0.422721
\(804\) 0 0
\(805\) 35.3256 + 44.1818i 1.24506 + 1.55720i
\(806\) −22.1105 + 0.288108i −0.778810 + 0.0101482i
\(807\) 0 0
\(808\) 4.14405 + 4.14405i 0.145787 + 0.145787i
\(809\) −1.54084 −0.0541732 −0.0270866 0.999633i \(-0.508623\pi\)
−0.0270866 + 0.999633i \(0.508623\pi\)
\(810\) 0 0
\(811\) 17.4392 + 17.4392i 0.612373 + 0.612373i 0.943564 0.331191i \(-0.107450\pi\)
−0.331191 + 0.943564i \(0.607450\pi\)
\(812\) 16.6326 + 1.85267i 0.583690 + 0.0650160i
\(813\) 0 0
\(814\) 2.61466 + 2.61466i 0.0916438 + 0.0916438i
\(815\) 66.2699i 2.32133i
\(816\) 0 0
\(817\) −30.1625 + 30.1625i −1.05525 + 1.05525i
\(818\) −10.9471 −0.382756
\(819\) 0 0
\(820\) 0.764127 0.0266845
\(821\) 20.4659 20.4659i 0.714266 0.714266i −0.253159 0.967425i \(-0.581469\pi\)
0.967425 + 0.253159i \(0.0814694\pi\)
\(822\) 0 0
\(823\) 7.39538i 0.257787i 0.991658 + 0.128893i \(0.0411425\pi\)
−0.991658 + 0.128893i \(0.958858\pi\)
\(824\) −6.48392 6.48392i −0.225878 0.225878i
\(825\) 0 0
\(826\) −11.8192 1.31651i −0.411241 0.0458073i
\(827\) 0.405564 + 0.405564i 0.0141029 + 0.0141029i 0.714123 0.700020i \(-0.246826\pi\)
−0.700020 + 0.714123i \(0.746826\pi\)
\(828\) 0 0
\(829\) −3.28950 −0.114249 −0.0571245 0.998367i \(-0.518193\pi\)
−0.0571245 + 0.998367i \(0.518193\pi\)
\(830\) −3.10072 3.10072i −0.107628 0.107628i
\(831\) 0 0
\(832\) −0.0469777 3.60525i −0.00162866 0.124989i
\(833\) 17.5805 + 3.96571i 0.609128 + 0.137404i
\(834\) 0 0
\(835\) 39.9787 1.38352
\(836\) −3.94335 −0.136384
\(837\) 0 0
\(838\) 26.3431 + 26.3431i 0.910008 + 0.910008i
\(839\) −8.32703 + 8.32703i −0.287481 + 0.287481i −0.836083 0.548602i \(-0.815160\pi\)
0.548602 + 0.836083i \(0.315160\pi\)
\(840\) 0 0
\(841\) 11.0109 0.379685
\(842\) 37.0136i 1.27557i
\(843\) 0 0
\(844\) 7.04407i 0.242467i
\(845\) −28.9128 27.4438i −0.994630 0.944097i
\(846\) 0 0
\(847\) 27.5237 + 3.06581i 0.945727 + 0.105343i
\(848\) −0.514936 −0.0176830
\(849\) 0 0
\(850\) −8.01581 8.01581i −0.274940 0.274940i
\(851\) 24.9790 24.9790i 0.856269 0.856269i
\(852\) 0 0
\(853\) 11.6895 11.6895i 0.400242 0.400242i −0.478076 0.878318i \(-0.658666\pi\)
0.878318 + 0.478076i \(0.158666\pi\)
\(854\) 13.2502 10.5942i 0.453411 0.362525i
\(855\) 0 0
\(856\) 5.59557 + 5.59557i 0.191253 + 0.191253i
\(857\) 17.6693 0.603573 0.301787 0.953376i \(-0.402417\pi\)
0.301787 + 0.953376i \(0.402417\pi\)
\(858\) 0 0
\(859\) 41.1971i 1.40563i −0.711374 0.702813i \(-0.751927\pi\)
0.711374 0.702813i \(-0.248073\pi\)
\(860\) −17.1184 17.1184i −0.583733 0.583733i
\(861\) 0 0
\(862\) 2.90127i 0.0988177i
\(863\) −5.50354 + 5.50354i −0.187343 + 0.187343i −0.794546 0.607204i \(-0.792291\pi\)
0.607204 + 0.794546i \(0.292291\pi\)
\(864\) 0 0
\(865\) −37.9002 37.9002i −1.28865 1.28865i
\(866\) 11.1449 11.1449i 0.378720 0.378720i
\(867\) 0 0
\(868\) 10.1329 + 12.6732i 0.343932 + 0.430156i
\(869\) −5.64869 5.64869i −0.191619 0.191619i
\(870\) 0 0
\(871\) 14.0954 14.4676i 0.477603 0.490214i
\(872\) −14.0054 −0.474282
\(873\) 0 0
\(874\) 37.6725i 1.27429i
\(875\) −3.02450 3.78274i −0.102247 0.127880i
\(876\) 0 0
\(877\) 14.6890 14.6890i 0.496012 0.496012i −0.414182 0.910194i \(-0.635932\pi\)
0.910194 + 0.414182i \(0.135932\pi\)
\(878\) 7.67131 7.67131i 0.258894 0.258894i
\(879\) 0 0
\(880\) 2.23801i 0.0754433i
\(881\) −9.22544 −0.310813 −0.155406 0.987851i \(-0.549669\pi\)
−0.155406 + 0.987851i \(0.549669\pi\)
\(882\) 0 0
\(883\) 26.4515i 0.890165i −0.895490 0.445083i \(-0.853174\pi\)
0.895490 0.445083i \(-0.146826\pi\)
\(884\) −0.120949 9.28208i −0.00406795 0.312190i
\(885\) 0 0
\(886\) 6.49912 6.49912i 0.218342 0.218342i
\(887\) 11.7136i 0.393303i −0.980473 0.196651i \(-0.936993\pi\)
0.980473 0.196651i \(-0.0630067\pi\)
\(888\) 0 0
\(889\) −50.5157 5.62684i −1.69424 0.188718i
\(890\) −3.40303 + 3.40303i −0.114070 + 0.114070i
\(891\) 0 0
\(892\) −9.71425 + 9.71425i −0.325257 + 0.325257i
\(893\) 10.8061 0.361611
\(894\) 0 0
\(895\) −39.7308 + 39.7308i −1.32805 + 1.32805i
\(896\) −2.06644 + 1.65222i −0.0690348 + 0.0551969i
\(897\) 0 0
\(898\) −22.0789 −0.736784
\(899\) 27.4308 + 27.4308i 0.914867 + 0.914867i
\(900\) 0 0
\(901\) −1.32576 −0.0441674
\(902\) 0.128601 + 0.128601i 0.00428194 + 0.00428194i
\(903\) 0 0
\(904\) 8.44636 + 8.44636i 0.280922 + 0.280922i
\(905\) 10.7641 + 10.7641i 0.357812 + 0.357812i
\(906\) 0 0
\(907\) 24.4074i 0.810436i 0.914220 + 0.405218i \(0.132804\pi\)
−0.914220 + 0.405218i \(0.867196\pi\)
\(908\) −13.9000 + 13.9000i −0.461288 + 0.461288i
\(909\) 0 0
\(910\) −2.85922 + 29.1119i −0.0947822 + 0.965049i
\(911\) 35.7796 1.18543 0.592715 0.805412i \(-0.298056\pi\)
0.592715 + 0.805412i \(0.298056\pi\)
\(912\) 0 0
\(913\) 1.04369i 0.0345411i
\(914\) 37.8155i 1.25083i
\(915\) 0 0
\(916\) −5.97035 5.97035i −0.197266 0.197266i
\(917\) −25.8494 2.87931i −0.853621 0.0950830i
\(918\) 0 0
\(919\) 21.9957 0.725572 0.362786 0.931872i \(-0.381826\pi\)
0.362786 + 0.931872i \(0.381826\pi\)
\(920\) −21.3807 −0.704900
\(921\) 0 0
\(922\) 24.3027 0.800368
\(923\) 28.8992 29.6622i 0.951227 0.976344i
\(924\) 0 0
\(925\) 15.7739 15.7739i 0.518643 0.518643i
\(926\) −24.0343 −0.789816
\(927\) 0 0
\(928\) −4.47274 + 4.47274i −0.146825 + 0.146825i
\(929\) −11.1005 11.1005i −0.364196 0.364196i 0.501159 0.865355i \(-0.332907\pi\)
−0.865355 + 0.501159i \(0.832907\pi\)
\(930\) 0 0
\(931\) −20.2033 31.9730i −0.662137 1.04787i
\(932\) 1.35293 0.0443168
\(933\) 0 0
\(934\) −5.46348 + 5.46348i −0.178771 + 0.178771i
\(935\) 5.76199i 0.188437i
\(936\) 0 0
\(937\) 32.9296i 1.07576i −0.843020 0.537882i \(-0.819225\pi\)
0.843020 0.537882i \(-0.180775\pi\)
\(938\) −14.7307 1.64082i −0.480975 0.0535748i
\(939\) 0 0
\(940\) 6.13287i 0.200032i
\(941\) −16.5400 16.5400i −0.539189 0.539189i 0.384102 0.923291i \(-0.374511\pi\)
−0.923291 + 0.384102i \(0.874511\pi\)
\(942\) 0 0
\(943\) 1.22858 1.22858i 0.0400081 0.0400081i
\(944\) 3.17834 3.17834i 0.103446 0.103446i
\(945\) 0 0
\(946\) 5.76199i 0.187338i
\(947\) −8.74592 8.74592i −0.284204 0.284204i 0.550579 0.834783i \(-0.314407\pi\)
−0.834783 + 0.550579i \(0.814407\pi\)
\(948\) 0 0
\(949\) 41.2959 42.3863i 1.34052 1.37592i
\(950\) 23.7897i 0.771841i
\(951\) 0 0
\(952\) −5.32026 + 4.25382i −0.172431 + 0.137867i
\(953\) 14.1171i 0.457296i 0.973509 + 0.228648i \(0.0734306\pi\)
−0.973509 + 0.228648i \(0.926569\pi\)
\(954\) 0 0
\(955\) 22.8597 + 22.8597i 0.739721 + 0.739721i
\(956\) 20.8904 + 20.8904i 0.675645 + 0.675645i
\(957\) 0 0
\(958\) 36.7810i 1.18834i
\(959\) 11.3394 9.06644i 0.366168 0.292771i
\(960\) 0 0
\(961\) 6.61213i 0.213295i
\(962\) 18.2657 0.238009i 0.588911 0.00767373i
\(963\) 0 0
\(964\) 11.1816 + 11.1816i 0.360134 + 0.360134i
\(965\) 59.1365i 1.90367i
\(966\) 0 0
\(967\) −17.8079 + 17.8079i −0.572664 + 0.572664i −0.932872 0.360208i \(-0.882706\pi\)
0.360208 + 0.932872i \(0.382706\pi\)
\(968\) −7.40152 + 7.40152i −0.237894 + 0.237894i
\(969\) 0 0
\(970\) −28.6508 28.6508i −0.919923 0.919923i
\(971\) 21.1673i 0.679291i 0.940554 + 0.339646i \(0.110307\pi\)
−0.940554 + 0.339646i \(0.889693\pi\)
\(972\) 0 0
\(973\) −8.74781 0.974400i −0.280442 0.0312378i
\(974\) 18.0512i 0.578398i
\(975\) 0 0
\(976\) 6.41208i 0.205246i
\(977\) −19.6568 + 19.6568i −0.628877 + 0.628877i −0.947786 0.318908i \(-0.896684\pi\)
0.318908 + 0.947786i \(0.396684\pi\)
\(978\) 0 0
\(979\) −1.14545 −0.0366086
\(980\) 18.1459 11.4662i 0.579651 0.366274i
\(981\) 0 0
\(982\) −30.9212 30.9212i −0.986735 0.986735i
\(983\) −17.7065 + 17.7065i −0.564749 + 0.564749i −0.930653 0.365904i \(-0.880760\pi\)
0.365904 + 0.930653i \(0.380760\pi\)
\(984\) 0 0
\(985\) 58.4024 1.86085
\(986\) −11.5155 + 11.5155i −0.366730 + 0.366730i
\(987\) 0 0
\(988\) −13.5944 + 13.9534i −0.432497 + 0.443917i
\(989\) −55.0468 −1.75039
\(990\) 0 0
\(991\) 26.3147 0.835913 0.417957 0.908467i \(-0.362746\pi\)
0.417957 + 0.908467i \(0.362746\pi\)
\(992\) −6.13287 −0.194719
\(993\) 0 0
\(994\) −30.2018 3.36411i −0.957943 0.106703i
\(995\) 12.8461 + 12.8461i 0.407249 + 0.407249i
\(996\) 0 0
\(997\) 3.40444i 0.107820i 0.998546 + 0.0539099i \(0.0171684\pi\)
−0.998546 + 0.0539099i \(0.982832\pi\)
\(998\) 8.92510i 0.282519i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1638.2.x.a.811.3 8
3.2 odd 2 546.2.o.c.265.2 yes 8
7.6 odd 2 1638.2.x.c.811.4 8
13.8 odd 4 1638.2.x.c.307.4 8
21.20 even 2 546.2.o.b.265.1 8
39.8 even 4 546.2.o.b.307.1 yes 8
91.34 even 4 inner 1638.2.x.a.307.3 8
273.125 odd 4 546.2.o.c.307.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.o.b.265.1 8 21.20 even 2
546.2.o.b.307.1 yes 8 39.8 even 4
546.2.o.c.265.2 yes 8 3.2 odd 2
546.2.o.c.307.2 yes 8 273.125 odd 4
1638.2.x.a.307.3 8 91.34 even 4 inner
1638.2.x.a.811.3 8 1.1 even 1 trivial
1638.2.x.c.307.4 8 13.8 odd 4
1638.2.x.c.811.4 8 7.6 odd 2