Properties

Label 325.2.x.b.93.5
Level $325$
Weight $2$
Character 325.93
Analytic conductor $2.595$
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] = [325,2,Mod(7,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("325.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.x (of order \(12\), degree \(4\), 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: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + 1263 x^{4} + 78 x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 93.5
Root \(-2.64975i\) of defining polynomial
Character \(\chi\) \(=\) 325.93
Dual form 325.2.x.b.7.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.29475 - 1.32488i) q^{2} +(-0.335680 + 1.25278i) q^{3} +(2.51060 - 4.34849i) q^{4} +(0.889471 + 3.31955i) q^{6} +(-0.0561740 + 0.0972962i) q^{7} -8.00544i q^{8} +(1.14131 + 0.658935i) q^{9} +O(q^{10})\) \(q+(2.29475 - 1.32488i) q^{2} +(-0.335680 + 1.25278i) q^{3} +(2.51060 - 4.34849i) q^{4} +(0.889471 + 3.31955i) q^{6} +(-0.0561740 + 0.0972962i) q^{7} -8.00544i q^{8} +(1.14131 + 0.658935i) q^{9} +(0.479564 - 1.78976i) q^{11} +(4.60492 + 4.60492i) q^{12} +(-2.96279 + 2.05471i) q^{13} +0.297695i q^{14} +(-5.58502 - 9.67354i) q^{16} +(2.63669 - 0.706500i) q^{17} +3.49203 q^{18} +(-6.72284 + 1.80138i) q^{19} +(-0.103034 - 0.103034i) q^{21} +(-1.27073 - 4.74241i) q^{22} +(3.10327 + 0.831519i) q^{23} +(10.0290 + 2.68727i) q^{24} +(-4.07664 + 8.64040i) q^{26} +(-3.95990 + 3.95990i) q^{27} +(0.282061 + 0.488544i) q^{28} +(-4.03134 + 2.32749i) q^{29} +(-0.624367 + 0.624367i) q^{31} +(-11.7667 - 6.79350i) q^{32} +(2.08118 + 1.20157i) q^{33} +(5.11454 - 5.11454i) q^{34} +(5.73074 - 3.30864i) q^{36} +(0.737435 + 1.27728i) q^{37} +(-13.0407 + 13.0407i) q^{38} +(-1.57955 - 4.40145i) q^{39} +(-5.24069 - 1.40424i) q^{41} +(-0.372945 - 0.0999302i) q^{42} +(-1.00860 - 3.76415i) q^{43} +(-6.57874 - 6.57874i) q^{44} +(8.22291 - 2.20332i) q^{46} +0.345095 q^{47} +(13.9936 - 3.74956i) q^{48} +(3.49369 + 6.05125i) q^{49} +3.54034i q^{51} +(1.49651 + 18.0422i) q^{52} +(3.59144 + 3.59144i) q^{53} +(-3.84062 + 14.3334i) q^{54} +(0.778898 + 0.449697i) q^{56} -9.02691i q^{57} +(-6.16729 + 10.6821i) q^{58} +(0.332494 + 1.24088i) q^{59} +(1.39151 - 2.41016i) q^{61} +(-0.605559 + 2.25998i) q^{62} +(-0.128224 + 0.0740300i) q^{63} -13.6621 q^{64} +6.36774 q^{66} +(-0.124992 + 0.0721643i) q^{67} +(3.54747 - 13.2394i) q^{68} +(-2.08342 + 3.60858i) q^{69} +(-1.41668 - 5.28713i) q^{71} +(5.27506 - 9.13667i) q^{72} -9.06221i q^{73} +(3.38447 + 1.95402i) q^{74} +(-9.04509 + 33.7567i) q^{76} +(0.147197 + 0.147197i) q^{77} +(-9.45605 - 8.00753i) q^{78} -15.1689i q^{79} +(-1.65480 - 2.86620i) q^{81} +(-13.8865 + 3.72089i) q^{82} -8.53853 q^{83} +(-0.706718 + 0.189365i) q^{84} +(-7.30152 - 7.30152i) q^{86} +(-1.56259 - 5.83166i) q^{87} +(-14.3278 - 3.83912i) q^{88} +(0.549735 + 0.147301i) q^{89} +(-0.0334840 - 0.403690i) q^{91} +(11.4069 - 11.4069i) q^{92} +(-0.572604 - 0.991779i) q^{93} +(0.791908 - 0.457208i) q^{94} +(12.4606 - 12.4606i) q^{96} +(12.9596 + 7.48223i) q^{97} +(16.0343 + 9.25742i) q^{98} +(1.72666 - 1.72666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27} - 18 q^{28} - 48 q^{32} - 18 q^{33} + 2 q^{34} + 36 q^{36} + 4 q^{37} + 8 q^{38} + 4 q^{39} + 10 q^{41} - 40 q^{42} - 10 q^{43} - 36 q^{44} + 4 q^{46} + 40 q^{47} + 56 q^{48} + 18 q^{49} + 30 q^{52} + 10 q^{53} - 48 q^{54} - 16 q^{59} - 16 q^{61} + 44 q^{62} + 36 q^{63} + 20 q^{64} - 32 q^{66} - 18 q^{67} - 22 q^{68} - 16 q^{69} - 16 q^{71} - 4 q^{72} + 18 q^{74} - 64 q^{76} + 28 q^{77} - 68 q^{78} - 14 q^{81} - 56 q^{82} - 48 q^{83} - 40 q^{84} + 60 q^{86} + 34 q^{87} - 82 q^{88} - 6 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 48 q^{94} + 56 q^{96} - 66 q^{97} + 30 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.29475 1.32488i 1.62264 0.936830i 0.636425 0.771338i \(-0.280412\pi\)
0.986211 0.165491i \(-0.0529210\pi\)
\(3\) −0.335680 + 1.25278i −0.193805 + 0.723291i 0.798768 + 0.601640i \(0.205486\pi\)
−0.992573 + 0.121651i \(0.961181\pi\)
\(4\) 2.51060 4.34849i 1.25530 2.17424i
\(5\) 0 0
\(6\) 0.889471 + 3.31955i 0.363125 + 1.35520i
\(7\) −0.0561740 + 0.0972962i −0.0212318 + 0.0367745i −0.876446 0.481500i \(-0.840092\pi\)
0.855214 + 0.518275i \(0.173425\pi\)
\(8\) 8.00544i 2.83035i
\(9\) 1.14131 + 0.658935i 0.380436 + 0.219645i
\(10\) 0 0
\(11\) 0.479564 1.78976i 0.144594 0.539632i −0.855179 0.518332i \(-0.826553\pi\)
0.999773 0.0212994i \(-0.00678031\pi\)
\(12\) 4.60492 + 4.60492i 1.32933 + 1.32933i
\(13\) −2.96279 + 2.05471i −0.821731 + 0.569875i
\(14\) 0.297695i 0.0795622i
\(15\) 0 0
\(16\) −5.58502 9.67354i −1.39626 2.41838i
\(17\) 2.63669 0.706500i 0.639492 0.171351i 0.0755186 0.997144i \(-0.475939\pi\)
0.563973 + 0.825793i \(0.309272\pi\)
\(18\) 3.49203 0.823080
\(19\) −6.72284 + 1.80138i −1.54233 + 0.413265i −0.927016 0.375021i \(-0.877636\pi\)
−0.615309 + 0.788286i \(0.710969\pi\)
\(20\) 0 0
\(21\) −0.103034 0.103034i −0.0224838 0.0224838i
\(22\) −1.27073 4.74241i −0.270920 1.01109i
\(23\) 3.10327 + 0.831519i 0.647077 + 0.173384i 0.567407 0.823438i \(-0.307947\pi\)
0.0796701 + 0.996821i \(0.474613\pi\)
\(24\) 10.0290 + 2.68727i 2.04717 + 0.548536i
\(25\) 0 0
\(26\) −4.07664 + 8.64040i −0.799495 + 1.69452i
\(27\) −3.95990 + 3.95990i −0.762083 + 0.762083i
\(28\) 0.282061 + 0.488544i 0.0533045 + 0.0923261i
\(29\) −4.03134 + 2.32749i −0.748601 + 0.432205i −0.825188 0.564858i \(-0.808931\pi\)
0.0765874 + 0.997063i \(0.475598\pi\)
\(30\) 0 0
\(31\) −0.624367 + 0.624367i −0.112140 + 0.112140i −0.760950 0.648810i \(-0.775267\pi\)
0.648810 + 0.760950i \(0.275267\pi\)
\(32\) −11.7667 6.79350i −2.08008 1.20093i
\(33\) 2.08118 + 1.20157i 0.362288 + 0.209167i
\(34\) 5.11454 5.11454i 0.877136 0.877136i
\(35\) 0 0
\(36\) 5.73074 3.30864i 0.955123 0.551441i
\(37\) 0.737435 + 1.27728i 0.121234 + 0.209983i 0.920254 0.391321i \(-0.127982\pi\)
−0.799021 + 0.601303i \(0.794648\pi\)
\(38\) −13.0407 + 13.0407i −2.11548 + 2.11548i
\(39\) −1.57955 4.40145i −0.252930 0.704795i
\(40\) 0 0
\(41\) −5.24069 1.40424i −0.818458 0.219305i −0.174786 0.984606i \(-0.555923\pi\)
−0.643672 + 0.765301i \(0.722590\pi\)
\(42\) −0.372945 0.0999302i −0.0575466 0.0154196i
\(43\) −1.00860 3.76415i −0.153810 0.574027i −0.999204 0.0398840i \(-0.987301\pi\)
0.845394 0.534143i \(-0.179366\pi\)
\(44\) −6.57874 6.57874i −0.991782 0.991782i
\(45\) 0 0
\(46\) 8.22291 2.20332i 1.21240 0.324862i
\(47\) 0.345095 0.0503372 0.0251686 0.999683i \(-0.491988\pi\)
0.0251686 + 0.999683i \(0.491988\pi\)
\(48\) 13.9936 3.74956i 2.01980 0.541203i
\(49\) 3.49369 + 6.05125i 0.499098 + 0.864464i
\(50\) 0 0
\(51\) 3.54034i 0.495747i
\(52\) 1.49651 + 18.0422i 0.207528 + 2.50201i
\(53\) 3.59144 + 3.59144i 0.493322 + 0.493322i 0.909351 0.416029i \(-0.136579\pi\)
−0.416029 + 0.909351i \(0.636579\pi\)
\(54\) −3.84062 + 14.3334i −0.522642 + 1.95053i
\(55\) 0 0
\(56\) 0.778898 + 0.449697i 0.104085 + 0.0600933i
\(57\) 9.02691i 1.19564i
\(58\) −6.16729 + 10.6821i −0.809805 + 1.40262i
\(59\) 0.332494 + 1.24088i 0.0432870 + 0.161549i 0.984186 0.177138i \(-0.0566839\pi\)
−0.940899 + 0.338687i \(0.890017\pi\)
\(60\) 0 0
\(61\) 1.39151 2.41016i 0.178164 0.308589i −0.763088 0.646295i \(-0.776318\pi\)
0.941252 + 0.337706i \(0.109651\pi\)
\(62\) −0.605559 + 2.25998i −0.0769061 + 0.287017i
\(63\) −0.128224 + 0.0740300i −0.0161547 + 0.00932691i
\(64\) −13.6621 −1.70776
\(65\) 0 0
\(66\) 6.36774 0.783815
\(67\) −0.124992 + 0.0721643i −0.0152702 + 0.00881627i −0.507616 0.861584i \(-0.669473\pi\)
0.492345 + 0.870400i \(0.336140\pi\)
\(68\) 3.54747 13.2394i 0.430194 1.60551i
\(69\) −2.08342 + 3.60858i −0.250814 + 0.434422i
\(70\) 0 0
\(71\) −1.41668 5.28713i −0.168129 0.627467i −0.997620 0.0689472i \(-0.978036\pi\)
0.829491 0.558520i \(-0.188631\pi\)
\(72\) 5.27506 9.13667i 0.621672 1.07677i
\(73\) 9.06221i 1.06065i −0.847794 0.530326i \(-0.822070\pi\)
0.847794 0.530326i \(-0.177930\pi\)
\(74\) 3.38447 + 1.95402i 0.393436 + 0.227151i
\(75\) 0 0
\(76\) −9.04509 + 33.7567i −1.03754 + 3.87216i
\(77\) 0.147197 + 0.147197i 0.0167747 + 0.0167747i
\(78\) −9.45605 8.00753i −1.07069 0.906675i
\(79\) 15.1689i 1.70664i −0.521388 0.853320i \(-0.674586\pi\)
0.521388 0.853320i \(-0.325414\pi\)
\(80\) 0 0
\(81\) −1.65480 2.86620i −0.183867 0.318467i
\(82\) −13.8865 + 3.72089i −1.53351 + 0.410903i
\(83\) −8.53853 −0.937226 −0.468613 0.883404i \(-0.655246\pi\)
−0.468613 + 0.883404i \(0.655246\pi\)
\(84\) −0.706718 + 0.189365i −0.0771093 + 0.0206614i
\(85\) 0 0
\(86\) −7.30152 7.30152i −0.787343 0.787343i
\(87\) −1.56259 5.83166i −0.167527 0.625219i
\(88\) −14.3278 3.83912i −1.52735 0.409251i
\(89\) 0.549735 + 0.147301i 0.0582718 + 0.0156139i 0.287837 0.957679i \(-0.407064\pi\)
−0.229565 + 0.973293i \(0.573730\pi\)
\(90\) 0 0
\(91\) −0.0334840 0.403690i −0.00351007 0.0423182i
\(92\) 11.4069 11.4069i 1.18925 1.18925i
\(93\) −0.572604 0.991779i −0.0593763 0.102843i
\(94\) 0.791908 0.457208i 0.0816791 0.0471574i
\(95\) 0 0
\(96\) 12.4606 12.4606i 1.27175 1.27175i
\(97\) 12.9596 + 7.48223i 1.31585 + 0.759705i 0.983058 0.183296i \(-0.0586766\pi\)
0.332790 + 0.943001i \(0.392010\pi\)
\(98\) 16.0343 + 9.25742i 1.61971 + 0.935140i
\(99\) 1.72666 1.72666i 0.173536 0.173536i
\(100\) 0 0
\(101\) 7.19717 4.15529i 0.716146 0.413467i −0.0971867 0.995266i \(-0.530984\pi\)
0.813332 + 0.581799i \(0.197651\pi\)
\(102\) 4.69052 + 8.12422i 0.464431 + 0.804418i
\(103\) 7.72940 7.72940i 0.761600 0.761600i −0.215011 0.976612i \(-0.568979\pi\)
0.976612 + 0.215011i \(0.0689789\pi\)
\(104\) 16.4489 + 23.7185i 1.61295 + 2.32579i
\(105\) 0 0
\(106\) 12.9997 + 3.48325i 1.26264 + 0.338324i
\(107\) −7.15177 1.91631i −0.691388 0.185257i −0.104018 0.994575i \(-0.533170\pi\)
−0.587370 + 0.809318i \(0.699837\pi\)
\(108\) 7.27785 + 27.1613i 0.700311 + 2.61360i
\(109\) 3.34544 + 3.34544i 0.320435 + 0.320435i 0.848934 0.528499i \(-0.177245\pi\)
−0.528499 + 0.848934i \(0.677245\pi\)
\(110\) 0 0
\(111\) −1.84768 + 0.495085i −0.175374 + 0.0469914i
\(112\) 1.25493 0.118580
\(113\) 5.90688 1.58274i 0.555672 0.148892i 0.0299550 0.999551i \(-0.490464\pi\)
0.525717 + 0.850659i \(0.323797\pi\)
\(114\) −11.9595 20.7145i −1.12011 1.94009i
\(115\) 0 0
\(116\) 23.3736i 2.17019i
\(117\) −4.73539 + 0.392775i −0.437787 + 0.0363121i
\(118\) 2.40701 + 2.40701i 0.221583 + 0.221583i
\(119\) −0.0793738 + 0.296227i −0.00727618 + 0.0271551i
\(120\) 0 0
\(121\) 6.55303 + 3.78340i 0.595730 + 0.343945i
\(122\) 7.37430i 0.667638i
\(123\) 3.51839 6.09404i 0.317243 0.549481i
\(124\) 1.14751 + 4.28258i 0.103050 + 0.384587i
\(125\) 0 0
\(126\) −0.196161 + 0.339761i −0.0174754 + 0.0302684i
\(127\) 3.01994 11.2706i 0.267976 1.00010i −0.692427 0.721488i \(-0.743459\pi\)
0.960403 0.278613i \(-0.0898747\pi\)
\(128\) −7.81784 + 4.51363i −0.691006 + 0.398953i
\(129\) 5.05420 0.444997
\(130\) 0 0
\(131\) 7.46380 0.652115 0.326058 0.945350i \(-0.394280\pi\)
0.326058 + 0.945350i \(0.394280\pi\)
\(132\) 10.4500 6.03333i 0.909559 0.525134i
\(133\) 0.202381 0.755298i 0.0175487 0.0654926i
\(134\) −0.191218 + 0.331199i −0.0165187 + 0.0286112i
\(135\) 0 0
\(136\) −5.65584 21.1079i −0.484984 1.80998i
\(137\) −9.24213 + 16.0078i −0.789608 + 1.36764i 0.136599 + 0.990626i \(0.456383\pi\)
−0.926207 + 0.377015i \(0.876950\pi\)
\(138\) 11.0411i 0.939879i
\(139\) −9.44862 5.45516i −0.801421 0.462701i 0.0425466 0.999094i \(-0.486453\pi\)
−0.843968 + 0.536394i \(0.819786\pi\)
\(140\) 0 0
\(141\) −0.115842 + 0.432327i −0.00975562 + 0.0364085i
\(142\) −10.2557 10.2557i −0.860643 0.860643i
\(143\) 2.25659 + 6.28804i 0.188705 + 0.525833i
\(144\) 14.7207i 1.22672i
\(145\) 0 0
\(146\) −12.0063 20.7955i −0.993650 1.72105i
\(147\) −8.75362 + 2.34553i −0.721987 + 0.193456i
\(148\) 7.40562 0.608738
\(149\) 13.4468 3.60307i 1.10161 0.295175i 0.338189 0.941078i \(-0.390186\pi\)
0.763419 + 0.645903i \(0.223519\pi\)
\(150\) 0 0
\(151\) −8.49593 8.49593i −0.691389 0.691389i 0.271149 0.962537i \(-0.412596\pi\)
−0.962537 + 0.271149i \(0.912596\pi\)
\(152\) 14.4208 + 53.8193i 1.16968 + 4.36532i
\(153\) 3.47482 + 0.931075i 0.280922 + 0.0752729i
\(154\) 0.532801 + 0.142763i 0.0429343 + 0.0115042i
\(155\) 0 0
\(156\) −23.1052 4.18163i −1.84990 0.334799i
\(157\) 5.14491 5.14491i 0.410609 0.410609i −0.471342 0.881951i \(-0.656230\pi\)
0.881951 + 0.471342i \(0.156230\pi\)
\(158\) −20.0970 34.8090i −1.59883 2.76926i
\(159\) −5.70484 + 3.29369i −0.452423 + 0.261207i
\(160\) 0 0
\(161\) −0.255227 + 0.255227i −0.0201147 + 0.0201147i
\(162\) −7.59474 4.38482i −0.596699 0.344504i
\(163\) −17.7686 10.2587i −1.39175 0.803526i −0.398239 0.917282i \(-0.630379\pi\)
−0.993509 + 0.113756i \(0.963712\pi\)
\(164\) −19.2636 + 19.2636i −1.50423 + 1.50423i
\(165\) 0 0
\(166\) −19.5938 + 11.3125i −1.52078 + 0.878021i
\(167\) −1.27050 2.20058i −0.0983146 0.170286i 0.812673 0.582721i \(-0.198012\pi\)
−0.910987 + 0.412435i \(0.864678\pi\)
\(168\) −0.824831 + 0.824831i −0.0636371 + 0.0636371i
\(169\) 4.55630 12.1754i 0.350484 0.936569i
\(170\) 0 0
\(171\) −8.85983 2.37398i −0.677528 0.181543i
\(172\) −18.9005 5.06438i −1.44115 0.386155i
\(173\) −0.0204199 0.0762079i −0.00155249 0.00579398i 0.965145 0.261715i \(-0.0842880\pi\)
−0.966698 + 0.255921i \(0.917621\pi\)
\(174\) −11.3120 11.3120i −0.857560 0.857560i
\(175\) 0 0
\(176\) −19.9916 + 5.35675i −1.50693 + 0.403780i
\(177\) −1.66616 −0.125236
\(178\) 1.45666 0.390312i 0.109182 0.0292551i
\(179\) 10.6120 + 18.3806i 0.793181 + 1.37383i 0.923988 + 0.382421i \(0.124910\pi\)
−0.130808 + 0.991408i \(0.541757\pi\)
\(180\) 0 0
\(181\) 22.5267i 1.67440i −0.546899 0.837198i \(-0.684192\pi\)
0.546899 0.837198i \(-0.315808\pi\)
\(182\) −0.611677 0.882008i −0.0453405 0.0653788i
\(183\) 2.55229 + 2.55229i 0.188671 + 0.188671i
\(184\) 6.65667 24.8430i 0.490737 1.83145i
\(185\) 0 0
\(186\) −2.62797 1.51726i −0.192692 0.111251i
\(187\) 5.05785i 0.369866i
\(188\) 0.866395 1.50064i 0.0631883 0.109445i
\(189\) −0.162840 0.607727i −0.0118449 0.0442056i
\(190\) 0 0
\(191\) −9.80326 + 16.9797i −0.709339 + 1.22861i 0.255764 + 0.966739i \(0.417673\pi\)
−0.965103 + 0.261872i \(0.915660\pi\)
\(192\) 4.58610 17.1156i 0.330974 1.23521i
\(193\) −14.4730 + 8.35601i −1.04179 + 0.601479i −0.920340 0.391119i \(-0.872088\pi\)
−0.121451 + 0.992597i \(0.538755\pi\)
\(194\) 39.6521 2.84686
\(195\) 0 0
\(196\) 35.0850 2.50607
\(197\) −13.1517 + 7.59315i −0.937021 + 0.540990i −0.889025 0.457858i \(-0.848617\pi\)
−0.0479960 + 0.998848i \(0.515283\pi\)
\(198\) 1.67465 6.24989i 0.119012 0.444160i
\(199\) −6.97357 + 12.0786i −0.494343 + 0.856228i −0.999979 0.00651960i \(-0.997925\pi\)
0.505636 + 0.862747i \(0.331258\pi\)
\(200\) 0 0
\(201\) −0.0484483 0.180811i −0.00341728 0.0127535i
\(202\) 11.0105 19.0707i 0.774696 1.34181i
\(203\) 0.522979i 0.0367059i
\(204\) 15.3951 + 8.88838i 1.07787 + 0.622311i
\(205\) 0 0
\(206\) 7.49657 27.9776i 0.522311 1.94929i
\(207\) 2.99388 + 2.99388i 0.208089 + 0.208089i
\(208\) 36.4236 + 17.1851i 2.52552 + 1.19157i
\(209\) 12.8961i 0.892044i
\(210\) 0 0
\(211\) 11.8091 + 20.4539i 0.812969 + 1.40810i 0.910777 + 0.412898i \(0.135483\pi\)
−0.0978083 + 0.995205i \(0.531183\pi\)
\(212\) 24.6340 6.60065i 1.69187 0.453335i
\(213\) 7.09915 0.486426
\(214\) −18.9504 + 5.07776i −1.29543 + 0.347108i
\(215\) 0 0
\(216\) 31.7007 + 31.7007i 2.15696 + 2.15696i
\(217\) −0.0256753 0.0958217i −0.00174296 0.00650480i
\(218\) 12.1093 + 3.24467i 0.820143 + 0.219757i
\(219\) 11.3529 + 3.04201i 0.767159 + 0.205560i
\(220\) 0 0
\(221\) −6.36032 + 7.51086i −0.427841 + 0.505235i
\(222\) −3.58405 + 3.58405i −0.240546 + 0.240546i
\(223\) 4.86319 + 8.42330i 0.325664 + 0.564066i 0.981646 0.190710i \(-0.0610790\pi\)
−0.655983 + 0.754776i \(0.727746\pi\)
\(224\) 1.32196 0.763236i 0.0883274 0.0509958i
\(225\) 0 0
\(226\) 11.4579 11.4579i 0.762168 0.762168i
\(227\) −7.94647 4.58790i −0.527426 0.304510i 0.212542 0.977152i \(-0.431826\pi\)
−0.739968 + 0.672642i \(0.765159\pi\)
\(228\) −39.2534 22.6629i −2.59962 1.50089i
\(229\) 12.5270 12.5270i 0.827811 0.827811i −0.159403 0.987214i \(-0.550957\pi\)
0.987214 + 0.159403i \(0.0509569\pi\)
\(230\) 0 0
\(231\) −0.233817 + 0.134994i −0.0153840 + 0.00888197i
\(232\) 18.6326 + 32.2726i 1.22329 + 2.11880i
\(233\) 11.8637 11.8637i 0.777214 0.777214i −0.202142 0.979356i \(-0.564790\pi\)
0.979356 + 0.202142i \(0.0647903\pi\)
\(234\) −10.3462 + 7.17513i −0.676350 + 0.469053i
\(235\) 0 0
\(236\) 6.23072 + 1.66952i 0.405585 + 0.108676i
\(237\) 19.0033 + 5.09192i 1.23440 + 0.330756i
\(238\) 0.210321 + 0.784929i 0.0136331 + 0.0508794i
\(239\) −18.2161 18.2161i −1.17830 1.17830i −0.980177 0.198124i \(-0.936515\pi\)
−0.198124 0.980177i \(-0.563485\pi\)
\(240\) 0 0
\(241\) −5.28403 + 1.41585i −0.340374 + 0.0912030i −0.424957 0.905213i \(-0.639711\pi\)
0.0845830 + 0.996416i \(0.473044\pi\)
\(242\) 20.0501 1.28887
\(243\) −12.0818 + 3.23730i −0.775046 + 0.207673i
\(244\) −6.98703 12.1019i −0.447299 0.774744i
\(245\) 0 0
\(246\) 18.6458i 1.18881i
\(247\) 16.2171 19.1506i 1.03187 1.21853i
\(248\) 4.99833 + 4.99833i 0.317394 + 0.317394i
\(249\) 2.86622 10.6969i 0.181639 0.677887i
\(250\) 0 0
\(251\) 11.3169 + 6.53384i 0.714319 + 0.412412i 0.812658 0.582741i \(-0.198020\pi\)
−0.0983394 + 0.995153i \(0.531353\pi\)
\(252\) 0.743439i 0.0468322i
\(253\) 2.97643 5.15533i 0.187127 0.324113i
\(254\) −8.00209 29.8642i −0.502096 1.87385i
\(255\) 0 0
\(256\) 1.70209 2.94811i 0.106381 0.184257i
\(257\) −4.51603 + 16.8541i −0.281702 + 1.05133i 0.669513 + 0.742800i \(0.266503\pi\)
−0.951215 + 0.308528i \(0.900164\pi\)
\(258\) 11.5981 6.69619i 0.722069 0.416887i
\(259\) −0.165699 −0.0102960
\(260\) 0 0
\(261\) −6.13467 −0.379727
\(262\) 17.1276 9.88862i 1.05815 0.610921i
\(263\) −5.39593 + 20.1379i −0.332727 + 1.24175i 0.573585 + 0.819146i \(0.305552\pi\)
−0.906312 + 0.422608i \(0.861115\pi\)
\(264\) 9.61911 16.6608i 0.592015 1.02540i
\(265\) 0 0
\(266\) −0.536261 2.00135i −0.0328803 0.122711i
\(267\) −0.369071 + 0.639249i −0.0225868 + 0.0391214i
\(268\) 0.724703i 0.0442683i
\(269\) −9.15088 5.28326i −0.557939 0.322126i 0.194379 0.980927i \(-0.437731\pi\)
−0.752318 + 0.658800i \(0.771064\pi\)
\(270\) 0 0
\(271\) −2.04739 + 7.64095i −0.124370 + 0.464155i −0.999816 0.0191601i \(-0.993901\pi\)
0.875446 + 0.483315i \(0.160567\pi\)
\(272\) −21.5603 21.5603i −1.30729 1.30729i
\(273\) 0.516973 + 0.0935629i 0.0312887 + 0.00566269i
\(274\) 48.9787i 2.95891i
\(275\) 0 0
\(276\) 10.4612 + 18.1194i 0.629693 + 1.09066i
\(277\) −9.86609 + 2.64361i −0.592796 + 0.158839i −0.542731 0.839907i \(-0.682610\pi\)
−0.0500653 + 0.998746i \(0.515943\pi\)
\(278\) −28.9097 −1.73389
\(279\) −1.12401 + 0.301178i −0.0672929 + 0.0180311i
\(280\) 0 0
\(281\) 12.4763 + 12.4763i 0.744271 + 0.744271i 0.973397 0.229126i \(-0.0735867\pi\)
−0.229126 + 0.973397i \(0.573587\pi\)
\(282\) 0.306952 + 1.14556i 0.0182787 + 0.0682171i
\(283\) 7.98478 + 2.13952i 0.474646 + 0.127181i 0.488208 0.872727i \(-0.337651\pi\)
−0.0135626 + 0.999908i \(0.504317\pi\)
\(284\) −26.5478 7.11345i −1.57532 0.422105i
\(285\) 0 0
\(286\) 13.5092 + 11.4398i 0.798816 + 0.676451i
\(287\) 0.431018 0.431018i 0.0254422 0.0254422i
\(288\) −8.95295 15.5070i −0.527557 0.913756i
\(289\) −8.26943 + 4.77436i −0.486437 + 0.280844i
\(290\) 0 0
\(291\) −13.7238 + 13.7238i −0.804506 + 0.804506i
\(292\) −39.4069 22.7516i −2.30611 1.33144i
\(293\) 5.52378 + 3.18916i 0.322703 + 0.186313i 0.652597 0.757705i \(-0.273680\pi\)
−0.329894 + 0.944018i \(0.607013\pi\)
\(294\) −16.9799 + 16.9799i −0.990287 + 0.990287i
\(295\) 0 0
\(296\) 10.2251 5.90349i 0.594325 0.343133i
\(297\) 5.18823 + 8.98628i 0.301052 + 0.521437i
\(298\) 26.0836 26.0836i 1.51098 1.51098i
\(299\) −10.9029 + 3.91272i −0.630531 + 0.226278i
\(300\) 0 0
\(301\) 0.422894 + 0.113314i 0.0243752 + 0.00653132i
\(302\) −30.7521 8.24001i −1.76959 0.474159i
\(303\) 2.78970 + 10.4113i 0.160264 + 0.598114i
\(304\) 54.9729 + 54.9729i 3.15291 + 3.15291i
\(305\) 0 0
\(306\) 9.20741 2.46712i 0.526353 0.141036i
\(307\) 26.5460 1.51506 0.757530 0.652801i \(-0.226406\pi\)
0.757530 + 0.652801i \(0.226406\pi\)
\(308\) 1.00964 0.270532i 0.0575296 0.0154150i
\(309\) 7.08860 + 12.2778i 0.403256 + 0.698460i
\(310\) 0 0
\(311\) 3.54417i 0.200972i −0.994938 0.100486i \(-0.967960\pi\)
0.994938 0.100486i \(-0.0320397\pi\)
\(312\) −35.2355 + 12.6450i −1.99482 + 0.715879i
\(313\) 6.21088 + 6.21088i 0.351060 + 0.351060i 0.860504 0.509444i \(-0.170149\pi\)
−0.509444 + 0.860504i \(0.670149\pi\)
\(314\) 4.98993 18.6227i 0.281598 1.05094i
\(315\) 0 0
\(316\) −65.9619 38.0831i −3.71065 2.14234i
\(317\) 8.52812i 0.478987i −0.970898 0.239494i \(-0.923019\pi\)
0.970898 0.239494i \(-0.0769814\pi\)
\(318\) −8.72748 + 15.1164i −0.489413 + 0.847688i
\(319\) 2.23236 + 8.33129i 0.124988 + 0.466463i
\(320\) 0 0
\(321\) 4.80142 8.31631i 0.267989 0.464171i
\(322\) −0.247539 + 0.923827i −0.0137948 + 0.0514829i
\(323\) −16.4534 + 9.49937i −0.915491 + 0.528559i
\(324\) −16.6182 −0.923233
\(325\) 0 0
\(326\) −54.3663 −3.01107
\(327\) −5.31409 + 3.06809i −0.293870 + 0.169666i
\(328\) −11.2415 + 41.9540i −0.620710 + 2.31652i
\(329\) −0.0193853 + 0.0335764i −0.00106875 + 0.00185113i
\(330\) 0 0
\(331\) 4.66054 + 17.3934i 0.256166 + 0.956026i 0.967438 + 0.253109i \(0.0814530\pi\)
−0.711271 + 0.702917i \(0.751880\pi\)
\(332\) −21.4368 + 37.1297i −1.17650 + 2.03776i
\(333\) 1.94369i 0.106513i
\(334\) −5.83099 3.36652i −0.319058 0.184208i
\(335\) 0 0
\(336\) −0.421256 + 1.57215i −0.0229814 + 0.0857677i
\(337\) 20.0865 + 20.0865i 1.09418 + 1.09418i 0.995077 + 0.0991030i \(0.0315973\pi\)
0.0991030 + 0.995077i \(0.468403\pi\)
\(338\) −5.67532 33.9761i −0.308697 1.84805i
\(339\) 7.93129i 0.430769i
\(340\) 0 0
\(341\) 0.818040 + 1.41689i 0.0442994 + 0.0767288i
\(342\) −23.4764 + 6.29048i −1.26946 + 0.340150i
\(343\) −1.57145 −0.0848505
\(344\) −30.1336 + 8.07428i −1.62470 + 0.435336i
\(345\) 0 0
\(346\) −0.147825 0.147825i −0.00794710 0.00794710i
\(347\) 1.85743 + 6.93201i 0.0997119 + 0.372130i 0.997692 0.0679068i \(-0.0216321\pi\)
−0.897980 + 0.440037i \(0.854965\pi\)
\(348\) −29.2819 7.84607i −1.56968 0.420593i
\(349\) 3.52885 + 0.945552i 0.188895 + 0.0506143i 0.352026 0.935990i \(-0.385493\pi\)
−0.163131 + 0.986604i \(0.552159\pi\)
\(350\) 0 0
\(351\) 3.59590 19.8688i 0.191935 1.06052i
\(352\) −17.8016 + 17.8016i −0.948827 + 0.948827i
\(353\) 0.881628 + 1.52702i 0.0469243 + 0.0812753i 0.888534 0.458812i \(-0.151725\pi\)
−0.841609 + 0.540087i \(0.818391\pi\)
\(354\) −3.82343 + 2.20746i −0.203213 + 0.117325i
\(355\) 0 0
\(356\) 2.02070 2.02070i 0.107097 0.107097i
\(357\) −0.344462 0.198875i −0.0182309 0.0105256i
\(358\) 48.7040 + 28.1193i 2.57409 + 1.48615i
\(359\) 8.58021 8.58021i 0.452846 0.452846i −0.443452 0.896298i \(-0.646246\pi\)
0.896298 + 0.443452i \(0.146246\pi\)
\(360\) 0 0
\(361\) 25.4972 14.7208i 1.34196 0.774778i
\(362\) −29.8451 51.6933i −1.56862 2.71694i
\(363\) −6.93947 + 6.93947i −0.364228 + 0.364228i
\(364\) −1.83951 0.867900i −0.0964163 0.0454903i
\(365\) 0 0
\(366\) 9.23835 + 2.47541i 0.482896 + 0.129392i
\(367\) −13.5337 3.62635i −0.706454 0.189294i −0.112334 0.993670i \(-0.535833\pi\)
−0.594120 + 0.804377i \(0.702499\pi\)
\(368\) −9.28811 34.6637i −0.484176 1.80697i
\(369\) −5.05594 5.05594i −0.263202 0.263202i
\(370\) 0 0
\(371\) −0.551179 + 0.147688i −0.0286158 + 0.00766757i
\(372\) −5.75032 −0.298140
\(373\) −27.9078 + 7.47789i −1.44501 + 0.387190i −0.894286 0.447495i \(-0.852316\pi\)
−0.550727 + 0.834685i \(0.685650\pi\)
\(374\) −6.70103 11.6065i −0.346502 0.600159i
\(375\) 0 0
\(376\) 2.76263i 0.142472i
\(377\) 7.16169 15.1791i 0.368846 0.781765i
\(378\) −1.17884 1.17884i −0.0606330 0.0606330i
\(379\) 2.45278 9.15390i 0.125991 0.470204i −0.873882 0.486138i \(-0.838405\pi\)
0.999873 + 0.0159336i \(0.00507204\pi\)
\(380\) 0 0
\(381\) 13.1058 + 7.56661i 0.671428 + 0.387649i
\(382\) 51.9525i 2.65812i
\(383\) −10.5361 + 18.2490i −0.538369 + 0.932483i 0.460623 + 0.887596i \(0.347626\pi\)
−0.998992 + 0.0448868i \(0.985707\pi\)
\(384\) −3.03028 11.3091i −0.154638 0.577118i
\(385\) 0 0
\(386\) −22.1414 + 38.3500i −1.12697 + 1.95196i
\(387\) 1.32920 4.96065i 0.0675672 0.252164i
\(388\) 65.0727 37.5698i 3.30357 1.90732i
\(389\) 0.0604806 0.00306649 0.00153324 0.999999i \(-0.499512\pi\)
0.00153324 + 0.999999i \(0.499512\pi\)
\(390\) 0 0
\(391\) 8.76984 0.443510
\(392\) 48.4429 27.9685i 2.44673 1.41262i
\(393\) −2.50545 + 9.35047i −0.126383 + 0.471669i
\(394\) −20.1200 + 34.8488i −1.01363 + 1.75566i
\(395\) 0 0
\(396\) −3.17341 11.8433i −0.159470 0.595150i
\(397\) 4.10812 7.11548i 0.206181 0.357116i −0.744327 0.667815i \(-0.767230\pi\)
0.950508 + 0.310699i \(0.100563\pi\)
\(398\) 36.9565i 1.85246i
\(399\) 0.878284 + 0.507077i 0.0439692 + 0.0253856i
\(400\) 0 0
\(401\) −2.32904 + 8.69210i −0.116307 + 0.434063i −0.999381 0.0351698i \(-0.988803\pi\)
0.883075 + 0.469233i \(0.155469\pi\)
\(402\) −0.350730 0.350730i −0.0174928 0.0174928i
\(403\) 0.566974 3.13276i 0.0282430 0.156054i
\(404\) 41.7291i 2.07610i
\(405\) 0 0
\(406\) −0.692882 1.20011i −0.0343872 0.0595603i
\(407\) 2.63966 0.707294i 0.130843 0.0350593i
\(408\) 28.3420 1.40314
\(409\) 34.6013 9.27138i 1.71092 0.458440i 0.735272 0.677772i \(-0.237054\pi\)
0.975650 + 0.219332i \(0.0703877\pi\)
\(410\) 0 0
\(411\) −16.9518 16.9518i −0.836173 0.836173i
\(412\) −14.2058 53.0166i −0.699867 2.61194i
\(413\) −0.139411 0.0373550i −0.00685995 0.00183812i
\(414\) 10.8367 + 2.90369i 0.532596 + 0.142709i
\(415\) 0 0
\(416\) 48.8209 4.04944i 2.39364 0.198540i
\(417\) 10.0058 10.0058i 0.489987 0.489987i
\(418\) 17.0858 + 29.5934i 0.835693 + 1.44746i
\(419\) −11.3282 + 6.54037i −0.553421 + 0.319518i −0.750501 0.660870i \(-0.770188\pi\)
0.197080 + 0.980387i \(0.436854\pi\)
\(420\) 0 0
\(421\) −13.7924 + 13.7924i −0.672203 + 0.672203i −0.958223 0.286021i \(-0.907667\pi\)
0.286021 + 0.958223i \(0.407667\pi\)
\(422\) 54.1978 + 31.2911i 2.63831 + 1.52323i
\(423\) 0.393860 + 0.227395i 0.0191501 + 0.0110563i
\(424\) 28.7510 28.7510i 1.39627 1.39627i
\(425\) 0 0
\(426\) 16.2908 9.40550i 0.789292 0.455698i
\(427\) 0.156333 + 0.270777i 0.00756548 + 0.0131038i
\(428\) −26.2883 + 26.2883i −1.27069 + 1.27069i
\(429\) −8.63501 + 0.716228i −0.416902 + 0.0345798i
\(430\) 0 0
\(431\) 21.4619 + 5.75070i 1.03378 + 0.277002i 0.735535 0.677487i \(-0.236931\pi\)
0.298249 + 0.954488i \(0.403597\pi\)
\(432\) 60.4224 + 16.1901i 2.90707 + 0.778948i
\(433\) −0.0475058 0.177294i −0.00228298 0.00852021i 0.964775 0.263077i \(-0.0847372\pi\)
−0.967058 + 0.254556i \(0.918071\pi\)
\(434\) −0.185871 0.185871i −0.00892207 0.00892207i
\(435\) 0 0
\(436\) 22.9467 6.14854i 1.09895 0.294462i
\(437\) −22.3607 −1.06966
\(438\) 30.0825 8.06057i 1.43740 0.385149i
\(439\) −8.64682 14.9767i −0.412690 0.714800i 0.582493 0.812836i \(-0.302077\pi\)
−0.995183 + 0.0980356i \(0.968744\pi\)
\(440\) 0 0
\(441\) 9.20846i 0.438498i
\(442\) −4.64440 + 25.6622i −0.220912 + 1.22063i
\(443\) −24.4472 24.4472i −1.16152 1.16152i −0.984143 0.177377i \(-0.943239\pi\)
−0.177377 0.984143i \(-0.556761\pi\)
\(444\) −2.48592 + 9.27758i −0.117977 + 0.440295i
\(445\) 0 0
\(446\) 22.3197 + 12.8863i 1.05687 + 0.610183i
\(447\) 18.0554i 0.853989i
\(448\) 0.767456 1.32927i 0.0362589 0.0628022i
\(449\) 9.62407 + 35.9175i 0.454188 + 1.69505i 0.690465 + 0.723366i \(0.257406\pi\)
−0.236277 + 0.971686i \(0.575927\pi\)
\(450\) 0 0
\(451\) −5.02649 + 8.70613i −0.236688 + 0.409956i
\(452\) 7.94727 29.6596i 0.373808 1.39507i
\(453\) 13.4954 7.79158i 0.634070 0.366080i
\(454\) −24.3136 −1.14109
\(455\) 0 0
\(456\) −72.2643 −3.38409
\(457\) 8.16394 4.71345i 0.381893 0.220486i −0.296749 0.954956i \(-0.595902\pi\)
0.678642 + 0.734470i \(0.262569\pi\)
\(458\) 12.1497 45.3433i 0.567718 2.11875i
\(459\) −7.64337 + 13.2387i −0.356762 + 0.617930i
\(460\) 0 0
\(461\) −8.51149 31.7653i −0.396419 1.47946i −0.819349 0.573295i \(-0.805665\pi\)
0.422930 0.906162i \(-0.361002\pi\)
\(462\) −0.357701 + 0.619557i −0.0166418 + 0.0288244i
\(463\) 18.6729i 0.867805i −0.900960 0.433903i \(-0.857136\pi\)
0.900960 0.433903i \(-0.142864\pi\)
\(464\) 45.0302 + 25.9982i 2.09047 + 1.20694i
\(465\) 0 0
\(466\) 11.5063 42.9421i 0.533019 1.98925i
\(467\) 12.1678 + 12.1678i 0.563057 + 0.563057i 0.930175 0.367118i \(-0.119655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(468\) −10.1807 + 21.5779i −0.470602 + 0.997437i
\(469\) 0.0162150i 0.000748740i
\(470\) 0 0
\(471\) 4.71838 + 8.17247i 0.217411 + 0.376568i
\(472\) 9.93381 2.66176i 0.457241 0.122517i
\(473\) −7.22059 −0.332003
\(474\) 50.3541 13.4923i 2.31284 0.619723i
\(475\) 0 0
\(476\) 1.08886 + 1.08886i 0.0499080 + 0.0499080i
\(477\) 1.73242 + 6.46546i 0.0793219 + 0.296033i
\(478\) −65.9355 17.6674i −3.01582 0.808087i
\(479\) −31.8403 8.53158i −1.45482 0.389818i −0.557123 0.830430i \(-0.688095\pi\)
−0.897697 + 0.440612i \(0.854761\pi\)
\(480\) 0 0
\(481\) −4.80931 2.26908i −0.219285 0.103461i
\(482\) −10.2497 + 10.2497i −0.466862 + 0.466862i
\(483\) −0.234068 0.405417i −0.0106504 0.0184471i
\(484\) 32.9041 18.9972i 1.49564 0.863508i
\(485\) 0 0
\(486\) −23.4357 + 23.4357i −1.06306 + 1.06306i
\(487\) −28.5670 16.4931i −1.29449 0.747376i −0.315045 0.949077i \(-0.602020\pi\)
−0.979447 + 0.201701i \(0.935353\pi\)
\(488\) −19.2944 11.1396i −0.873415 0.504267i
\(489\) 18.8165 18.8165i 0.850911 0.850911i
\(490\) 0 0
\(491\) −18.4427 + 10.6479i −0.832307 + 0.480533i −0.854642 0.519218i \(-0.826223\pi\)
0.0223350 + 0.999751i \(0.492890\pi\)
\(492\) −17.6666 30.5994i −0.796470 1.37953i
\(493\) −8.98502 + 8.98502i −0.404665 + 0.404665i
\(494\) 11.8420 65.4317i 0.532795 2.94391i
\(495\) 0 0
\(496\) 9.52693 + 2.55273i 0.427772 + 0.114621i
\(497\) 0.593999 + 0.159161i 0.0266445 + 0.00713937i
\(498\) −7.59477 28.3441i −0.340330 1.27013i
\(499\) −14.9199 14.9199i −0.667904 0.667904i 0.289326 0.957231i \(-0.406569\pi\)
−0.957231 + 0.289326i \(0.906569\pi\)
\(500\) 0 0
\(501\) 3.18332 0.852967i 0.142220 0.0381077i
\(502\) 34.6261 1.54544
\(503\) 42.1943 11.3059i 1.88135 0.504106i 0.881881 0.471471i \(-0.156277\pi\)
0.999467 0.0326345i \(-0.0103897\pi\)
\(504\) 0.592643 + 1.02649i 0.0263984 + 0.0457234i
\(505\) 0 0
\(506\) 15.7736i 0.701224i
\(507\) 13.7236 + 9.79506i 0.609486 + 0.435014i
\(508\) −41.4280 41.4280i −1.83807 1.83807i
\(509\) −9.67023 + 36.0898i −0.428626 + 1.59965i 0.327250 + 0.944938i \(0.393878\pi\)
−0.755876 + 0.654715i \(0.772789\pi\)
\(510\) 0 0
\(511\) 0.881719 + 0.509060i 0.0390049 + 0.0225195i
\(512\) 27.0748i 1.19655i
\(513\) 19.4885 33.7551i 0.860438 1.49032i
\(514\) 11.9664 + 44.6591i 0.527814 + 1.96983i
\(515\) 0 0
\(516\) 12.6891 21.9781i 0.558605 0.967533i
\(517\) 0.165495 0.617635i 0.00727846 0.0271636i
\(518\) −0.380238 + 0.219530i −0.0167067 + 0.00964562i
\(519\) 0.102326 0.00449161
\(520\) 0 0
\(521\) −35.6853 −1.56340 −0.781701 0.623653i \(-0.785648\pi\)
−0.781701 + 0.623653i \(0.785648\pi\)
\(522\) −14.0776 + 8.12768i −0.616158 + 0.355739i
\(523\) 1.11694 4.16849i 0.0488406 0.182275i −0.937196 0.348802i \(-0.886589\pi\)
0.986037 + 0.166527i \(0.0532552\pi\)
\(524\) 18.7386 32.4562i 0.818600 1.41786i
\(525\) 0 0
\(526\) 14.2979 + 53.3604i 0.623417 + 2.32662i
\(527\) −1.20515 + 2.08738i −0.0524971 + 0.0909276i
\(528\) 26.8432i 1.16820i
\(529\) −10.9797 6.33914i −0.477379 0.275615i
\(530\) 0 0
\(531\) −0.438183 + 1.63532i −0.0190155 + 0.0709670i
\(532\) −2.77630 2.77630i −0.120368 0.120368i
\(533\) 18.4124 6.60765i 0.797529 0.286209i
\(534\) 1.95589i 0.0846398i
\(535\) 0 0
\(536\) 0.577707 + 1.00062i 0.0249531 + 0.0432201i
\(537\) −26.5890 + 7.12450i −1.14740 + 0.307445i
\(538\) −27.9987 −1.20711
\(539\) 12.5057 3.35089i 0.538659 0.144333i
\(540\) 0 0
\(541\) −5.42748 5.42748i −0.233345 0.233345i 0.580742 0.814088i \(-0.302762\pi\)
−0.814088 + 0.580742i \(0.802762\pi\)
\(542\) 5.42507 + 20.2467i 0.233027 + 0.869668i
\(543\) 28.2209 + 7.56177i 1.21108 + 0.324507i
\(544\) −35.8247 9.59920i −1.53597 0.411563i
\(545\) 0 0
\(546\) 1.31029 0.470222i 0.0560751 0.0201237i
\(547\) −11.6940 + 11.6940i −0.500000 + 0.500000i −0.911438 0.411438i \(-0.865027\pi\)
0.411438 + 0.911438i \(0.365027\pi\)
\(548\) 46.4066 + 80.3785i 1.98239 + 3.43360i
\(549\) 3.17628 1.83382i 0.135560 0.0782657i
\(550\) 0 0
\(551\) 22.9093 22.9093i 0.975971 0.975971i
\(552\) 28.8883 + 16.6786i 1.22957 + 0.709890i
\(553\) 1.47588 + 0.852100i 0.0627608 + 0.0362350i
\(554\) −19.1378 + 19.1378i −0.813087 + 0.813087i
\(555\) 0 0
\(556\) −47.4434 + 27.3915i −2.01205 + 1.16166i
\(557\) −2.43751 4.22190i −0.103281 0.178888i 0.809754 0.586770i \(-0.199601\pi\)
−0.913034 + 0.407882i \(0.866267\pi\)
\(558\) −2.18031 + 2.18031i −0.0922998 + 0.0922998i
\(559\) 10.7225 + 9.08000i 0.453514 + 0.384043i
\(560\) 0 0
\(561\) 6.33635 + 1.69782i 0.267521 + 0.0716820i
\(562\) 45.1595 + 12.1004i 1.90494 + 0.510426i
\(563\) 10.0853 + 37.6390i 0.425047 + 1.58630i 0.763821 + 0.645428i \(0.223321\pi\)
−0.338774 + 0.940868i \(0.610012\pi\)
\(564\) 1.58913 + 1.58913i 0.0669146 + 0.0669146i
\(565\) 0 0
\(566\) 21.1577 5.66919i 0.889325 0.238294i
\(567\) 0.371828 0.0156153
\(568\) −42.3258 + 11.3412i −1.77595 + 0.475865i
\(569\) 1.84104 + 3.18877i 0.0771804 + 0.133680i 0.902032 0.431668i \(-0.142075\pi\)
−0.824852 + 0.565349i \(0.808742\pi\)
\(570\) 0 0
\(571\) 2.96698i 0.124164i −0.998071 0.0620821i \(-0.980226\pi\)
0.998071 0.0620821i \(-0.0197741\pi\)
\(572\) 33.0089 + 5.97401i 1.38017 + 0.249786i
\(573\) −17.9811 17.9811i −0.751170 0.751170i
\(574\) 0.418034 1.56012i 0.0174484 0.0651184i
\(575\) 0 0
\(576\) −15.5927 9.00245i −0.649696 0.375102i
\(577\) 35.0533i 1.45929i −0.683827 0.729644i \(-0.739686\pi\)
0.683827 0.729644i \(-0.260314\pi\)
\(578\) −12.6509 + 21.9120i −0.526207 + 0.911417i
\(579\) −5.60990 20.9364i −0.233139 0.870088i
\(580\) 0 0
\(581\) 0.479643 0.830767i 0.0198990 0.0344660i
\(582\) −13.3104 + 49.6753i −0.551736 + 2.05911i
\(583\) 8.15012 4.70547i 0.337543 0.194881i
\(584\) −72.5469 −3.00201
\(585\) 0 0
\(586\) 16.9010 0.698173
\(587\) 6.10926 3.52719i 0.252156 0.145583i −0.368595 0.929590i \(-0.620161\pi\)
0.620751 + 0.784008i \(0.286828\pi\)
\(588\) −11.7774 + 43.9537i −0.485690 + 1.81262i
\(589\) 3.07280 5.32224i 0.126612 0.219299i
\(590\) 0 0
\(591\) −5.09774 19.0250i −0.209693 0.782585i
\(592\) 8.23718 14.2672i 0.338546 0.586379i
\(593\) 40.0169i 1.64330i −0.569993 0.821649i \(-0.693054\pi\)
0.569993 0.821649i \(-0.306946\pi\)
\(594\) 23.8114 + 13.7475i 0.976995 + 0.564068i
\(595\) 0 0
\(596\) 18.0917 67.5192i 0.741066 2.76570i
\(597\) −12.7909 12.7909i −0.523495 0.523495i
\(598\) −19.8356 + 23.4237i −0.811138 + 0.957867i
\(599\) 13.9207i 0.568784i −0.958708 0.284392i \(-0.908208\pi\)
0.958708 0.284392i \(-0.0917918\pi\)
\(600\) 0 0
\(601\) 1.15689 + 2.00379i 0.0471906 + 0.0817365i 0.888656 0.458575i \(-0.151640\pi\)
−0.841465 + 0.540311i \(0.818307\pi\)
\(602\) 1.12057 0.300255i 0.0456708 0.0122375i
\(603\) −0.190206 −0.00774580
\(604\) −58.2743 + 15.6145i −2.37115 + 0.635347i
\(605\) 0 0
\(606\) 20.1954 + 20.1954i 0.820381 + 0.820381i
\(607\) −6.10830 22.7965i −0.247928 0.925282i −0.971889 0.235440i \(-0.924347\pi\)
0.723960 0.689842i \(-0.242320\pi\)
\(608\) 91.3432 + 24.4753i 3.70446 + 0.992606i
\(609\) 0.655175 + 0.175554i 0.0265490 + 0.00711379i
\(610\) 0 0
\(611\) −1.02244 + 0.709071i −0.0413637 + 0.0286860i
\(612\) 12.7726 12.7726i 0.516303 0.516303i
\(613\) −5.32964 9.23121i −0.215262 0.372845i 0.738091 0.674701i \(-0.235727\pi\)
−0.953354 + 0.301856i \(0.902394\pi\)
\(614\) 60.9165 35.1702i 2.45839 1.41935i
\(615\) 0 0
\(616\) 1.17838 1.17838i 0.0474783 0.0474783i
\(617\) 11.8892 + 6.86421i 0.478639 + 0.276343i 0.719849 0.694130i \(-0.244211\pi\)
−0.241210 + 0.970473i \(0.577544\pi\)
\(618\) 32.5332 + 18.7830i 1.30868 + 0.755565i
\(619\) 16.8604 16.8604i 0.677679 0.677679i −0.281796 0.959474i \(-0.590930\pi\)
0.959474 + 0.281796i \(0.0909301\pi\)
\(620\) 0 0
\(621\) −15.5814 + 8.99592i −0.625260 + 0.360994i
\(622\) −4.69560 8.13301i −0.188276 0.326104i
\(623\) −0.0452127 + 0.0452127i −0.00181141 + 0.00181141i
\(624\) −33.7558 + 39.8620i −1.35131 + 1.59576i
\(625\) 0 0
\(626\) 22.4811 + 6.02379i 0.898526 + 0.240759i
\(627\) −16.1560 4.32898i −0.645207 0.172883i
\(628\) −9.45576 35.2894i −0.377326 1.40820i
\(629\) 2.84678 + 2.84678i 0.113509 + 0.113509i
\(630\) 0 0
\(631\) 29.5533 7.91879i 1.17650 0.315242i 0.382962 0.923764i \(-0.374904\pi\)
0.793537 + 0.608522i \(0.208237\pi\)
\(632\) −121.434 −4.83038
\(633\) −29.5882 + 7.92814i −1.17603 + 0.315115i
\(634\) −11.2987 19.5700i −0.448729 0.777222i
\(635\) 0 0
\(636\) 33.0766i 1.31157i
\(637\) −22.7847 10.7501i −0.902761 0.425933i
\(638\) 16.1607 + 16.1607i 0.639807 + 0.639807i
\(639\) 1.86700 6.96776i 0.0738576 0.275640i
\(640\) 0 0
\(641\) −13.2495 7.64957i −0.523322 0.302140i 0.214971 0.976620i \(-0.431034\pi\)
−0.738293 + 0.674480i \(0.764368\pi\)
\(642\) 25.4452i 1.00424i
\(643\) 11.1740 19.3539i 0.440660 0.763245i −0.557079 0.830460i \(-0.688078\pi\)
0.997739 + 0.0672147i \(0.0214113\pi\)
\(644\) 0.469078 + 1.75062i 0.0184843 + 0.0689842i
\(645\) 0 0
\(646\) −25.1710 + 43.5974i −0.990340 + 1.71532i
\(647\) −1.21024 + 4.51668i −0.0475795 + 0.177569i −0.985627 0.168939i \(-0.945966\pi\)
0.938047 + 0.346508i \(0.112633\pi\)
\(648\) −22.9452 + 13.2474i −0.901373 + 0.520408i
\(649\) 2.38033 0.0934361
\(650\) 0 0
\(651\) 0.128662 0.00504265
\(652\) −89.2199 + 51.5111i −3.49412 + 2.01733i
\(653\) −6.34274 + 23.6714i −0.248211 + 0.926335i 0.723532 + 0.690291i \(0.242518\pi\)
−0.971742 + 0.236044i \(0.924149\pi\)
\(654\) −8.12969 + 14.0810i −0.317896 + 0.550612i
\(655\) 0 0
\(656\) 15.6854 + 58.5387i 0.612412 + 2.28555i
\(657\) 5.97141 10.3428i 0.232967 0.403510i
\(658\) 0.102733i 0.00400494i
\(659\) 35.2803 + 20.3691i 1.37433 + 0.793467i 0.991469 0.130341i \(-0.0416072\pi\)
0.382856 + 0.923808i \(0.374941\pi\)
\(660\) 0 0
\(661\) 4.42523 16.5152i 0.172122 0.642367i −0.824902 0.565275i \(-0.808770\pi\)
0.997024 0.0770916i \(-0.0245634\pi\)
\(662\) 33.7389 + 33.7389i 1.31130 + 1.31130i
\(663\) −7.27440 10.4893i −0.282514 0.407371i
\(664\) 68.3547i 2.65268i
\(665\) 0 0
\(666\) 2.57515 + 4.46029i 0.0997850 + 0.172833i
\(667\) −14.4457 + 3.87071i −0.559340 + 0.149875i
\(668\) −12.7589 −0.493657
\(669\) −12.1850 + 3.26496i −0.471099 + 0.126231i
\(670\) 0 0
\(671\) −3.64628 3.64628i −0.140763 0.140763i
\(672\) 0.512407 + 1.91233i 0.0197665 + 0.0737696i
\(673\) 23.0041 + 6.16392i 0.886742 + 0.237602i 0.673314 0.739357i \(-0.264870\pi\)
0.213428 + 0.976959i \(0.431537\pi\)
\(674\) 72.7057 + 19.4814i 2.80052 + 0.750396i
\(675\) 0 0
\(676\) −41.5055 50.3805i −1.59636 1.93771i
\(677\) −26.1344 + 26.1344i −1.00443 + 1.00443i −0.00443504 + 0.999990i \(0.501412\pi\)
−0.999990 + 0.00443504i \(0.998588\pi\)
\(678\) 10.5080 + 18.2004i 0.403557 + 0.698981i
\(679\) −1.45598 + 0.840613i −0.0558756 + 0.0322598i
\(680\) 0 0
\(681\) 8.41509 8.41509i 0.322467 0.322467i
\(682\) 3.75440 + 2.16761i 0.143764 + 0.0830019i
\(683\) 23.1988 + 13.3938i 0.887676 + 0.512500i 0.873181 0.487395i \(-0.162053\pi\)
0.0144941 + 0.999895i \(0.495386\pi\)
\(684\) −32.5667 + 32.5667i −1.24522 + 1.24522i
\(685\) 0 0
\(686\) −3.60610 + 2.08198i −0.137682 + 0.0794905i
\(687\) 11.4885 + 19.8987i 0.438314 + 0.759182i
\(688\) −30.7796 + 30.7796i −1.17346 + 1.17346i
\(689\) −18.0201 3.26131i −0.686510 0.124246i
\(690\) 0 0
\(691\) −38.9899 10.4473i −1.48325 0.397435i −0.575796 0.817593i \(-0.695308\pi\)
−0.907451 + 0.420158i \(0.861975\pi\)
\(692\) −0.382655 0.102532i −0.0145464 0.00389769i
\(693\) 0.0710042 + 0.264991i 0.00269723 + 0.0100662i
\(694\) 13.4464 + 13.4464i 0.510419 + 0.510419i
\(695\) 0 0
\(696\) −46.6850 + 12.5092i −1.76959 + 0.474160i
\(697\) −14.8102 −0.560976
\(698\) 9.35058 2.50548i 0.353925 0.0948339i
\(699\) 10.8801 + 18.8449i 0.411524 + 0.712780i
\(700\) 0 0
\(701\) 24.9781i 0.943410i −0.881756 0.471705i \(-0.843639\pi\)
0.881756 0.471705i \(-0.156361\pi\)
\(702\) −18.0721 50.3582i −0.682086 1.90065i
\(703\) −7.25852 7.25852i −0.273760 0.273760i
\(704\) −6.55185 + 24.4519i −0.246932 + 0.921564i
\(705\) 0 0
\(706\) 4.04624 + 2.33610i 0.152282 + 0.0879202i
\(707\) 0.933677i 0.0351145i
\(708\) −4.18306 + 7.24528i −0.157209 + 0.272294i
\(709\) −2.64139 9.85779i −0.0991993 0.370217i 0.898423 0.439130i \(-0.144713\pi\)
−0.997623 + 0.0689135i \(0.978047\pi\)
\(710\) 0 0
\(711\) 9.99535 17.3124i 0.374855 0.649268i
\(712\) 1.17921 4.40087i 0.0441927 0.164930i
\(713\) −2.45675 + 1.41841i −0.0920061 + 0.0531198i
\(714\) −1.05394 −0.0394428
\(715\) 0 0
\(716\) 106.570 3.98272
\(717\) 28.9355 16.7059i 1.08061 0.623893i
\(718\) 8.32175 31.0572i 0.310565 1.15904i
\(719\) −14.2117 + 24.6153i −0.530005 + 0.917996i 0.469382 + 0.882995i \(0.344477\pi\)
−0.999387 + 0.0350008i \(0.988857\pi\)
\(720\) 0 0
\(721\) 0.317850 + 1.18623i 0.0118373 + 0.0441776i
\(722\) 39.0065 67.5612i 1.45167 2.51437i
\(723\) 7.09498i 0.263865i
\(724\) −97.9570 56.5555i −3.64054 2.10187i
\(725\) 0 0
\(726\) −6.73044 + 25.1183i −0.249790 + 0.932229i
\(727\) 8.56116 + 8.56116i 0.317516 + 0.317516i 0.847812 0.530296i \(-0.177919\pi\)
−0.530296 + 0.847812i \(0.677919\pi\)
\(728\) −3.23172 + 0.268054i −0.119775 + 0.00993473i
\(729\) 26.1513i 0.968566i
\(730\) 0 0
\(731\) −5.31873 9.21232i −0.196720 0.340730i
\(732\) 17.5064 4.69082i 0.647054 0.173378i
\(733\) 17.2200 0.636036 0.318018 0.948085i \(-0.396983\pi\)
0.318018 + 0.948085i \(0.396983\pi\)
\(734\) −35.8610 + 9.60893i −1.32365 + 0.354672i
\(735\) 0 0
\(736\) −30.8663 30.8663i −1.13775 1.13775i
\(737\) 0.0692148 + 0.258313i 0.00254956 + 0.00951508i
\(738\) −18.3007 4.90365i −0.673656 0.180506i
\(739\) −15.7497 4.22013i −0.579364 0.155240i −0.0427762 0.999085i \(-0.513620\pi\)
−0.536588 + 0.843845i \(0.680287\pi\)
\(740\) 0 0
\(741\) 18.5477 + 26.7449i 0.681367 + 0.982497i
\(742\) −1.06915 + 1.06915i −0.0392498 + 0.0392498i
\(743\) −16.5599 28.6826i −0.607525 1.05226i −0.991647 0.128982i \(-0.958829\pi\)
0.384122 0.923282i \(-0.374504\pi\)
\(744\) −7.93963 + 4.58395i −0.291081 + 0.168056i
\(745\) 0 0
\(746\) −54.1344 + 54.1344i −1.98200 + 1.98200i
\(747\) −9.74510 5.62634i −0.356555 0.205857i
\(748\) −21.9940 12.6982i −0.804179 0.464293i
\(749\) 0.588194 0.588194i 0.0214921 0.0214921i
\(750\) 0 0
\(751\) 18.9961 10.9674i 0.693176 0.400205i −0.111625 0.993750i \(-0.535605\pi\)
0.804801 + 0.593545i \(0.202272\pi\)
\(752\) −1.92736 3.33829i −0.0702836 0.121735i
\(753\) −11.9843 + 11.9843i −0.436732 + 0.436732i
\(754\) −3.67617 44.3207i −0.133878 1.61407i
\(755\) 0 0
\(756\) −3.05152 0.817652i −0.110983 0.0297377i
\(757\) 2.84678 + 0.762791i 0.103468 + 0.0277241i 0.310181 0.950677i \(-0.399610\pi\)
−0.206714 + 0.978401i \(0.566277\pi\)
\(758\) −6.49926 24.2556i −0.236064 0.881002i
\(759\) 5.45935 + 5.45935i 0.198162 + 0.198162i
\(760\) 0 0
\(761\) −21.2875 + 5.70396i −0.771670 + 0.206768i −0.623109 0.782135i \(-0.714131\pi\)
−0.148561 + 0.988903i \(0.547464\pi\)
\(762\) 40.0993 1.45265
\(763\) −0.513426 + 0.137572i −0.0185873 + 0.00498044i
\(764\) 49.2241 + 85.2587i 1.78087 + 3.08455i
\(765\) 0 0
\(766\) 55.8361i 2.01744i
\(767\) −3.53477 2.99330i −0.127633 0.108082i
\(768\) 3.12197 + 3.12197i 0.112654 + 0.112654i
\(769\) −5.46718 + 20.4038i −0.197152 + 0.735780i 0.794548 + 0.607202i \(0.207708\pi\)
−0.991699 + 0.128578i \(0.958959\pi\)
\(770\) 0 0
\(771\) −19.5984 11.3152i −0.705820 0.407506i
\(772\) 83.9143i 3.02014i
\(773\) 9.34781 16.1909i 0.336217 0.582346i −0.647500 0.762065i \(-0.724186\pi\)
0.983718 + 0.179719i \(0.0575189\pi\)
\(774\) −3.52206 13.1445i −0.126598 0.472470i
\(775\) 0 0
\(776\) 59.8985 103.747i 2.15023 3.72431i
\(777\) 0.0556218 0.207583i 0.00199542 0.00744702i
\(778\) 0.138788 0.0801293i 0.00497579 0.00287278i
\(779\) 37.7619 1.35296
\(780\) 0 0
\(781\) −10.1421 −0.362912
\(782\) 20.1246 11.6190i 0.719656 0.415493i
\(783\) 6.74705 25.1803i 0.241120 0.899872i
\(784\) 39.0246 67.5927i 1.39374 2.41402i
\(785\) 0 0
\(786\) 6.63883 + 24.7764i 0.236799 + 0.883747i
\(787\) −21.6615 + 37.5189i −0.772150 + 1.33740i 0.164232 + 0.986422i \(0.447485\pi\)
−0.936382 + 0.350981i \(0.885848\pi\)
\(788\) 76.2534i 2.71642i
\(789\) −23.4169 13.5198i −0.833665 0.481317i
\(790\) 0 0
\(791\) −0.177818 + 0.663626i −0.00632248 + 0.0235958i
\(792\) −13.8227 13.8227i −0.491168 0.491168i
\(793\) 0.829444 + 9.99995i 0.0294544 + 0.355109i
\(794\) 21.7710i 0.772625i
\(795\) 0 0
\(796\) 35.0157 + 60.6489i 1.24110 + 2.14964i
\(797\) 33.9650 9.10089i 1.20310 0.322370i 0.399050 0.916929i \(-0.369340\pi\)
0.804052 + 0.594559i \(0.202673\pi\)
\(798\) 2.68726 0.0951280
\(799\) 0.909909 0.243809i 0.0321903 0.00862535i
\(800\) 0 0
\(801\) 0.530356 + 0.530356i 0.0187392 + 0.0187392i
\(802\) 6.17139 + 23.0319i 0.217919 + 0.813286i
\(803\) −16.2191 4.34591i −0.572361 0.153364i
\(804\) −0.907890 0.243268i −0.0320188 0.00857942i
\(805\) 0 0
\(806\) −2.84946 7.94010i −0.100368 0.279678i
\(807\) 9.69052 9.69052i 0.341122 0.341122i
\(808\) −33.2649 57.6165i −1.17026 2.02694i
\(809\) −17.8779 + 10.3218i −0.628554 + 0.362896i −0.780192 0.625540i \(-0.784879\pi\)
0.151638 + 0.988436i \(0.451545\pi\)
\(810\) 0 0
\(811\) −22.0471 + 22.0471i −0.774178 + 0.774178i −0.978834 0.204656i \(-0.934392\pi\)
0.204656 + 0.978834i \(0.434392\pi\)
\(812\) −2.27416 1.31299i −0.0798075 0.0460769i
\(813\) −8.88514 5.12984i −0.311615 0.179911i
\(814\) 5.12029 5.12029i 0.179466 0.179466i
\(815\) 0 0
\(816\) 34.2477 19.7729i 1.19891 0.692190i
\(817\) 13.5613 + 23.4889i 0.474450 + 0.821772i
\(818\) 67.1180 67.1180i 2.34672 2.34672i
\(819\) 0.227790 0.482799i 0.00795963 0.0168704i
\(820\) 0 0
\(821\) 35.4477 + 9.49818i 1.23713 + 0.331489i 0.817353 0.576137i \(-0.195441\pi\)
0.419780 + 0.907626i \(0.362107\pi\)
\(822\) −61.3594 16.4412i −2.14016 0.573453i
\(823\) −6.11025 22.8038i −0.212990 0.794889i −0.986865 0.161550i \(-0.948351\pi\)
0.773875 0.633339i \(-0.218316\pi\)
\(824\) −61.8772 61.8772i −2.15559 2.15559i
\(825\) 0 0
\(826\) −0.369404 + 0.0989816i −0.0128532 + 0.00344401i
\(827\) 4.44429 0.154543 0.0772716 0.997010i \(-0.475379\pi\)
0.0772716 + 0.997010i \(0.475379\pi\)
\(828\) 20.5352 5.50240i 0.713649 0.191222i
\(829\) −14.6685 25.4065i −0.509457 0.882406i −0.999940 0.0109548i \(-0.996513\pi\)
0.490483 0.871451i \(-0.336820\pi\)
\(830\) 0 0
\(831\) 13.2474i 0.459548i
\(832\) 40.4780 28.0718i 1.40332 0.973213i
\(833\) 13.4870 + 13.4870i 0.467296 + 0.467296i
\(834\) 9.70441 36.2174i 0.336036 1.25410i
\(835\) 0 0
\(836\) 56.0786 + 32.3770i 1.93952 + 1.11978i
\(837\) 4.94486i 0.170919i
\(838\) −17.3304 + 30.0171i −0.598668 + 1.03692i
\(839\) −2.19656 8.19766i −0.0758336 0.283015i 0.917587 0.397534i \(-0.130134\pi\)
−0.993421 + 0.114519i \(0.963467\pi\)
\(840\) 0 0
\(841\) −3.66554 + 6.34891i −0.126398 + 0.218928i
\(842\) −13.3770 + 49.9236i −0.461001 + 1.72048i
\(843\) −19.8180 + 11.4419i −0.682568 + 0.394081i
\(844\) 118.591 4.08208
\(845\) 0 0
\(846\) 1.20508 0.0414316
\(847\) −0.736220 + 0.425057i −0.0252968 + 0.0146051i
\(848\) 14.6837 54.8002i 0.504239 1.88185i
\(849\) −5.36067 + 9.28495i −0.183978 + 0.318659i
\(850\) 0 0
\(851\) 1.22638 + 4.57693i 0.0420399 + 0.156895i
\(852\) 17.8231 30.8705i 0.610610 1.05761i
\(853\) 34.3415i 1.17583i 0.808923 + 0.587915i \(0.200051\pi\)
−0.808923 + 0.587915i \(0.799949\pi\)
\(854\) 0.717491 + 0.414244i 0.0245521 + 0.0141751i
\(855\) 0 0
\(856\) −15.3409 + 57.2531i −0.524342 + 1.95687i
\(857\) −24.6090 24.6090i −0.840626 0.840626i 0.148314 0.988940i \(-0.452615\pi\)
−0.988940 + 0.148314i \(0.952615\pi\)
\(858\) −18.8663 + 13.0839i −0.644085 + 0.446677i
\(859\) 12.8606i 0.438798i 0.975635 + 0.219399i \(0.0704097\pi\)
−0.975635 + 0.219399i \(0.929590\pi\)
\(860\) 0 0
\(861\) 0.395284 + 0.684653i 0.0134713 + 0.0233329i
\(862\) 56.8688 15.2379i 1.93696 0.519007i
\(863\) 2.75373 0.0937379 0.0468690 0.998901i \(-0.485076\pi\)
0.0468690 + 0.998901i \(0.485076\pi\)
\(864\) 73.4965 19.6933i 2.50040 0.669980i
\(865\) 0 0
\(866\) −0.343907 0.343907i −0.0116864 0.0116864i
\(867\) −3.20532 11.9624i −0.108858 0.406264i
\(868\) −0.481140 0.128921i −0.0163309 0.00437586i
\(869\) −27.1487 7.27447i −0.920957 0.246770i
\(870\) 0 0
\(871\) 0.222049 0.470631i 0.00752385 0.0159467i
\(872\) 26.7817 26.7817i 0.906944 0.906944i
\(873\) 9.86060 + 17.0791i 0.333731 + 0.578039i
\(874\) −51.3123 + 29.6252i −1.73566 + 1.00209i
\(875\) 0 0
\(876\) 41.7308 41.7308i 1.40995 1.40995i
\(877\) 40.9311 + 23.6316i 1.38214 + 0.797981i 0.992413 0.122948i \(-0.0392349\pi\)
0.389730 + 0.920929i \(0.372568\pi\)
\(878\) −39.6847 22.9119i −1.33929 0.773241i
\(879\) −5.84953 + 5.84953i −0.197300 + 0.197300i
\(880\) 0 0
\(881\) 35.7854 20.6607i 1.20564 0.696077i 0.243837 0.969816i \(-0.421594\pi\)
0.961804 + 0.273739i \(0.0882605\pi\)
\(882\) 12.2001 + 21.1311i 0.410798 + 0.711523i
\(883\) −13.4808 + 13.4808i −0.453666 + 0.453666i −0.896569 0.442903i \(-0.853949\pi\)
0.442903 + 0.896569i \(0.353949\pi\)
\(884\) 16.6927 + 46.5145i 0.561435 + 1.56445i
\(885\) 0 0
\(886\) −88.4897 23.7108i −2.97287 0.796578i
\(887\) 22.1438 + 5.93341i 0.743516 + 0.199225i 0.610640 0.791908i \(-0.290912\pi\)
0.132876 + 0.991133i \(0.457579\pi\)
\(888\) 3.96337 + 14.7915i 0.133002 + 0.496371i
\(889\) 0.926941 + 0.926941i 0.0310886 + 0.0310886i
\(890\) 0 0
\(891\) −5.92339 + 1.58717i −0.198441 + 0.0531721i
\(892\) 48.8381 1.63522
\(893\) −2.32002 + 0.621647i −0.0776364 + 0.0208026i
\(894\) 23.9211 + 41.4326i 0.800042 + 1.38571i
\(895\) 0 0
\(896\) 1.01420i 0.0338819i
\(897\) −1.24187 14.9723i −0.0414650 0.499911i
\(898\) 69.6712 + 69.6712i 2.32496 + 2.32496i
\(899\) 1.06382 3.97024i 0.0354805 0.132415i
\(900\) 0 0
\(901\) 12.0069 + 6.93217i 0.400007 + 0.230944i
\(902\) 26.6379i 0.886946i
\(903\) −0.283915 + 0.491754i −0.00944808 + 0.0163646i
\(904\) −12.6705 47.2871i −0.421416 1.57275i
\(905\) 0 0
\(906\) 20.6458 35.7595i 0.685910 1.18803i
\(907\) 6.24222 23.2963i 0.207270 0.773541i −0.781476 0.623935i \(-0.785533\pi\)
0.988746 0.149606i \(-0.0478004\pi\)
\(908\) −39.9008 + 23.0367i −1.32416 + 0.764501i
\(909\) 10.9523 0.363264
\(910\) 0 0
\(911\) 58.5135 1.93864 0.969320 0.245803i \(-0.0790515\pi\)
0.969320 + 0.245803i \(0.0790515\pi\)
\(912\) −87.3221 + 50.4154i −2.89152 + 1.66942i
\(913\) −4.09477 + 15.2819i −0.135517 + 0.505757i
\(914\) 12.4895 21.6324i 0.413116 0.715537i
\(915\) 0 0
\(916\) −23.0233 85.9241i −0.760711 2.83901i
\(917\) −0.419271 + 0.726199i −0.0138456 + 0.0239812i
\(918\) 40.5061i 1.33690i
\(919\) 38.8451 + 22.4272i 1.28138 + 0.739806i 0.977101 0.212776i \(-0.0682506\pi\)
0.304281 + 0.952582i \(0.401584\pi\)
\(920\) 0 0
\(921\) −8.91097 + 33.2562i −0.293626 + 1.09583i
\(922\) −61.6169 61.6169i −2.02924 2.02924i
\(923\) 15.0609 + 12.7538i 0.495735 + 0.419797i
\(924\) 1.35567i 0.0445981i
\(925\) 0 0
\(926\) −24.7394 42.8498i −0.812986 1.40813i
\(927\) 13.9148 3.72846i 0.457022 0.122459i
\(928\) 63.2473 2.07619
\(929\) −27.1090 + 7.26384i −0.889418 + 0.238319i −0.674466 0.738306i \(-0.735626\pi\)
−0.214952 + 0.976625i \(0.568960\pi\)
\(930\) 0 0
\(931\) −34.3881 34.3881i −1.12702 1.12702i
\(932\) −21.8041 81.3738i −0.714215 2.66549i
\(933\) 4.44006 + 1.18971i 0.145361 + 0.0389493i
\(934\) 44.0428 + 11.8012i 1.44113 + 0.386148i
\(935\) 0 0
\(936\) 3.14434 + 37.9088i 0.102776 + 1.23909i
\(937\) −20.7545 + 20.7545i −0.678019 + 0.678019i −0.959552 0.281533i \(-0.909157\pi\)
0.281533 + 0.959552i \(0.409157\pi\)
\(938\) −0.0214829 0.0372095i −0.000701442 0.00121493i
\(939\) −9.86572 + 5.69597i −0.321955 + 0.185881i
\(940\) 0 0
\(941\) −6.70533 + 6.70533i −0.218588 + 0.218588i −0.807903 0.589315i \(-0.799398\pi\)
0.589315 + 0.807903i \(0.299398\pi\)
\(942\) 21.6550 + 12.5025i 0.705559 + 0.407355i
\(943\) −15.0956 8.71547i −0.491582 0.283815i
\(944\) 10.1467 10.1467i 0.330249 0.330249i
\(945\) 0 0
\(946\) −16.5695 + 9.56639i −0.538720 + 0.311030i
\(947\) 2.25542 + 3.90651i 0.0732915 + 0.126945i 0.900342 0.435183i \(-0.143316\pi\)
−0.827051 + 0.562128i \(0.809983\pi\)
\(948\) 69.8518 69.8518i 2.26868 2.26868i
\(949\) 18.6203 + 26.8495i 0.604439 + 0.871570i
\(950\) 0 0
\(951\) 10.6838 + 2.86272i 0.346447 + 0.0928302i
\(952\) 2.37143 + 0.635422i 0.0768584 + 0.0205941i
\(953\) 1.48646 + 5.54756i 0.0481513 + 0.179703i 0.985813 0.167845i \(-0.0536809\pi\)
−0.937662 + 0.347548i \(0.887014\pi\)
\(954\) 12.5414 + 12.5414i 0.406043 + 0.406043i
\(955\) 0 0
\(956\) −124.946 + 33.4791i −4.04103 + 1.08279i
\(957\) −11.1866 −0.361612
\(958\) −84.3690 + 22.6066i −2.72584 + 0.730386i
\(959\) −1.03833 1.79845i −0.0335296 0.0580749i
\(960\) 0 0
\(961\) 30.2203i 0.974849i
\(962\) −14.0424 + 1.16475i −0.452746 + 0.0375529i
\(963\) −6.89966 6.89966i −0.222338 0.222338i
\(964\) −7.10927 + 26.5322i −0.228974 + 0.854543i
\(965\) 0 0
\(966\) −1.07426 0.620222i −0.0345636 0.0199553i
\(967\) 17.6414i 0.567310i −0.958926 0.283655i \(-0.908453\pi\)
0.958926 0.283655i \(-0.0915470\pi\)
\(968\) 30.2877 52.4599i 0.973485 1.68612i
\(969\) −6.37750 23.8012i −0.204875 0.764604i
\(970\) 0 0
\(971\) −16.6987 + 28.9229i −0.535886 + 0.928181i 0.463234 + 0.886236i \(0.346689\pi\)
−0.999120 + 0.0419454i \(0.986644\pi\)
\(972\) −16.2551 + 60.6650i −0.521384 + 1.94583i
\(973\) 1.06153 0.612876i 0.0340312 0.0196479i
\(974\) −87.4056 −2.80065
\(975\) 0 0
\(976\) −31.0864 −0.995050
\(977\) −13.2886 + 7.67217i −0.425139 + 0.245454i −0.697274 0.716805i \(-0.745604\pi\)
0.272134 + 0.962259i \(0.412270\pi\)
\(978\) 18.2497 68.1088i 0.583561 2.17788i
\(979\) 0.527266 0.913252i 0.0168515 0.0291877i
\(980\) 0 0
\(981\) 1.61375 + 6.02261i 0.0515232 + 0.192287i
\(982\) −28.2143 + 48.8686i −0.900354 + 1.55946i
\(983\) 4.80751i 0.153336i 0.997057 + 0.0766679i \(0.0244281\pi\)
−0.997057 + 0.0766679i \(0.975572\pi\)
\(984\) −48.7854 28.1663i −1.55522 0.897908i
\(985\) 0 0
\(986\) −8.71437 + 32.5225i −0.277522 + 1.03573i
\(987\) −0.0355565 0.0355565i −0.00113177 0.00113177i
\(988\) −42.5617 118.599i −1.35407 3.77315i
\(989\) 12.5198i 0.398108i
\(990\) 0 0
\(991\) −0.219558 0.380286i −0.00697450 0.0120802i 0.862517 0.506028i \(-0.168887\pi\)
−0.869492 + 0.493948i \(0.835553\pi\)
\(992\) 11.5884 3.10509i 0.367931 0.0985867i
\(993\) −23.3545 −0.741131
\(994\) 1.57395 0.421739i 0.0499227 0.0133767i
\(995\) 0 0
\(996\) −39.3193 39.3193i −1.24588 1.24588i
\(997\) 1.70003 + 6.34461i 0.0538406 + 0.200936i 0.987607 0.156947i \(-0.0501653\pi\)
−0.933766 + 0.357883i \(0.883499\pi\)
\(998\) −54.0044 14.4704i −1.70948 0.458053i
\(999\) −7.97806 2.13771i −0.252415 0.0676343i
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 325.2.x.b.93.5 20
5.2 odd 4 325.2.s.b.132.5 20
5.3 odd 4 65.2.o.a.2.1 20
5.4 even 2 65.2.t.a.28.1 yes 20
13.7 odd 12 325.2.s.b.293.5 20
15.8 even 4 585.2.cf.a.262.5 20
15.14 odd 2 585.2.dp.a.28.5 20
65.3 odd 12 845.2.k.e.577.10 20
65.4 even 6 845.2.t.e.188.1 20
65.7 even 12 inner 325.2.x.b.7.5 20
65.8 even 4 845.2.t.f.427.5 20
65.9 even 6 845.2.t.f.188.5 20
65.18 even 4 845.2.t.e.427.1 20
65.19 odd 12 845.2.o.g.488.5 20
65.23 odd 12 845.2.k.d.577.1 20
65.24 odd 12 845.2.k.e.268.10 20
65.28 even 12 845.2.f.d.437.1 20
65.29 even 6 845.2.f.e.408.1 20
65.33 even 12 65.2.t.a.7.1 yes 20
65.34 odd 4 845.2.o.e.258.1 20
65.38 odd 4 845.2.o.g.587.5 20
65.43 odd 12 845.2.o.f.357.5 20
65.44 odd 4 845.2.o.f.258.5 20
65.48 odd 12 845.2.o.e.357.1 20
65.49 even 6 845.2.f.d.408.10 20
65.54 odd 12 845.2.k.d.268.1 20
65.58 even 12 845.2.t.g.657.5 20
65.59 odd 12 65.2.o.a.33.1 yes 20
65.63 even 12 845.2.f.e.437.10 20
65.64 even 2 845.2.t.g.418.5 20
195.59 even 12 585.2.cf.a.163.5 20
195.98 odd 12 585.2.dp.a.397.5 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.o.a.2.1 20 5.3 odd 4
65.2.o.a.33.1 yes 20 65.59 odd 12
65.2.t.a.7.1 yes 20 65.33 even 12
65.2.t.a.28.1 yes 20 5.4 even 2
325.2.s.b.132.5 20 5.2 odd 4
325.2.s.b.293.5 20 13.7 odd 12
325.2.x.b.7.5 20 65.7 even 12 inner
325.2.x.b.93.5 20 1.1 even 1 trivial
585.2.cf.a.163.5 20 195.59 even 12
585.2.cf.a.262.5 20 15.8 even 4
585.2.dp.a.28.5 20 15.14 odd 2
585.2.dp.a.397.5 20 195.98 odd 12
845.2.f.d.408.10 20 65.49 even 6
845.2.f.d.437.1 20 65.28 even 12
845.2.f.e.408.1 20 65.29 even 6
845.2.f.e.437.10 20 65.63 even 12
845.2.k.d.268.1 20 65.54 odd 12
845.2.k.d.577.1 20 65.23 odd 12
845.2.k.e.268.10 20 65.24 odd 12
845.2.k.e.577.10 20 65.3 odd 12
845.2.o.e.258.1 20 65.34 odd 4
845.2.o.e.357.1 20 65.48 odd 12
845.2.o.f.258.5 20 65.44 odd 4
845.2.o.f.357.5 20 65.43 odd 12
845.2.o.g.488.5 20 65.19 odd 12
845.2.o.g.587.5 20 65.38 odd 4
845.2.t.e.188.1 20 65.4 even 6
845.2.t.e.427.1 20 65.18 even 4
845.2.t.f.188.5 20 65.9 even 6
845.2.t.f.427.5 20 65.8 even 4
845.2.t.g.418.5 20 65.64 even 2
845.2.t.g.657.5 20 65.58 even 12