Properties

Label 304.2.k.b.77.8
Level $304$
Weight $2$
Character 304.77
Analytic conductor $2.427$
Analytic rank $0$
Dimension $68$
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] = [304,2,Mod(77,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.k (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: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.8
Character \(\chi\) \(=\) 304.77
Dual form 304.2.k.b.229.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18841 - 0.766601i) q^{2} +(0.982629 + 0.982629i) q^{3} +(0.824645 + 1.82208i) q^{4} +(-2.22243 + 2.22243i) q^{5} +(-0.414483 - 1.92105i) q^{6} +0.518576i q^{7} +(0.416789 - 2.79755i) q^{8} -1.06888i q^{9} +O(q^{10})\) \(q+(-1.18841 - 0.766601i) q^{2} +(0.982629 + 0.982629i) q^{3} +(0.824645 + 1.82208i) q^{4} +(-2.22243 + 2.22243i) q^{5} +(-0.414483 - 1.92105i) q^{6} +0.518576i q^{7} +(0.416789 - 2.79755i) q^{8} -1.06888i q^{9} +(4.34488 - 0.937444i) q^{10} +(-2.50778 + 2.50778i) q^{11} +(-0.980105 + 2.60075i) q^{12} +(2.14144 + 2.14144i) q^{13} +(0.397541 - 0.616281i) q^{14} -4.36765 q^{15} +(-2.63992 + 3.00513i) q^{16} -8.17716 q^{17} +(-0.819405 + 1.27027i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-5.88215 - 2.21672i) q^{20} +(-0.509568 + 0.509568i) q^{21} +(4.90275 - 1.05781i) q^{22} +3.67724i q^{23} +(3.15850 - 2.33941i) q^{24} -4.87839i q^{25} +(-0.903283 - 4.18655i) q^{26} +(3.99820 - 3.99820i) q^{27} +(-0.944884 + 0.427641i) q^{28} +(5.60762 + 5.60762i) q^{29} +(5.19057 + 3.34825i) q^{30} -5.48577 q^{31} +(5.44105 - 1.54756i) q^{32} -4.92844 q^{33} +(9.71783 + 6.26862i) q^{34} +(-1.15250 - 1.15250i) q^{35} +(1.94758 - 0.881446i) q^{36} +(-5.30795 + 5.30795i) q^{37} +(0.298265 + 1.38240i) q^{38} +4.20849i q^{39} +(5.29108 + 7.14364i) q^{40} +4.28518i q^{41} +(0.996211 - 0.214941i) q^{42} +(5.38822 - 5.38822i) q^{43} +(-6.63740 - 2.50134i) q^{44} +(2.37551 + 2.37551i) q^{45} +(2.81898 - 4.37007i) q^{46} +7.68662 q^{47} +(-5.54699 + 0.358864i) q^{48} +6.73108 q^{49} +(-3.73978 + 5.79754i) q^{50} +(-8.03511 - 8.03511i) q^{51} +(-2.13594 + 5.66781i) q^{52} +(-2.40234 + 2.40234i) q^{53} +(-7.81653 + 1.68648i) q^{54} -11.1468i q^{55} +(1.45074 + 0.216137i) q^{56} -1.38965i q^{57} +(-2.36535 - 10.9630i) q^{58} +(5.28583 - 5.28583i) q^{59} +(-3.60176 - 7.95819i) q^{60} +(5.16376 + 5.16376i) q^{61} +(6.51935 + 4.20540i) q^{62} +0.554295 q^{63} +(-7.65257 - 2.33198i) q^{64} -9.51842 q^{65} +(5.85702 + 3.77815i) q^{66} +(0.328680 + 0.328680i) q^{67} +(-6.74325 - 14.8994i) q^{68} +(-3.61336 + 3.61336i) q^{69} +(0.486136 + 2.25315i) q^{70} -8.49376i q^{71} +(-2.99024 - 0.445497i) q^{72} +10.7641i q^{73} +(10.3771 - 2.23895i) q^{74} +(4.79365 - 4.79365i) q^{75} +(0.705291 - 1.87151i) q^{76} +(-1.30048 - 1.30048i) q^{77} +(3.22624 - 5.00142i) q^{78} +7.35306 q^{79} +(-0.811648 - 12.5457i) q^{80} +4.65086 q^{81} +(3.28502 - 5.09256i) q^{82} +(-6.00404 - 6.00404i) q^{83} +(-1.34868 - 0.508259i) q^{84} +(18.1732 - 18.1732i) q^{85} +(-10.5340 + 2.27281i) q^{86} +11.0204i q^{87} +(5.97044 + 8.06087i) q^{88} -9.35796i q^{89} +(-1.00201 - 4.64415i) q^{90} +(-1.11050 + 1.11050i) q^{91} +(-6.70021 + 3.03242i) q^{92} +(-5.39047 - 5.39047i) q^{93} +(-9.13486 - 5.89257i) q^{94} +3.14299 q^{95} +(6.86722 + 3.82586i) q^{96} -4.65969 q^{97} +(-7.99929 - 5.16005i) q^{98} +(2.68052 + 2.68052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18841 0.766601i −0.840334 0.542069i
\(3\) 0.982629 + 0.982629i 0.567321 + 0.567321i 0.931377 0.364056i \(-0.118608\pi\)
−0.364056 + 0.931377i \(0.618608\pi\)
\(4\) 0.824645 + 1.82208i 0.412322 + 0.911038i
\(5\) −2.22243 + 2.22243i −0.993901 + 0.993901i −0.999982 0.00608049i \(-0.998065\pi\)
0.00608049 + 0.999982i \(0.498065\pi\)
\(6\) −0.414483 1.92105i −0.169212 0.784267i
\(7\) 0.518576i 0.196003i 0.995186 + 0.0980016i \(0.0312450\pi\)
−0.995186 + 0.0980016i \(0.968755\pi\)
\(8\) 0.416789 2.79755i 0.147357 0.989083i
\(9\) 1.06888i 0.356293i
\(10\) 4.34488 0.937444i 1.37397 0.296446i
\(11\) −2.50778 + 2.50778i −0.756125 + 0.756125i −0.975615 0.219489i \(-0.929561\pi\)
0.219489 + 0.975615i \(0.429561\pi\)
\(12\) −0.980105 + 2.60075i −0.282932 + 0.750770i
\(13\) 2.14144 + 2.14144i 0.593930 + 0.593930i 0.938691 0.344761i \(-0.112040\pi\)
−0.344761 + 0.938691i \(0.612040\pi\)
\(14\) 0.397541 0.616281i 0.106247 0.164708i
\(15\) −4.36765 −1.12772
\(16\) −2.63992 + 3.00513i −0.659981 + 0.751283i
\(17\) −8.17716 −1.98325 −0.991626 0.129144i \(-0.958777\pi\)
−0.991626 + 0.129144i \(0.958777\pi\)
\(18\) −0.819405 + 1.27027i −0.193136 + 0.299405i
\(19\) −0.707107 0.707107i −0.162221 0.162221i
\(20\) −5.88215 2.21672i −1.31529 0.495674i
\(21\) −0.509568 + 0.509568i −0.111197 + 0.111197i
\(22\) 4.90275 1.05781i 1.04527 0.225526i
\(23\) 3.67724i 0.766758i 0.923591 + 0.383379i \(0.125240\pi\)
−0.923591 + 0.383379i \(0.874760\pi\)
\(24\) 3.15850 2.33941i 0.644727 0.477529i
\(25\) 4.87839i 0.975678i
\(26\) −0.903283 4.18655i −0.177148 0.821050i
\(27\) 3.99820 3.99820i 0.769454 0.769454i
\(28\) −0.944884 + 0.427641i −0.178566 + 0.0808165i
\(29\) 5.60762 + 5.60762i 1.04131 + 1.04131i 0.999109 + 0.0422006i \(0.0134369\pi\)
0.0422006 + 0.999109i \(0.486563\pi\)
\(30\) 5.19057 + 3.34825i 0.947663 + 0.611303i
\(31\) −5.48577 −0.985273 −0.492636 0.870235i \(-0.663967\pi\)
−0.492636 + 0.870235i \(0.663967\pi\)
\(32\) 5.44105 1.54756i 0.961851 0.273573i
\(33\) −4.92844 −0.857932
\(34\) 9.71783 + 6.26862i 1.66659 + 1.07506i
\(35\) −1.15250 1.15250i −0.194808 0.194808i
\(36\) 1.94758 0.881446i 0.324597 0.146908i
\(37\) −5.30795 + 5.30795i −0.872621 + 0.872621i −0.992757 0.120136i \(-0.961667\pi\)
0.120136 + 0.992757i \(0.461667\pi\)
\(38\) 0.298265 + 1.38240i 0.0483850 + 0.224255i
\(39\) 4.20849i 0.673898i
\(40\) 5.29108 + 7.14364i 0.836593 + 1.12951i
\(41\) 4.28518i 0.669233i 0.942354 + 0.334616i \(0.108607\pi\)
−0.942354 + 0.334616i \(0.891393\pi\)
\(42\) 0.996211 0.214941i 0.153719 0.0331661i
\(43\) 5.38822 5.38822i 0.821696 0.821696i −0.164655 0.986351i \(-0.552651\pi\)
0.986351 + 0.164655i \(0.0526512\pi\)
\(44\) −6.63740 2.50134i −1.00063 0.377092i
\(45\) 2.37551 + 2.37551i 0.354120 + 0.354120i
\(46\) 2.81898 4.37007i 0.415636 0.644332i
\(47\) 7.68662 1.12121 0.560604 0.828084i \(-0.310569\pi\)
0.560604 + 0.828084i \(0.310569\pi\)
\(48\) −5.54699 + 0.358864i −0.800640 + 0.0517975i
\(49\) 6.73108 0.961583
\(50\) −3.73978 + 5.79754i −0.528885 + 0.819896i
\(51\) −8.03511 8.03511i −1.12514 1.12514i
\(52\) −2.13594 + 5.66781i −0.296202 + 0.785983i
\(53\) −2.40234 + 2.40234i −0.329987 + 0.329987i −0.852581 0.522594i \(-0.824964\pi\)
0.522594 + 0.852581i \(0.324964\pi\)
\(54\) −7.81653 + 1.68648i −1.06370 + 0.229501i
\(55\) 11.1468i 1.50303i
\(56\) 1.45074 + 0.216137i 0.193863 + 0.0288825i
\(57\) 1.38965i 0.184063i
\(58\) −2.36535 10.9630i −0.310586 1.43951i
\(59\) 5.28583 5.28583i 0.688156 0.688156i −0.273668 0.961824i \(-0.588237\pi\)
0.961824 + 0.273668i \(0.0882370\pi\)
\(60\) −3.60176 7.95819i −0.464985 1.02740i
\(61\) 5.16376 + 5.16376i 0.661151 + 0.661151i 0.955651 0.294500i \(-0.0951532\pi\)
−0.294500 + 0.955651i \(0.595153\pi\)
\(62\) 6.51935 + 4.20540i 0.827958 + 0.534086i
\(63\) 0.554295 0.0698346
\(64\) −7.65257 2.33198i −0.956572 0.291497i
\(65\) −9.51842 −1.18061
\(66\) 5.85702 + 3.77815i 0.720949 + 0.465058i
\(67\) 0.328680 + 0.328680i 0.0401547 + 0.0401547i 0.726899 0.686744i \(-0.240961\pi\)
−0.686744 + 0.726899i \(0.740961\pi\)
\(68\) −6.74325 14.8994i −0.817739 1.80682i
\(69\) −3.61336 + 3.61336i −0.434998 + 0.434998i
\(70\) 0.486136 + 2.25315i 0.0581043 + 0.269303i
\(71\) 8.49376i 1.00802i −0.863697 0.504012i \(-0.831857\pi\)
0.863697 0.504012i \(-0.168143\pi\)
\(72\) −2.99024 0.445497i −0.352404 0.0525024i
\(73\) 10.7641i 1.25984i 0.776661 + 0.629919i \(0.216912\pi\)
−0.776661 + 0.629919i \(0.783088\pi\)
\(74\) 10.3771 2.23895i 1.20631 0.260272i
\(75\) 4.79365 4.79365i 0.553523 0.553523i
\(76\) 0.705291 1.87151i 0.0809024 0.214677i
\(77\) −1.30048 1.30048i −0.148203 0.148203i
\(78\) 3.22624 5.00142i 0.365299 0.566299i
\(79\) 7.35306 0.827284 0.413642 0.910440i \(-0.364256\pi\)
0.413642 + 0.910440i \(0.364256\pi\)
\(80\) −0.811648 12.5457i −0.0907450 1.40266i
\(81\) 4.65086 0.516762
\(82\) 3.28502 5.09256i 0.362770 0.562379i
\(83\) −6.00404 6.00404i −0.659029 0.659029i 0.296121 0.955150i \(-0.404307\pi\)
−0.955150 + 0.296121i \(0.904307\pi\)
\(84\) −1.34868 0.508259i −0.147153 0.0554556i
\(85\) 18.1732 18.1732i 1.97116 1.97116i
\(86\) −10.5340 + 2.27281i −1.13591 + 0.245083i
\(87\) 11.0204i 1.18151i
\(88\) 5.97044 + 8.06087i 0.636451 + 0.859292i
\(89\) 9.35796i 0.991941i −0.868339 0.495971i \(-0.834812\pi\)
0.868339 0.495971i \(-0.165188\pi\)
\(90\) −1.00201 4.64415i −0.105622 0.489537i
\(91\) −1.11050 + 1.11050i −0.116412 + 0.116412i
\(92\) −6.70021 + 3.03242i −0.698545 + 0.316151i
\(93\) −5.39047 5.39047i −0.558966 0.558966i
\(94\) −9.13486 5.89257i −0.942189 0.607772i
\(95\) 3.14299 0.322464
\(96\) 6.86722 + 3.82586i 0.700882 + 0.390475i
\(97\) −4.65969 −0.473120 −0.236560 0.971617i \(-0.576020\pi\)
−0.236560 + 0.971617i \(0.576020\pi\)
\(98\) −7.99929 5.16005i −0.808051 0.521244i
\(99\) 2.68052 + 2.68052i 0.269402 + 0.269402i
\(100\) 8.88880 4.02294i 0.888880 0.402294i
\(101\) −3.60362 + 3.60362i −0.358574 + 0.358574i −0.863287 0.504713i \(-0.831598\pi\)
0.504713 + 0.863287i \(0.331598\pi\)
\(102\) 3.38929 + 15.7088i 0.335590 + 1.55540i
\(103\) 7.32138i 0.721397i −0.932682 0.360699i \(-0.882538\pi\)
0.932682 0.360699i \(-0.117462\pi\)
\(104\) 6.88333 5.09827i 0.674966 0.499926i
\(105\) 2.26496i 0.221037i
\(106\) 4.69661 1.01333i 0.456175 0.0984236i
\(107\) −8.23856 + 8.23856i −0.796451 + 0.796451i −0.982534 0.186083i \(-0.940421\pi\)
0.186083 + 0.982534i \(0.440421\pi\)
\(108\) 10.5821 + 3.98793i 1.01826 + 0.383739i
\(109\) 12.9093 + 12.9093i 1.23648 + 1.23648i 0.961429 + 0.275055i \(0.0886960\pi\)
0.275055 + 0.961429i \(0.411304\pi\)
\(110\) −8.54512 + 13.2469i −0.814745 + 1.26305i
\(111\) −10.4315 −0.990113
\(112\) −1.55839 1.36900i −0.147254 0.129358i
\(113\) 7.27746 0.684606 0.342303 0.939590i \(-0.388793\pi\)
0.342303 + 0.939590i \(0.388793\pi\)
\(114\) −1.06531 + 1.65147i −0.0997750 + 0.154675i
\(115\) −8.17241 8.17241i −0.762081 0.762081i
\(116\) −5.59322 + 14.8418i −0.519318 + 1.37803i
\(117\) 2.28895 2.28895i 0.211613 0.211613i
\(118\) −10.3339 + 2.22962i −0.951309 + 0.205253i
\(119\) 4.24047i 0.388724i
\(120\) −1.82039 + 12.2187i −0.166178 + 1.11541i
\(121\) 1.57797i 0.143451i
\(122\) −2.17812 10.0952i −0.197198 0.913977i
\(123\) −4.21074 + 4.21074i −0.379670 + 0.379670i
\(124\) −4.52381 9.99548i −0.406250 0.897621i
\(125\) −0.270264 0.270264i −0.0241732 0.0241732i
\(126\) −0.658731 0.424923i −0.0586844 0.0378552i
\(127\) −8.85350 −0.785621 −0.392810 0.919619i \(-0.628497\pi\)
−0.392810 + 0.919619i \(0.628497\pi\)
\(128\) 7.30671 + 8.63782i 0.645828 + 0.763483i
\(129\) 10.5892 0.932331
\(130\) 11.3118 + 7.29684i 0.992111 + 0.639975i
\(131\) 10.9432 + 10.9432i 0.956116 + 0.956116i 0.999077 0.0429611i \(-0.0136791\pi\)
−0.0429611 + 0.999077i \(0.513679\pi\)
\(132\) −4.06421 8.98000i −0.353745 0.781609i
\(133\) 0.366688 0.366688i 0.0317959 0.0317959i
\(134\) −0.138641 0.642574i −0.0119767 0.0555099i
\(135\) 17.7714i 1.52952i
\(136\) −3.40815 + 22.8760i −0.292246 + 1.96160i
\(137\) 12.6102i 1.07737i 0.842509 + 0.538683i \(0.181078\pi\)
−0.842509 + 0.538683i \(0.818922\pi\)
\(138\) 7.06417 1.52415i 0.601342 0.129745i
\(139\) 10.0742 10.0742i 0.854479 0.854479i −0.136202 0.990681i \(-0.543490\pi\)
0.990681 + 0.136202i \(0.0434896\pi\)
\(140\) 1.14954 3.05034i 0.0971537 0.257801i
\(141\) 7.55309 + 7.55309i 0.636085 + 0.636085i
\(142\) −6.51133 + 10.0941i −0.546419 + 0.847077i
\(143\) −10.7406 −0.898171
\(144\) 3.21212 + 2.82176i 0.267677 + 0.235147i
\(145\) −24.9251 −2.06992
\(146\) 8.25174 12.7921i 0.682919 1.05868i
\(147\) 6.61416 + 6.61416i 0.545526 + 0.545526i
\(148\) −14.0487 5.29432i −1.15479 0.435190i
\(149\) 2.60931 2.60931i 0.213763 0.213763i −0.592101 0.805864i \(-0.701701\pi\)
0.805864 + 0.592101i \(0.201701\pi\)
\(150\) −9.37165 + 2.02201i −0.765192 + 0.165097i
\(151\) 15.7722i 1.28352i 0.766905 + 0.641761i \(0.221796\pi\)
−0.766905 + 0.641761i \(0.778204\pi\)
\(152\) −2.27288 + 1.68345i −0.184355 + 0.136546i
\(153\) 8.74040i 0.706619i
\(154\) 0.548554 + 2.54245i 0.0442037 + 0.204876i
\(155\) 12.1917 12.1917i 0.979263 0.979263i
\(156\) −7.66819 + 3.47051i −0.613947 + 0.277863i
\(157\) −1.91124 1.91124i −0.152533 0.152533i 0.626715 0.779248i \(-0.284399\pi\)
−0.779248 + 0.626715i \(0.784399\pi\)
\(158\) −8.73847 5.63687i −0.695195 0.448445i
\(159\) −4.72122 −0.374417
\(160\) −8.65301 + 15.5317i −0.684080 + 1.22789i
\(161\) −1.90693 −0.150287
\(162\) −5.52713 3.56535i −0.434253 0.280121i
\(163\) −2.74842 2.74842i −0.215273 0.215273i 0.591230 0.806503i \(-0.298643\pi\)
−0.806503 + 0.591230i \(0.798643\pi\)
\(164\) −7.80792 + 3.53375i −0.609696 + 0.275939i
\(165\) 10.9531 10.9531i 0.852700 0.852700i
\(166\) 2.53257 + 11.7380i 0.196565 + 0.911044i
\(167\) 2.00369i 0.155050i 0.996990 + 0.0775252i \(0.0247018\pi\)
−0.996990 + 0.0775252i \(0.975298\pi\)
\(168\) 1.21316 + 1.63792i 0.0935972 + 0.126369i
\(169\) 3.82843i 0.294495i
\(170\) −35.5288 + 7.66562i −2.72493 + 0.587927i
\(171\) −0.755812 + 0.755812i −0.0577984 + 0.0577984i
\(172\) 14.2611 + 5.37438i 1.08740 + 0.409793i
\(173\) −6.45544 6.45544i −0.490798 0.490798i 0.417759 0.908558i \(-0.362816\pi\)
−0.908558 + 0.417759i \(0.862816\pi\)
\(174\) 8.44828 13.0968i 0.640462 0.992867i
\(175\) 2.52982 0.191236
\(176\) −0.915862 14.1566i −0.0690357 1.06709i
\(177\) 10.3880 0.780811
\(178\) −7.17382 + 11.1211i −0.537701 + 0.833562i
\(179\) 13.5884 + 13.5884i 1.01565 + 1.01565i 0.999876 + 0.0157707i \(0.00502019\pi\)
0.0157707 + 0.999876i \(0.494980\pi\)
\(180\) −2.36941 + 6.28731i −0.176605 + 0.468629i
\(181\) −0.0664873 + 0.0664873i −0.00494196 + 0.00494196i −0.709573 0.704631i \(-0.751112\pi\)
0.704631 + 0.709573i \(0.251112\pi\)
\(182\) 2.17104 0.468421i 0.160928 0.0347217i
\(183\) 10.1481i 0.750170i
\(184\) 10.2873 + 1.53263i 0.758387 + 0.112987i
\(185\) 23.5931i 1.73460i
\(186\) 2.27376 + 10.5384i 0.166720 + 0.772716i
\(187\) 20.5065 20.5065i 1.49959 1.49959i
\(188\) 6.33873 + 14.0056i 0.462299 + 1.02146i
\(189\) 2.07337 + 2.07337i 0.150815 + 0.150815i
\(190\) −3.73517 2.40942i −0.270978 0.174798i
\(191\) 18.9056 1.36796 0.683982 0.729499i \(-0.260246\pi\)
0.683982 + 0.729499i \(0.260246\pi\)
\(192\) −5.22817 9.81111i −0.377311 0.708056i
\(193\) −2.20445 −0.158680 −0.0793398 0.996848i \(-0.525281\pi\)
−0.0793398 + 0.996848i \(0.525281\pi\)
\(194\) 5.53763 + 3.57212i 0.397579 + 0.256464i
\(195\) −9.35308 9.35308i −0.669788 0.669788i
\(196\) 5.55075 + 12.2645i 0.396482 + 0.876038i
\(197\) 3.12323 3.12323i 0.222521 0.222521i −0.587038 0.809559i \(-0.699706\pi\)
0.809559 + 0.587038i \(0.199706\pi\)
\(198\) −1.13067 5.24045i −0.0803533 0.372423i
\(199\) 12.4844i 0.884997i −0.896769 0.442499i \(-0.854092\pi\)
0.896769 0.442499i \(-0.145908\pi\)
\(200\) −13.6475 2.03326i −0.965027 0.143773i
\(201\) 0.645941i 0.0455612i
\(202\) 7.04513 1.52005i 0.495694 0.106950i
\(203\) −2.90798 + 2.90798i −0.204100 + 0.204100i
\(204\) 8.01448 21.2667i 0.561126 1.48897i
\(205\) −9.52351 9.52351i −0.665151 0.665151i
\(206\) −5.61258 + 8.70081i −0.391047 + 0.606214i
\(207\) 3.93053 0.273190
\(208\) −12.0886 + 0.782071i −0.838191 + 0.0542269i
\(209\) 3.54654 0.245319
\(210\) −1.73632 + 2.69170i −0.119817 + 0.185745i
\(211\) 8.02018 + 8.02018i 0.552132 + 0.552132i 0.927056 0.374924i \(-0.122331\pi\)
−0.374924 + 0.927056i \(0.622331\pi\)
\(212\) −6.35833 2.39617i −0.436692 0.164570i
\(213\) 8.34622 8.34622i 0.571874 0.571874i
\(214\) 16.1065 3.47511i 1.10102 0.237553i
\(215\) 23.9499i 1.63337i
\(216\) −9.51876 12.8516i −0.647670 0.874439i
\(217\) 2.84478i 0.193117i
\(218\) −5.44526 25.2378i −0.368800 1.70932i
\(219\) −10.5771 + 10.5771i −0.714733 + 0.714733i
\(220\) 20.3102 9.19211i 1.36932 0.619732i
\(221\) −17.5109 17.5109i −1.17791 1.17791i
\(222\) 12.3969 + 7.99680i 0.832026 + 0.536710i
\(223\) −23.2799 −1.55893 −0.779467 0.626443i \(-0.784510\pi\)
−0.779467 + 0.626443i \(0.784510\pi\)
\(224\) 0.802529 + 2.82160i 0.0536212 + 0.188526i
\(225\) −5.21441 −0.347628
\(226\) −8.64862 5.57891i −0.575298 0.371104i
\(227\) 5.82988 + 5.82988i 0.386943 + 0.386943i 0.873595 0.486653i \(-0.161782\pi\)
−0.486653 + 0.873595i \(0.661782\pi\)
\(228\) 2.53204 1.14597i 0.167689 0.0758934i
\(229\) −16.9493 + 16.9493i −1.12004 + 1.12004i −0.128307 + 0.991734i \(0.540954\pi\)
−0.991734 + 0.128307i \(0.959046\pi\)
\(230\) 3.44721 + 15.9772i 0.227302 + 1.05350i
\(231\) 2.55577i 0.168157i
\(232\) 18.0248 13.3504i 1.18339 0.876498i
\(233\) 12.5017i 0.819016i −0.912306 0.409508i \(-0.865700\pi\)
0.912306 0.409508i \(-0.134300\pi\)
\(234\) −4.47492 + 0.965501i −0.292535 + 0.0631168i
\(235\) −17.0830 + 17.0830i −1.11437 + 1.11437i
\(236\) 13.9901 + 5.27225i 0.910679 + 0.343194i
\(237\) 7.22534 + 7.22534i 0.469336 + 0.469336i
\(238\) −3.25075 + 5.03943i −0.210715 + 0.326658i
\(239\) −10.1018 −0.653432 −0.326716 0.945123i \(-0.605942\pi\)
−0.326716 + 0.945123i \(0.605942\pi\)
\(240\) 11.5303 13.1254i 0.744275 0.847238i
\(241\) −12.0760 −0.777885 −0.388942 0.921262i \(-0.627160\pi\)
−0.388942 + 0.921262i \(0.627160\pi\)
\(242\) −1.20967 + 1.87527i −0.0777606 + 0.120547i
\(243\) −7.42453 7.42453i −0.476284 0.476284i
\(244\) −5.15049 + 13.6670i −0.329727 + 0.874941i
\(245\) −14.9594 + 14.9594i −0.955718 + 0.955718i
\(246\) 8.23206 1.77613i 0.524857 0.113242i
\(247\) 3.02846i 0.192696i
\(248\) −2.28641 + 15.3467i −0.145187 + 0.974517i
\(249\) 11.7995i 0.747763i
\(250\) 0.114000 + 0.528370i 0.00721001 + 0.0334171i
\(251\) 16.1217 16.1217i 1.01759 1.01759i 0.0177490 0.999842i \(-0.494350\pi\)
0.999842 0.0177490i \(-0.00564999\pi\)
\(252\) 0.457096 + 1.00997i 0.0287944 + 0.0636220i
\(253\) −9.22173 9.22173i −0.579765 0.579765i
\(254\) 10.5216 + 6.78710i 0.660184 + 0.425861i
\(255\) 35.7150 2.23656
\(256\) −2.06162 15.8666i −0.128851 0.991664i
\(257\) −8.63368 −0.538554 −0.269277 0.963063i \(-0.586785\pi\)
−0.269277 + 0.963063i \(0.586785\pi\)
\(258\) −12.5844 8.11773i −0.783469 0.505388i
\(259\) −2.75257 2.75257i −0.171037 0.171037i
\(260\) −7.84931 17.3433i −0.486794 1.07559i
\(261\) 5.99388 5.99388i 0.371012 0.371012i
\(262\) −4.61597 21.3942i −0.285176 1.32174i
\(263\) 12.5077i 0.771258i −0.922654 0.385629i \(-0.873985\pi\)
0.922654 0.385629i \(-0.126015\pi\)
\(264\) −2.05412 + 13.7876i −0.126422 + 0.848566i
\(265\) 10.6781i 0.655949i
\(266\) −0.716881 + 0.154673i −0.0439548 + 0.00948360i
\(267\) 9.19540 9.19540i 0.562749 0.562749i
\(268\) −0.327836 + 0.869924i −0.0200258 + 0.0531391i
\(269\) 2.84573 + 2.84573i 0.173507 + 0.173507i 0.788518 0.615011i \(-0.210849\pi\)
−0.615011 + 0.788518i \(0.710849\pi\)
\(270\) 13.6236 21.1198i 0.829107 1.28531i
\(271\) −26.1363 −1.58767 −0.793834 0.608134i \(-0.791918\pi\)
−0.793834 + 0.608134i \(0.791918\pi\)
\(272\) 21.5871 24.5734i 1.30891 1.48998i
\(273\) −2.18242 −0.132086
\(274\) 9.66703 14.9862i 0.584007 0.905347i
\(275\) 12.2340 + 12.2340i 0.737735 + 0.737735i
\(276\) −9.56356 3.60408i −0.575659 0.216940i
\(277\) 1.11397 1.11397i 0.0669318 0.0669318i −0.672848 0.739780i \(-0.734929\pi\)
0.739780 + 0.672848i \(0.234929\pi\)
\(278\) −19.6951 + 4.24938i −1.18123 + 0.254861i
\(279\) 5.86362i 0.351046i
\(280\) −3.70452 + 2.74382i −0.221387 + 0.163975i
\(281\) 3.69892i 0.220659i −0.993895 0.110330i \(-0.964809\pi\)
0.993895 0.110330i \(-0.0351906\pi\)
\(282\) −3.18597 14.7664i −0.189722 0.879326i
\(283\) −10.2024 + 10.2024i −0.606471 + 0.606471i −0.942022 0.335551i \(-0.891077\pi\)
0.335551 + 0.942022i \(0.391077\pi\)
\(284\) 15.4763 7.00434i 0.918348 0.415631i
\(285\) 3.08839 + 3.08839i 0.182941 + 0.182941i
\(286\) 12.7642 + 8.23373i 0.754764 + 0.486871i
\(287\) −2.22219 −0.131172
\(288\) −1.65416 5.81583i −0.0974722 0.342701i
\(289\) 49.8659 2.93329
\(290\) 29.6213 + 19.1076i 1.73942 + 1.12204i
\(291\) −4.57875 4.57875i −0.268411 0.268411i
\(292\) −19.6129 + 8.87652i −1.14776 + 0.519459i
\(293\) −16.9050 + 16.9050i −0.987603 + 0.987603i −0.999924 0.0123212i \(-0.996078\pi\)
0.0123212 + 0.999924i \(0.496078\pi\)
\(294\) −2.78992 12.9308i −0.162711 0.754137i
\(295\) 23.4948i 1.36792i
\(296\) 12.6370 + 17.0615i 0.734508 + 0.991682i
\(297\) 20.0532i 1.16361i
\(298\) −5.10123 + 1.10063i −0.295506 + 0.0637579i
\(299\) −7.87461 + 7.87461i −0.455400 + 0.455400i
\(300\) 12.6875 + 4.78134i 0.732511 + 0.276051i
\(301\) 2.79420 + 2.79420i 0.161055 + 0.161055i
\(302\) 12.0910 18.7438i 0.695757 1.07859i
\(303\) −7.08205 −0.406853
\(304\) 3.99166 0.258241i 0.228937 0.0148111i
\(305\) −22.9522 −1.31424
\(306\) 6.70040 10.3872i 0.383036 0.593796i
\(307\) −2.84284 2.84284i −0.162250 0.162250i 0.621313 0.783563i \(-0.286600\pi\)
−0.783563 + 0.621313i \(0.786600\pi\)
\(308\) 1.29714 3.44200i 0.0739112 0.196126i
\(309\) 7.19420 7.19420i 0.409264 0.409264i
\(310\) −23.8350 + 5.14260i −1.35374 + 0.292080i
\(311\) 25.9320i 1.47047i −0.677812 0.735235i \(-0.737072\pi\)
0.677812 0.735235i \(-0.262928\pi\)
\(312\) 11.7735 + 1.75405i 0.666541 + 0.0993037i
\(313\) 11.4082i 0.644828i −0.946599 0.322414i \(-0.895506\pi\)
0.946599 0.322414i \(-0.104494\pi\)
\(314\) 0.806180 + 3.73649i 0.0454953 + 0.210863i
\(315\) −1.23188 + 1.23188i −0.0694087 + 0.0694087i
\(316\) 6.06366 + 13.3978i 0.341108 + 0.753688i
\(317\) 11.2287 + 11.2287i 0.630669 + 0.630669i 0.948236 0.317567i \(-0.102866\pi\)
−0.317567 + 0.948236i \(0.602866\pi\)
\(318\) 5.61076 + 3.61930i 0.314636 + 0.202960i
\(319\) −28.1254 −1.57472
\(320\) 22.1900 11.8247i 1.24046 0.661018i
\(321\) −16.1909 −0.903688
\(322\) 2.26621 + 1.46185i 0.126291 + 0.0814659i
\(323\) 5.78212 + 5.78212i 0.321726 + 0.321726i
\(324\) 3.83530 + 8.47422i 0.213072 + 0.470790i
\(325\) 10.4468 10.4468i 0.579485 0.579485i
\(326\) 1.15931 + 5.37320i 0.0642084 + 0.297594i
\(327\) 25.3700i 1.40297i
\(328\) 11.9880 + 1.78602i 0.661927 + 0.0986162i
\(329\) 3.98609i 0.219760i
\(330\) −21.4135 + 4.62014i −1.17877 + 0.254330i
\(331\) −7.05044 + 7.05044i −0.387527 + 0.387527i −0.873804 0.486277i \(-0.838354\pi\)
0.486277 + 0.873804i \(0.338354\pi\)
\(332\) 5.98862 15.8910i 0.328668 0.872133i
\(333\) 5.67356 + 5.67356i 0.310909 + 0.310909i
\(334\) 1.53603 2.38121i 0.0840480 0.130294i
\(335\) −1.46094 −0.0798195
\(336\) −0.186098 2.87654i −0.0101525 0.156928i
\(337\) −22.3426 −1.21708 −0.608539 0.793524i \(-0.708244\pi\)
−0.608539 + 0.793524i \(0.708244\pi\)
\(338\) −2.93488 + 4.54975i −0.159636 + 0.247474i
\(339\) 7.15105 + 7.15105i 0.388392 + 0.388392i
\(340\) 48.0993 + 18.1265i 2.60855 + 0.983047i
\(341\) 13.7571 13.7571i 0.744990 0.744990i
\(342\) 1.47762 0.318809i 0.0799007 0.0172392i
\(343\) 7.12060i 0.384476i
\(344\) −12.8281 17.3196i −0.691643 0.933808i
\(345\) 16.0609i 0.864690i
\(346\) 2.72297 + 12.6205i 0.146388 + 0.678481i
\(347\) −23.3395 + 23.3395i −1.25293 + 1.25293i −0.298527 + 0.954401i \(0.596495\pi\)
−0.954401 + 0.298527i \(0.903505\pi\)
\(348\) −20.0801 + 9.08794i −1.07640 + 0.487165i
\(349\) 17.6030 + 17.6030i 0.942267 + 0.942267i 0.998422 0.0561552i \(-0.0178842\pi\)
−0.0561552 + 0.998422i \(0.517884\pi\)
\(350\) −3.00646 1.93936i −0.160702 0.103663i
\(351\) 17.1238 0.914003
\(352\) −9.76403 + 17.5259i −0.520425 + 0.934136i
\(353\) 0.192537 0.0102477 0.00512387 0.999987i \(-0.498369\pi\)
0.00512387 + 0.999987i \(0.498369\pi\)
\(354\) −12.3452 7.96347i −0.656142 0.423254i
\(355\) 18.8768 + 18.8768i 1.00188 + 1.00188i
\(356\) 17.0509 7.71699i 0.903696 0.409000i
\(357\) 4.16681 4.16681i 0.220531 0.220531i
\(358\) −5.73174 26.5655i −0.302932 1.40403i
\(359\) 0.665573i 0.0351276i −0.999846 0.0175638i \(-0.994409\pi\)
0.999846 0.0175638i \(-0.00559102\pi\)
\(360\) 7.63570 5.65552i 0.402437 0.298072i
\(361\) 1.00000i 0.0526316i
\(362\) 0.129984 0.0280450i 0.00683178 0.00147401i
\(363\) 1.55056 1.55056i 0.0813830 0.0813830i
\(364\) −2.93919 1.10765i −0.154055 0.0580566i
\(365\) −23.9224 23.9224i −1.25215 1.25215i
\(366\) 7.77956 12.0601i 0.406644 0.630393i
\(367\) −4.73699 −0.247269 −0.123634 0.992328i \(-0.539455\pi\)
−0.123634 + 0.992328i \(0.539455\pi\)
\(368\) −11.0506 9.70763i −0.576052 0.506045i
\(369\) 4.58034 0.238443
\(370\) −18.0865 + 28.0383i −0.940272 + 1.45764i
\(371\) −1.24580 1.24580i −0.0646785 0.0646785i
\(372\) 5.37663 14.2671i 0.278765 0.739714i
\(373\) 6.02933 6.02933i 0.312187 0.312187i −0.533569 0.845756i \(-0.679150\pi\)
0.845756 + 0.533569i \(0.179150\pi\)
\(374\) −40.0906 + 8.64987i −2.07303 + 0.447274i
\(375\) 0.531139i 0.0274279i
\(376\) 3.20370 21.5037i 0.165218 1.10897i
\(377\) 24.0168i 1.23693i
\(378\) −0.874568 4.05346i −0.0449829 0.208488i
\(379\) −19.2425 + 19.2425i −0.988420 + 0.988420i −0.999934 0.0115132i \(-0.996335\pi\)
0.0115132 + 0.999934i \(0.496335\pi\)
\(380\) 2.59185 + 5.72677i 0.132959 + 0.293777i
\(381\) −8.69970 8.69970i −0.445699 0.445699i
\(382\) −22.4677 14.4931i −1.14955 0.741531i
\(383\) 27.5509 1.40778 0.703892 0.710307i \(-0.251444\pi\)
0.703892 + 0.710307i \(0.251444\pi\)
\(384\) −1.30799 + 15.6676i −0.0667479 + 0.799532i
\(385\) 5.78043 0.294598
\(386\) 2.61979 + 1.68993i 0.133344 + 0.0860153i
\(387\) −5.75936 5.75936i −0.292765 0.292765i
\(388\) −3.84259 8.49031i −0.195078 0.431030i
\(389\) −1.99617 + 1.99617i −0.101210 + 0.101210i −0.755899 0.654689i \(-0.772800\pi\)
0.654689 + 0.755899i \(0.272800\pi\)
\(390\) 3.94522 + 18.2854i 0.199774 + 0.925917i
\(391\) 30.0694i 1.52067i
\(392\) 2.80544 18.8305i 0.141696 0.951085i
\(393\) 21.5063i 1.08485i
\(394\) −6.10596 + 1.31741i −0.307614 + 0.0663702i
\(395\) −16.3417 + 16.3417i −0.822239 + 0.822239i
\(396\) −2.67363 + 7.09459i −0.134355 + 0.356516i
\(397\) −18.2874 18.2874i −0.917820 0.917820i 0.0790506 0.996871i \(-0.474811\pi\)
−0.996871 + 0.0790506i \(0.974811\pi\)
\(398\) −9.57058 + 14.8366i −0.479730 + 0.743693i
\(399\) 0.720637 0.0360770
\(400\) 14.6602 + 12.8786i 0.733010 + 0.643929i
\(401\) 36.9382 1.84461 0.922304 0.386466i \(-0.126304\pi\)
0.922304 + 0.386466i \(0.126304\pi\)
\(402\) 0.495180 0.767644i 0.0246973 0.0382866i
\(403\) −11.7475 11.7475i −0.585183 0.585183i
\(404\) −9.53778 3.59437i −0.474522 0.178826i
\(405\) −10.3362 + 10.3362i −0.513610 + 0.513610i
\(406\) 5.68513 1.22661i 0.282148 0.0608759i
\(407\) 26.6224i 1.31962i
\(408\) −25.8276 + 19.1297i −1.27866 + 0.947061i
\(409\) 20.8320i 1.03007i −0.857168 0.515037i \(-0.827778\pi\)
0.857168 0.515037i \(-0.172222\pi\)
\(410\) 4.01712 + 18.6186i 0.198391 + 0.919507i
\(411\) −12.3912 + 12.3912i −0.611212 + 0.611212i
\(412\) 13.3401 6.03754i 0.657220 0.297448i
\(413\) 2.74110 + 2.74110i 0.134881 + 0.134881i
\(414\) −4.67108 3.01315i −0.229571 0.148088i
\(415\) 26.6871 1.31002
\(416\) 14.9657 + 8.33769i 0.733755 + 0.408789i
\(417\) 19.7983 0.969528
\(418\) −4.21475 2.71878i −0.206150 0.132980i
\(419\) −16.7006 16.7006i −0.815877 0.815877i 0.169631 0.985508i \(-0.445743\pi\)
−0.985508 + 0.169631i \(0.945743\pi\)
\(420\) 4.12692 1.86778i 0.201373 0.0911385i
\(421\) −12.7537 + 12.7537i −0.621577 + 0.621577i −0.945935 0.324357i \(-0.894852\pi\)
0.324357 + 0.945935i \(0.394852\pi\)
\(422\) −3.38299 15.6796i −0.164682 0.763269i
\(423\) 8.21607i 0.399479i
\(424\) 5.71940 + 7.72194i 0.277759 + 0.375011i
\(425\) 39.8914i 1.93502i
\(426\) −16.3170 + 3.52052i −0.790560 + 0.170570i
\(427\) −2.67780 + 2.67780i −0.129588 + 0.129588i
\(428\) −21.8052 8.21740i −1.05399 0.397203i
\(429\) −10.5540 10.5540i −0.509551 0.509551i
\(430\) 18.3600 28.4623i 0.885398 1.37257i
\(431\) 12.5666 0.605311 0.302656 0.953100i \(-0.402127\pi\)
0.302656 + 0.953100i \(0.402127\pi\)
\(432\) 1.46017 + 22.5701i 0.0702526 + 1.08590i
\(433\) 13.0595 0.627601 0.313801 0.949489i \(-0.398398\pi\)
0.313801 + 0.949489i \(0.398398\pi\)
\(434\) −2.18082 + 3.38078i −0.104683 + 0.162282i
\(435\) −24.4921 24.4921i −1.17431 1.17431i
\(436\) −12.8761 + 34.1672i −0.616654 + 1.63631i
\(437\) 2.60020 2.60020i 0.124385 0.124385i
\(438\) 20.6783 4.46152i 0.988049 0.213180i
\(439\) 3.55838i 0.169832i −0.996388 0.0849161i \(-0.972938\pi\)
0.996388 0.0849161i \(-0.0270622\pi\)
\(440\) −31.1836 4.64584i −1.48662 0.221482i
\(441\) 7.19471i 0.342605i
\(442\) 7.38629 + 34.2341i 0.351330 + 1.62835i
\(443\) 19.9992 19.9992i 0.950190 0.950190i −0.0486271 0.998817i \(-0.515485\pi\)
0.998817 + 0.0486271i \(0.0154846\pi\)
\(444\) −8.60227 19.0070i −0.408246 0.902031i
\(445\) 20.7974 + 20.7974i 0.985892 + 0.985892i
\(446\) 27.6660 + 17.8464i 1.31003 + 0.845050i
\(447\) 5.12796 0.242544
\(448\) 1.20931 3.96844i 0.0571343 0.187491i
\(449\) 5.72617 0.270235 0.135117 0.990830i \(-0.456859\pi\)
0.135117 + 0.990830i \(0.456859\pi\)
\(450\) 6.19687 + 3.99738i 0.292123 + 0.188438i
\(451\) −10.7463 10.7463i −0.506024 0.506024i
\(452\) 6.00132 + 13.2601i 0.282278 + 0.623702i
\(453\) −15.4982 + 15.4982i −0.728169 + 0.728169i
\(454\) −2.45910 11.3975i −0.115411 0.534911i
\(455\) 4.93602i 0.231404i
\(456\) −3.88761 0.579190i −0.182054 0.0271230i
\(457\) 23.3540i 1.09246i −0.837637 0.546228i \(-0.816063\pi\)
0.837637 0.546228i \(-0.183937\pi\)
\(458\) 33.1361 7.14939i 1.54835 0.334069i
\(459\) −32.6939 + 32.6939i −1.52602 + 1.52602i
\(460\) 8.15142 21.6301i 0.380062 1.00851i
\(461\) −7.15231 7.15231i −0.333116 0.333116i 0.520653 0.853769i \(-0.325689\pi\)
−0.853769 + 0.520653i \(0.825689\pi\)
\(462\) −1.95926 + 3.03731i −0.0911529 + 0.141308i
\(463\) 13.8558 0.643932 0.321966 0.946751i \(-0.395656\pi\)
0.321966 + 0.946751i \(0.395656\pi\)
\(464\) −31.6553 + 2.04795i −1.46956 + 0.0950735i
\(465\) 23.9599 1.11111
\(466\) −9.58385 + 14.8572i −0.443963 + 0.688247i
\(467\) −2.57565 2.57565i −0.119187 0.119187i 0.644998 0.764185i \(-0.276858\pi\)
−0.764185 + 0.644998i \(0.776858\pi\)
\(468\) 6.05820 + 2.28307i 0.280040 + 0.105535i
\(469\) −0.170445 + 0.170445i −0.00787044 + 0.00787044i
\(470\) 33.3974 7.20577i 1.54051 0.332377i
\(471\) 3.75608i 0.173071i
\(472\) −12.5843 16.9904i −0.579239 0.782049i
\(473\) 27.0250i 1.24261i
\(474\) −3.04772 14.1256i −0.139986 0.648812i
\(475\) −3.44954 + 3.44954i −0.158276 + 0.158276i
\(476\) 7.72647 3.49688i 0.354142 0.160279i
\(477\) 2.56782 + 2.56782i 0.117572 + 0.117572i
\(478\) 12.0051 + 7.74406i 0.549101 + 0.354205i
\(479\) 1.05236 0.0480835 0.0240418 0.999711i \(-0.492347\pi\)
0.0240418 + 0.999711i \(0.492347\pi\)
\(480\) −23.7646 + 6.75921i −1.08470 + 0.308515i
\(481\) −22.7334 −1.03655
\(482\) 14.3513 + 9.25750i 0.653683 + 0.421667i
\(483\) −1.87380 1.87380i −0.0852610 0.0852610i
\(484\) 2.87517 1.30126i 0.130690 0.0591482i
\(485\) 10.3558 10.3558i 0.470234 0.470234i
\(486\) 3.13174 + 14.5151i 0.142059 + 0.658416i
\(487\) 18.1274i 0.821432i −0.911763 0.410716i \(-0.865279\pi\)
0.911763 0.410716i \(-0.134721\pi\)
\(488\) 16.5981 12.2937i 0.751359 0.556508i
\(489\) 5.40136i 0.244258i
\(490\) 29.2457 6.31001i 1.32119 0.285057i
\(491\) 24.7876 24.7876i 1.11865 1.11865i 0.126709 0.991940i \(-0.459558\pi\)
0.991940 0.126709i \(-0.0404416\pi\)
\(492\) −11.1447 4.19993i −0.502440 0.189347i
\(493\) −45.8544 45.8544i −2.06518 2.06518i
\(494\) −2.32162 + 3.59906i −0.104455 + 0.161929i
\(495\) −11.9145 −0.535519
\(496\) 14.4820 16.4854i 0.650261 0.740218i
\(497\) 4.40466 0.197576
\(498\) −9.04551 + 14.0227i −0.405339 + 0.628370i
\(499\) 0.386258 + 0.386258i 0.0172913 + 0.0172913i 0.715700 0.698408i \(-0.246108\pi\)
−0.698408 + 0.715700i \(0.746108\pi\)
\(500\) 0.269570 0.715314i 0.0120555 0.0319898i
\(501\) −1.96889 + 1.96889i −0.0879634 + 0.0879634i
\(502\) −31.5181 + 6.80029i −1.40672 + 0.303512i
\(503\) 38.3162i 1.70843i 0.519917 + 0.854217i \(0.325963\pi\)
−0.519917 + 0.854217i \(0.674037\pi\)
\(504\) 0.231024 1.55067i 0.0102906 0.0690722i
\(505\) 16.0176i 0.712774i
\(506\) 3.88982 + 18.0286i 0.172924 + 0.801469i
\(507\) 3.76193 3.76193i 0.167073 0.167073i
\(508\) −7.30099 16.1317i −0.323929 0.715730i
\(509\) 7.78865 + 7.78865i 0.345226 + 0.345226i 0.858328 0.513102i \(-0.171504\pi\)
−0.513102 + 0.858328i \(0.671504\pi\)
\(510\) −42.4441 27.3791i −1.87945 1.21237i
\(511\) −5.58198 −0.246932
\(512\) −9.71333 + 20.4365i −0.429273 + 0.903175i
\(513\) −5.65431 −0.249644
\(514\) 10.2604 + 6.61859i 0.452565 + 0.291934i
\(515\) 16.2713 + 16.2713i 0.716997 + 0.716997i
\(516\) 8.73236 + 19.2944i 0.384421 + 0.849389i
\(517\) −19.2764 + 19.2764i −0.847774 + 0.847774i
\(518\) 1.16106 + 5.38132i 0.0510142 + 0.236441i
\(519\) 12.6866i 0.556881i
\(520\) −3.96717 + 26.6283i −0.173972 + 1.16773i
\(521\) 22.2075i 0.972930i 0.873700 + 0.486465i \(0.161714\pi\)
−0.873700 + 0.486465i \(0.838286\pi\)
\(522\) −11.7181 + 2.52828i −0.512888 + 0.110660i
\(523\) 0.541177 0.541177i 0.0236640 0.0236640i −0.695176 0.718840i \(-0.744673\pi\)
0.718840 + 0.695176i \(0.244673\pi\)
\(524\) −10.9151 + 28.9637i −0.476830 + 1.26529i
\(525\) 2.48587 + 2.48587i 0.108492 + 0.108492i
\(526\) −9.58842 + 14.8643i −0.418075 + 0.648114i
\(527\) 44.8580 1.95404
\(528\) 13.0107 14.8106i 0.566219 0.644549i
\(529\) 9.47791 0.412083
\(530\) −8.18583 + 12.6900i −0.355570 + 0.551216i
\(531\) −5.64991 5.64991i −0.245185 0.245185i
\(532\) 0.970522 + 0.365747i 0.0420775 + 0.0158571i
\(533\) −9.17647 + 9.17647i −0.397477 + 0.397477i
\(534\) −17.9771 + 3.87871i −0.777947 + 0.167848i
\(535\) 36.6192i 1.58319i
\(536\) 1.05649 0.782509i 0.0456334 0.0337992i
\(537\) 26.7048i 1.15240i
\(538\) −1.20036 5.56343i −0.0517510 0.239857i
\(539\) −16.8801 + 16.8801i −0.727077 + 0.727077i
\(540\) −32.3809 + 14.6551i −1.39345 + 0.630656i
\(541\) −10.6946 10.6946i −0.459797 0.459797i 0.438792 0.898589i \(-0.355406\pi\)
−0.898589 + 0.438792i \(0.855406\pi\)
\(542\) 31.0607 + 20.0361i 1.33417 + 0.860626i
\(543\) −0.130665 −0.00560736
\(544\) −44.4923 + 12.6547i −1.90759 + 0.542564i
\(545\) −57.3799 −2.45788
\(546\) 2.59362 + 1.67305i 0.110996 + 0.0715998i
\(547\) 27.7156 + 27.7156i 1.18503 + 1.18503i 0.978423 + 0.206611i \(0.0662434\pi\)
0.206611 + 0.978423i \(0.433757\pi\)
\(548\) −22.9768 + 10.3990i −0.981521 + 0.444222i
\(549\) 5.51943 5.51943i 0.235564 0.235564i
\(550\) −5.16041 23.9175i −0.220041 1.01985i
\(551\) 7.93038i 0.337845i
\(552\) 8.60256 + 11.6146i 0.366149 + 0.494349i
\(553\) 3.81312i 0.162150i
\(554\) −2.17782 + 0.469883i −0.0925268 + 0.0199634i
\(555\) 23.1833 23.1833i 0.984075 0.984075i
\(556\) 26.6635 + 10.0483i 1.13078 + 0.426142i
\(557\) −0.803237 0.803237i −0.0340343 0.0340343i 0.689885 0.723919i \(-0.257661\pi\)
−0.723919 + 0.689885i \(0.757661\pi\)
\(558\) 4.49506 6.96840i 0.190291 0.294996i
\(559\) 23.0771 0.976059
\(560\) 6.50591 0.420901i 0.274925 0.0177863i
\(561\) 40.3007 1.70150
\(562\) −2.83560 + 4.39584i −0.119612 + 0.185427i
\(563\) −16.8339 16.8339i −0.709466 0.709466i 0.256957 0.966423i \(-0.417280\pi\)
−0.966423 + 0.256957i \(0.917280\pi\)
\(564\) −7.53369 + 19.9909i −0.317226 + 0.841770i
\(565\) −16.1737 + 16.1737i −0.680431 + 0.680431i
\(566\) 19.9459 4.30348i 0.838387 0.180889i
\(567\) 2.41182i 0.101287i
\(568\) −23.7617 3.54011i −0.997020 0.148540i
\(569\) 37.6346i 1.57772i 0.614570 + 0.788862i \(0.289330\pi\)
−0.614570 + 0.788862i \(0.710670\pi\)
\(570\) −1.30272 6.03785i −0.0545648 0.252898i
\(571\) 20.2923 20.2923i 0.849205 0.849205i −0.140829 0.990034i \(-0.544977\pi\)
0.990034 + 0.140829i \(0.0449767\pi\)
\(572\) −8.85715 19.5701i −0.370336 0.818268i
\(573\) 18.5772 + 18.5772i 0.776075 + 0.776075i
\(574\) 2.64088 + 1.70353i 0.110228 + 0.0711041i
\(575\) 17.9390 0.748109
\(576\) −2.49260 + 8.17968i −0.103858 + 0.340820i
\(577\) 1.24449 0.0518090 0.0259045 0.999664i \(-0.491753\pi\)
0.0259045 + 0.999664i \(0.491753\pi\)
\(578\) −59.2612 38.2273i −2.46494 1.59004i
\(579\) −2.16615 2.16615i −0.0900223 0.0900223i
\(580\) −20.5544 45.4154i −0.853473 1.88577i
\(581\) 3.11355 3.11355i 0.129172 0.129172i
\(582\) 1.93136 + 8.95151i 0.0800575 + 0.371052i
\(583\) 12.0491i 0.499023i
\(584\) 30.1130 + 4.48634i 1.24608 + 0.185646i
\(585\) 10.1740i 0.420645i
\(586\) 33.0496 7.13072i 1.36527 0.294567i
\(587\) −8.89264 + 8.89264i −0.367038 + 0.367038i −0.866396 0.499358i \(-0.833569\pi\)
0.499358 + 0.866396i \(0.333569\pi\)
\(588\) −6.59717 + 17.5058i −0.272063 + 0.721928i
\(589\) 3.87902 + 3.87902i 0.159832 + 0.159832i
\(590\) 18.0111 27.9215i 0.741506 1.14951i
\(591\) 6.13796 0.252482
\(592\) −1.93850 29.9636i −0.0796719 1.23150i
\(593\) 47.5658 1.95330 0.976648 0.214848i \(-0.0689255\pi\)
0.976648 + 0.214848i \(0.0689255\pi\)
\(594\) 15.3728 23.8315i 0.630756 0.977819i
\(595\) 9.42416 + 9.42416i 0.386353 + 0.386353i
\(596\) 6.90611 + 2.60260i 0.282885 + 0.106607i
\(597\) 12.2676 12.2676i 0.502078 0.502078i
\(598\) 15.3950 3.32159i 0.629547 0.135830i
\(599\) 24.1212i 0.985564i 0.870153 + 0.492782i \(0.164020\pi\)
−0.870153 + 0.492782i \(0.835980\pi\)
\(600\) −11.4125 15.4084i −0.465915 0.629046i
\(601\) 31.2134i 1.27322i −0.771185 0.636611i \(-0.780336\pi\)
0.771185 0.636611i \(-0.219664\pi\)
\(602\) −1.17862 5.46270i −0.0480370 0.222643i
\(603\) 0.351319 0.351319i 0.0143068 0.0143068i
\(604\) −28.7381 + 13.0064i −1.16934 + 0.529224i
\(605\) 3.50692 + 3.50692i 0.142577 + 0.142577i
\(606\) 8.41639 + 5.42911i 0.341893 + 0.220543i
\(607\) 32.2613 1.30945 0.654723 0.755869i \(-0.272785\pi\)
0.654723 + 0.755869i \(0.272785\pi\)
\(608\) −4.94170 2.75311i −0.200412 0.111653i
\(609\) −5.71493 −0.231581
\(610\) 27.2766 + 17.5952i 1.10440 + 0.712408i
\(611\) 16.4605 + 16.4605i 0.665919 + 0.665919i
\(612\) −15.9257 + 7.20772i −0.643757 + 0.291355i
\(613\) −6.65388 + 6.65388i −0.268748 + 0.268748i −0.828595 0.559848i \(-0.810860\pi\)
0.559848 + 0.828595i \(0.310860\pi\)
\(614\) 1.19914 + 5.55779i 0.0483934 + 0.224294i
\(615\) 18.7162i 0.754709i
\(616\) −4.18017 + 3.09612i −0.168424 + 0.124746i
\(617\) 9.85131i 0.396599i −0.980141 0.198299i \(-0.936458\pi\)
0.980141 0.198299i \(-0.0635419\pi\)
\(618\) −14.0648 + 3.03459i −0.565768 + 0.122069i
\(619\) −6.57288 + 6.57288i −0.264186 + 0.264186i −0.826752 0.562566i \(-0.809814\pi\)
0.562566 + 0.826752i \(0.309814\pi\)
\(620\) 32.2681 + 12.1604i 1.29592 + 0.488374i
\(621\) 14.7023 + 14.7023i 0.589985 + 0.589985i
\(622\) −19.8795 + 30.8179i −0.797096 + 1.23569i
\(623\) 4.85281 0.194424
\(624\) −12.6471 11.1101i −0.506288 0.444760i
\(625\) 25.5932 1.02373
\(626\) −8.74552 + 13.5576i −0.349541 + 0.541871i
\(627\) 3.48494 + 3.48494i 0.139175 + 0.139175i
\(628\) 1.90633 5.05851i 0.0760708 0.201857i
\(629\) 43.4039 43.4039i 1.73063 1.73063i
\(630\) 2.40835 0.519620i 0.0959508 0.0207022i
\(631\) 27.2487i 1.08475i −0.840136 0.542376i \(-0.817525\pi\)
0.840136 0.542376i \(-0.182475\pi\)
\(632\) 3.06468 20.5706i 0.121906 0.818253i
\(633\) 15.7617i 0.626473i
\(634\) −4.73640 21.9523i −0.188106 0.871838i
\(635\) 19.6763 19.6763i 0.780829 0.780829i
\(636\) −3.89333 8.60243i −0.154381 0.341109i
\(637\) 14.4142 + 14.4142i 0.571113 + 0.571113i
\(638\) 33.4246 + 21.5610i 1.32329 + 0.853608i
\(639\) −9.07881 −0.359152
\(640\) −35.4356 2.95830i −1.40072 0.116937i
\(641\) −36.8300 −1.45470 −0.727349 0.686268i \(-0.759248\pi\)
−0.727349 + 0.686268i \(0.759248\pi\)
\(642\) 19.2414 + 12.4120i 0.759399 + 0.489861i
\(643\) −9.87365 9.87365i −0.389379 0.389379i 0.485087 0.874466i \(-0.338788\pi\)
−0.874466 + 0.485087i \(0.838788\pi\)
\(644\) −1.57254 3.47457i −0.0619666 0.136917i
\(645\) −23.5339 + 23.5339i −0.926645 + 0.926645i
\(646\) −2.43896 11.3041i −0.0959595 0.444755i
\(647\) 31.5428i 1.24007i −0.784572 0.620037i \(-0.787117\pi\)
0.784572 0.620037i \(-0.212883\pi\)
\(648\) 1.93843 13.0110i 0.0761486 0.511121i
\(649\) 26.5114i 1.04066i
\(650\) −20.4236 + 4.40657i −0.801081 + 0.172840i
\(651\) 2.79537 2.79537i 0.109559 0.109559i
\(652\) 2.74136 7.27430i 0.107360 0.284884i
\(653\) −4.98004 4.98004i −0.194884 0.194884i 0.602919 0.797803i \(-0.294004\pi\)
−0.797803 + 0.602919i \(0.794004\pi\)
\(654\) 19.4487 30.1501i 0.760505 1.17896i
\(655\) −48.6412 −1.90057
\(656\) −12.8775 11.3125i −0.502783 0.441681i
\(657\) 11.5055 0.448872
\(658\) 3.05574 4.73712i 0.119125 0.184672i
\(659\) 21.6158 + 21.6158i 0.842033 + 0.842033i 0.989123 0.147090i \(-0.0469906\pi\)
−0.147090 + 0.989123i \(0.546991\pi\)
\(660\) 28.9899 + 10.9250i 1.12843 + 0.425255i
\(661\) 31.1470 31.1470i 1.21148 1.21148i 0.240935 0.970541i \(-0.422546\pi\)
0.970541 0.240935i \(-0.0774540\pi\)
\(662\) 13.7837 2.97395i 0.535719 0.115586i
\(663\) 34.4135i 1.33651i
\(664\) −19.2990 + 14.2942i −0.748948 + 0.554722i
\(665\) 1.62988i 0.0632040i
\(666\) −2.39316 11.0919i −0.0927332 0.429802i
\(667\) −20.6206 + 20.6206i −0.798432 + 0.798432i
\(668\) −3.65088 + 1.65233i −0.141257 + 0.0639307i
\(669\) −22.8755 22.8755i −0.884416 0.884416i
\(670\) 1.73619 + 1.11996i 0.0670750 + 0.0432677i
\(671\) −25.8992 −0.999826
\(672\) −1.98400 + 3.56117i −0.0765343 + 0.137375i
\(673\) 10.9006 0.420187 0.210093 0.977681i \(-0.432623\pi\)
0.210093 + 0.977681i \(0.432623\pi\)
\(674\) 26.5522 + 17.1279i 1.02275 + 0.659741i
\(675\) −19.5048 19.5048i −0.750740 0.750740i
\(676\) 6.97569 3.15709i 0.268296 0.121427i
\(677\) −14.9245 + 14.9245i −0.573594 + 0.573594i −0.933131 0.359537i \(-0.882935\pi\)
0.359537 + 0.933131i \(0.382935\pi\)
\(678\) −3.01638 13.9804i −0.115844 0.536914i
\(679\) 2.41640i 0.0927330i
\(680\) −43.2660 58.4147i −1.65917 2.24010i
\(681\) 11.4572i 0.439041i
\(682\) −26.8953 + 5.80289i −1.02988 + 0.222204i
\(683\) 22.8976 22.8976i 0.876154 0.876154i −0.116980 0.993134i \(-0.537321\pi\)
0.993134 + 0.116980i \(0.0373215\pi\)
\(684\) −2.00042 0.753871i −0.0764881 0.0288250i
\(685\) −28.0254 28.0254i −1.07079 1.07079i
\(686\) 5.45866 8.46221i 0.208413 0.323089i
\(687\) −33.3098 −1.27085
\(688\) 1.96782 + 30.4168i 0.0750223 + 1.15963i
\(689\) −10.2890 −0.391978
\(690\) −12.3123 + 19.0870i −0.468721 + 0.726628i
\(691\) 28.7834 + 28.7834i 1.09497 + 1.09497i 0.994989 + 0.0999813i \(0.0318783\pi\)
0.0999813 + 0.994989i \(0.468122\pi\)
\(692\) 6.43886 17.0858i 0.244769 0.649503i
\(693\) −1.39005 + 1.39005i −0.0528037 + 0.0528037i
\(694\) 45.6290 9.84483i 1.73205 0.373705i
\(695\) 44.7782i 1.69854i
\(696\) 30.8302 + 4.59319i 1.16862 + 0.174105i
\(697\) 35.0406i 1.32726i
\(698\) −7.42512 34.4141i −0.281045 1.30259i
\(699\) 12.2846 12.2846i 0.464645 0.464645i
\(700\) 2.08620 + 4.60952i 0.0788509 + 0.174223i
\(701\) −0.585300 0.585300i −0.0221065 0.0221065i 0.695967 0.718074i \(-0.254976\pi\)
−0.718074 + 0.695967i \(0.754976\pi\)
\(702\) −20.3502 13.1272i −0.768068 0.495453i
\(703\) 7.50657 0.283116
\(704\) 25.0391 13.3429i 0.943697 0.502880i
\(705\) −33.5724 −1.26441
\(706\) −0.228814 0.147599i −0.00861152 0.00555498i
\(707\) −1.86875 1.86875i −0.0702816 0.0702816i
\(708\) 8.56642 + 18.9278i 0.321946 + 0.711349i
\(709\) −9.30375 + 9.30375i −0.349410 + 0.349410i −0.859890 0.510480i \(-0.829468\pi\)
0.510480 + 0.859890i \(0.329468\pi\)
\(710\) −7.96243 36.9044i −0.298825 1.38500i
\(711\) 7.85954i 0.294756i
\(712\) −26.1794 3.90029i −0.981113 0.146170i
\(713\) 20.1725i 0.755465i
\(714\) −8.14618 + 1.75760i −0.304863 + 0.0657767i
\(715\) 23.8702 23.8702i 0.892693 0.892693i
\(716\) −13.5535 + 35.9648i −0.506519 + 1.34407i
\(717\) −9.92633 9.92633i −0.370706 0.370706i
\(718\) −0.510229 + 0.790975i −0.0190416 + 0.0295189i
\(719\) −19.6784 −0.733880 −0.366940 0.930245i \(-0.619594\pi\)
−0.366940 + 0.930245i \(0.619594\pi\)
\(720\) −13.4099 + 0.867554i −0.499757 + 0.0323318i
\(721\) 3.79669 0.141396
\(722\) 0.766601 1.18841i 0.0285300 0.0442281i
\(723\) −11.8663 11.8663i −0.441311 0.441311i
\(724\) −0.175973 0.0663165i −0.00654000 0.00246463i
\(725\) 27.3562 27.3562i 1.01598 1.01598i
\(726\) −3.03136 + 0.654040i −0.112504 + 0.0242737i
\(727\) 2.04226i 0.0757432i 0.999283 + 0.0378716i \(0.0120578\pi\)
−0.999283 + 0.0378716i \(0.987942\pi\)
\(728\) 2.64384 + 3.56953i 0.0979871 + 0.132295i
\(729\) 28.5437i 1.05717i
\(730\) 10.0907 + 46.7685i 0.373474 + 1.73098i
\(731\) −44.0603 + 44.0603i −1.62963 + 1.62963i
\(732\) −18.4906 + 8.36859i −0.683434 + 0.309312i
\(733\) 28.0186 + 28.0186i 1.03489 + 1.03489i 0.999369 + 0.0355234i \(0.0113098\pi\)
0.0355234 + 0.999369i \(0.488690\pi\)
\(734\) 5.62949 + 3.63138i 0.207788 + 0.134037i
\(735\) −29.3990 −1.08440
\(736\) 5.69076 + 20.0081i 0.209764 + 0.737507i
\(737\) −1.64852 −0.0607239
\(738\) −5.44333 3.51130i −0.200372 0.129253i
\(739\) 12.9329 + 12.9329i 0.475746 + 0.475746i 0.903768 0.428022i \(-0.140789\pi\)
−0.428022 + 0.903768i \(0.640789\pi\)
\(740\) 42.9884 19.4559i 1.58029 0.715214i
\(741\) 2.97585 2.97585i 0.109321 0.109321i
\(742\) 0.525490 + 2.43555i 0.0192913 + 0.0894118i
\(743\) 24.3241i 0.892363i −0.894943 0.446181i \(-0.852784\pi\)
0.894943 0.446181i \(-0.147216\pi\)
\(744\) −17.3268 + 12.8334i −0.635232 + 0.470496i
\(745\) 11.5980i 0.424918i
\(746\) −11.7874 + 2.54323i −0.431568 + 0.0931144i
\(747\) −6.41760 + 6.41760i −0.234808 + 0.234808i
\(748\) 54.2751 + 20.4539i 1.98449 + 0.747868i
\(749\) −4.27232 4.27232i −0.156107 0.156107i
\(750\) −0.407172 + 0.631212i −0.0148678 + 0.0230486i
\(751\) −1.33891 −0.0488575 −0.0244288 0.999702i \(-0.507777\pi\)
−0.0244288 + 0.999702i \(0.507777\pi\)
\(752\) −20.2921 + 23.0993i −0.739976 + 0.842344i
\(753\) 31.6833 1.15460
\(754\) 18.4113 28.5419i 0.670501 1.03943i
\(755\) −35.0526 35.0526i −1.27569 1.27569i
\(756\) −2.06804 + 5.48763i −0.0752140 + 0.199583i
\(757\) −31.7159 + 31.7159i −1.15273 + 1.15273i −0.166731 + 0.986002i \(0.553321\pi\)
−0.986002 + 0.166731i \(0.946679\pi\)
\(758\) 37.6193 8.11668i 1.36640 0.294811i
\(759\) 18.1231i 0.657826i
\(760\) 1.30996 8.79268i 0.0475174 0.318944i
\(761\) 2.84907i 0.103279i 0.998666 + 0.0516394i \(0.0164446\pi\)
−0.998666 + 0.0516394i \(0.983555\pi\)
\(762\) 3.66962 + 17.0080i 0.132936 + 0.616136i
\(763\) −6.69443 + 6.69443i −0.242355 + 0.242355i
\(764\) 15.5904 + 34.4475i 0.564042 + 1.24627i
\(765\) −19.4249 19.4249i −0.702309 0.702309i
\(766\) −32.7418 21.1205i −1.18301 0.763116i
\(767\) 22.6386 0.817433
\(768\) 13.5652 17.6168i 0.489492 0.635692i
\(769\) 42.0931 1.51792 0.758958 0.651139i \(-0.225709\pi\)
0.758958 + 0.651139i \(0.225709\pi\)
\(770\) −6.86954 4.43129i −0.247561 0.159693i
\(771\) −8.48371 8.48371i −0.305533 0.305533i
\(772\) −1.81789 4.01667i −0.0654271 0.144563i
\(773\) 13.6204 13.6204i 0.489891 0.489891i −0.418381 0.908272i \(-0.637402\pi\)
0.908272 + 0.418381i \(0.137402\pi\)
\(774\) 2.42936 + 11.2596i 0.0873214 + 0.404719i
\(775\) 26.7617i 0.961309i
\(776\) −1.94211 + 13.0357i −0.0697176 + 0.467955i
\(777\) 5.40952i 0.194065i
\(778\) 3.90254 0.842006i 0.139913 0.0301874i
\(779\) 3.03008 3.03008i 0.108564 0.108564i
\(780\) 9.32906 24.7550i 0.334034 0.886371i
\(781\) 21.3005 + 21.3005i 0.762193 + 0.762193i
\(782\) −23.0512 + 35.7348i −0.824310 + 1.27787i
\(783\) 44.8408 1.60248
\(784\) −17.7695 + 20.2278i −0.634626 + 0.722420i
\(785\) 8.49518 0.303206
\(786\) 16.4868 25.5583i 0.588063 0.911636i
\(787\) 27.0243 + 27.0243i 0.963312 + 0.963312i 0.999350 0.0360382i \(-0.0114738\pi\)
−0.0360382 + 0.999350i \(0.511474\pi\)
\(788\) 8.26633 + 3.11521i 0.294476 + 0.110975i
\(789\) 12.2904 12.2904i 0.437551 0.437551i
\(790\) 31.9482 6.89309i 1.13667 0.245245i
\(791\) 3.77391i 0.134185i
\(792\) 8.61610 6.38168i 0.306160 0.226763i
\(793\) 22.1158i 0.785355i
\(794\) 7.71383 + 35.7522i 0.273753 + 1.26880i
\(795\) 10.4926 10.4926i 0.372134 0.372134i
\(796\) 22.7476 10.2952i 0.806266 0.364904i
\(797\) 28.7589 + 28.7589i 1.01869 + 1.01869i 0.999822 + 0.0188715i \(0.00600735\pi\)
0.0188715 + 0.999822i \(0.493993\pi\)
\(798\) −0.856414 0.552442i −0.0303167 0.0195562i
\(799\) −62.8547 −2.22364
\(800\) −7.54962 26.5436i −0.266919 0.938458i
\(801\) −10.0025 −0.353422
\(802\) −43.8978 28.3169i −1.55009 0.999905i
\(803\) −26.9939 26.9939i −0.952595 0.952595i
\(804\) −1.17695 + 0.532672i −0.0415080 + 0.0187859i
\(805\) 4.23801 4.23801i 0.149370 0.149370i
\(806\) 4.95520 + 22.9664i 0.174539 + 0.808958i
\(807\) 5.59259i 0.196868i
\(808\) 8.57937 + 11.5833i 0.301821 + 0.407498i
\(809\) 40.9557i 1.43993i −0.694012 0.719964i \(-0.744158\pi\)
0.694012 0.719964i \(-0.255842\pi\)
\(810\) 20.2074 4.35992i 0.710016 0.153192i
\(811\) −10.7575 + 10.7575i −0.377746 + 0.377746i −0.870288 0.492543i \(-0.836068\pi\)
0.492543 + 0.870288i \(0.336068\pi\)
\(812\) −7.69660 2.90051i −0.270098 0.101788i
\(813\) −25.6823 25.6823i −0.900718 0.900718i
\(814\) −20.4088 + 31.6383i −0.715326 + 1.10892i
\(815\) 12.2163 0.427920
\(816\) 45.3586 2.93448i 1.58787 0.102727i
\(817\) −7.62009 −0.266593
\(818\) −15.9698 + 24.7569i −0.558371 + 0.865606i
\(819\) 1.18699 + 1.18699i 0.0414769 + 0.0414769i
\(820\) 9.49905 25.2061i 0.331721 0.880234i
\(821\) −29.4421 + 29.4421i −1.02753 + 1.02753i −0.0279247 + 0.999610i \(0.508890\pi\)
−0.999610 + 0.0279247i \(0.991110\pi\)
\(822\) 24.2249 5.22673i 0.844942 0.182303i
\(823\) 22.2738i 0.776416i 0.921572 + 0.388208i \(0.126906\pi\)
−0.921572 + 0.388208i \(0.873094\pi\)
\(824\) −20.4819 3.05147i −0.713522 0.106303i
\(825\) 24.0429i 0.837066i
\(826\) −1.15622 5.35889i −0.0402302 0.186460i
\(827\) 31.3520 31.3520i 1.09022 1.09022i 0.0947117 0.995505i \(-0.469807\pi\)
0.995505 0.0947117i \(-0.0301929\pi\)
\(828\) 3.24129 + 7.16172i 0.112643 + 0.248887i
\(829\) 1.27686 + 1.27686i 0.0443473 + 0.0443473i 0.728933 0.684585i \(-0.240017\pi\)
−0.684585 + 0.728933i \(0.740017\pi\)
\(830\) −31.7153 20.4584i −1.10085 0.710121i
\(831\) 2.18923 0.0759437
\(832\) −11.3938 21.3814i −0.395008 0.741265i
\(833\) −55.0411 −1.90706
\(834\) −23.5286 15.1774i −0.814728 0.525551i
\(835\) −4.45307 4.45307i −0.154105 0.154105i
\(836\) 2.92464 + 6.46207i 0.101151 + 0.223495i
\(837\) −21.9332 + 21.9332i −0.758122 + 0.758122i
\(838\) 7.04448 + 32.6499i 0.243347 + 1.12787i
\(839\) 45.4357i 1.56861i 0.620372 + 0.784307i \(0.286981\pi\)
−0.620372 + 0.784307i \(0.713019\pi\)
\(840\) −6.33633 0.944009i −0.218624 0.0325714i
\(841\) 33.8909i 1.16865i
\(842\) 24.9336 5.37964i 0.859270 0.185395i
\(843\) 3.63467 3.63467i 0.125185 0.125185i
\(844\) −7.99958 + 21.2272i −0.275357 + 0.730670i
\(845\) 8.50842 + 8.50842i 0.292699 + 0.292699i
\(846\) −6.29845 + 9.76407i −0.216545 + 0.335696i
\(847\) 0.818295 0.0281169
\(848\) −0.877353 13.5614i −0.0301284 0.465699i
\(849\) −20.0504 −0.688128
\(850\) 30.5808 47.4074i 1.04891 1.62606i
\(851\) −19.5186 19.5186i −0.669089 0.669089i
\(852\) 22.0901 + 8.32478i 0.756795 + 0.285202i
\(853\) −19.3036 + 19.3036i −0.660943 + 0.660943i −0.955602 0.294660i \(-0.904794\pi\)
0.294660 + 0.955602i \(0.404794\pi\)
\(854\) 5.23513 1.12952i 0.179142 0.0386515i
\(855\) 3.35948i 0.114892i
\(856\) 19.6140 + 26.4815i 0.670394 + 0.905120i
\(857\) 19.2716i 0.658305i 0.944277 + 0.329152i \(0.106763\pi\)
−0.944277 + 0.329152i \(0.893237\pi\)
\(858\) 4.45178 + 20.6332i 0.151981 + 0.704405i
\(859\) 24.6106 24.6106i 0.839702 0.839702i −0.149118 0.988819i \(-0.547643\pi\)
0.988819 + 0.149118i \(0.0476434\pi\)
\(860\) −43.6385 + 19.7501i −1.48806 + 0.673474i
\(861\) −2.18359 2.18359i −0.0744165 0.0744165i
\(862\) −14.9343 9.63356i −0.508664 0.328120i
\(863\) −6.90091 −0.234910 −0.117455 0.993078i \(-0.537474\pi\)
−0.117455 + 0.993078i \(0.537474\pi\)
\(864\) 15.5669 27.9419i 0.529598 0.950602i
\(865\) 28.6935 0.975610
\(866\) −15.5201 10.0115i −0.527395 0.340203i
\(867\) 48.9997 + 48.9997i 1.66412 + 1.66412i
\(868\) 5.18341 2.34594i 0.175937 0.0796263i
\(869\) −18.4399 + 18.4399i −0.625531 + 0.625531i
\(870\) 10.3310 + 47.8825i 0.350255 + 1.62337i
\(871\) 1.40770i 0.0476981i
\(872\) 41.4948 30.7339i 1.40519 1.04078i
\(873\) 4.98065i 0.168569i
\(874\) −5.08343 + 1.09679i −0.171950 + 0.0370995i
\(875\) 0.140152 0.140152i 0.00473802 0.00473802i
\(876\) −27.9946 10.5499i −0.945849 0.356448i
\(877\) 18.6196 + 18.6196i 0.628740 + 0.628740i 0.947751 0.319011i \(-0.103351\pi\)
−0.319011 + 0.947751i \(0.603351\pi\)
\(878\) −2.72786 + 4.22882i −0.0920608 + 0.142716i
\(879\) −33.2228 −1.12058
\(880\) 33.4974 + 29.4266i 1.12920 + 0.991969i
\(881\) 5.78877 0.195029 0.0975143 0.995234i \(-0.468911\pi\)
0.0975143 + 0.995234i \(0.468911\pi\)
\(882\) −5.51548 + 8.55028i −0.185716 + 0.287903i
\(883\) 0.739375 + 0.739375i 0.0248819 + 0.0248819i 0.719438 0.694556i \(-0.244399\pi\)
−0.694556 + 0.719438i \(0.744399\pi\)
\(884\) 17.4660 46.3465i 0.587444 1.55880i
\(885\) −23.0866 + 23.0866i −0.776049 + 0.776049i
\(886\) −39.0987 + 8.43586i −1.31355 + 0.283408i
\(887\) 34.9584i 1.17379i −0.809663 0.586895i \(-0.800350\pi\)
0.809663 0.586895i \(-0.199650\pi\)
\(888\) −4.34773 + 29.1826i −0.145900 + 0.979305i
\(889\) 4.59121i 0.153984i
\(890\) −8.77256 40.6592i −0.294057 1.36290i
\(891\) −11.6633 + 11.6633i −0.390737 + 0.390737i
\(892\) −19.1976 42.4177i −0.642783 1.42025i
\(893\) −5.43526 5.43526i −0.181884 0.181884i
\(894\) −6.09413 3.93110i −0.203818 0.131476i
\(895\) −60.3986 −2.01890
\(896\) −4.47936 + 3.78908i −0.149645 + 0.126584i
\(897\) −15.4756 −0.516716
\(898\) −6.80505 4.38969i −0.227087 0.146486i
\(899\) −30.7621 30.7621i −1.02597 1.02597i
\(900\) −4.30004 9.50106i −0.143335 0.316702i
\(901\) 19.6443 19.6443i 0.654448 0.654448i
\(902\) 4.53290 + 21.0092i 0.150929 + 0.699529i
\(903\) 5.49132i 0.182740i
\(904\) 3.03317 20.3591i 0.100882 0.677132i
\(905\) 0.295527i 0.00982364i
\(906\) 30.2992 6.53730i 1.00662 0.217187i
\(907\) 10.2520 10.2520i 0.340411 0.340411i −0.516111 0.856522i \(-0.672621\pi\)
0.856522 + 0.516111i \(0.172621\pi\)
\(908\) −5.81490 + 15.4301i −0.192974 + 0.512064i
\(909\) 3.85184 + 3.85184i 0.127757 + 0.127757i
\(910\) −3.78396 + 5.86603i −0.125437 + 0.194457i
\(911\) 48.1075 1.59387 0.796935 0.604064i \(-0.206453\pi\)
0.796935 + 0.604064i \(0.206453\pi\)
\(912\) 4.17607 + 3.66856i 0.138284 + 0.121478i
\(913\) 30.1137 0.996618
\(914\) −17.9032 + 27.7542i −0.592186 + 0.918028i
\(915\) −22.5535 22.5535i −0.745595 0.745595i
\(916\) −44.8601 16.9058i −1.48222 0.558582i
\(917\) −5.67490 + 5.67490i −0.187402 + 0.187402i
\(918\) 63.9170 13.7906i 2.10958 0.455158i
\(919\) 45.3411i 1.49567i −0.663887 0.747833i \(-0.731094\pi\)
0.663887 0.747833i \(-0.268906\pi\)
\(920\) −26.2689 + 19.4566i −0.866060 + 0.641464i
\(921\) 5.58692i 0.184095i
\(922\) 3.01692 + 13.9829i 0.0993568 + 0.460501i
\(923\) 18.1889 18.1889i 0.598696 0.598696i
\(924\) 4.65681 2.10760i 0.153198 0.0693350i
\(925\) 25.8943 + 25.8943i 0.851398 + 0.851398i
\(926\) −16.4663 10.6218i −0.541118 0.349056i
\(927\) −7.82567 −0.257029
\(928\) 39.1895 + 21.8332i 1.28646 + 0.716711i
\(929\) −48.8327 −1.60215 −0.801075 0.598565i \(-0.795738\pi\)
−0.801075 + 0.598565i \(0.795738\pi\)
\(930\) −28.4742 18.3677i −0.933707 0.602300i
\(931\) −4.75959 4.75959i −0.155989 0.155989i
\(932\) 22.7791 10.3095i 0.746155 0.337699i
\(933\) 25.4816 25.4816i 0.834229 0.834229i
\(934\) 1.08644 + 5.03543i 0.0355493 + 0.164764i
\(935\) 91.1487i 2.98088i
\(936\) −5.44943 7.35745i −0.178120 0.240486i
\(937\) 43.1736i 1.41042i 0.708998 + 0.705211i \(0.249148\pi\)
−0.708998 + 0.705211i \(0.750852\pi\)
\(938\) 0.333223 0.0718957i 0.0108801 0.00234748i
\(939\) 11.2100 11.2100i 0.365825 0.365825i
\(940\) −45.2138 17.0391i −1.47471 0.555754i
\(941\) −11.9634 11.9634i −0.389995 0.389995i 0.484691 0.874686i \(-0.338932\pi\)
−0.874686 + 0.484691i \(0.838932\pi\)
\(942\) −2.87941 + 4.46376i −0.0938163 + 0.145437i
\(943\) −15.7576 −0.513139
\(944\) 1.93042 + 29.8388i 0.0628299 + 0.971169i
\(945\) −9.21584 −0.299791
\(946\) 20.7174 32.1168i 0.673580 1.04421i
\(947\) 24.5656 + 24.5656i 0.798274 + 0.798274i 0.982823 0.184549i \(-0.0590824\pi\)
−0.184549 + 0.982823i \(0.559082\pi\)
\(948\) −7.20678 + 19.1234i −0.234065 + 0.621101i
\(949\) −23.0506 + 23.0506i −0.748255 + 0.748255i
\(950\) 6.74390 1.45505i 0.218801 0.0472082i
\(951\) 22.0674i 0.715583i
\(952\) −11.8629 1.76738i −0.384480 0.0572812i
\(953\) 16.8701i 0.546476i −0.961946 0.273238i \(-0.911905\pi\)
0.961946 0.273238i \(-0.0880947\pi\)
\(954\) −1.08313 5.02011i −0.0350677 0.162532i
\(955\) −42.0165 + 42.0165i −1.35962 + 1.35962i
\(956\) −8.33040 18.4063i −0.269424 0.595301i
\(957\) −27.6369 27.6369i −0.893373 0.893373i
\(958\) −1.25064 0.806740i −0.0404062 0.0260646i
\(959\) −6.53937 −0.211167
\(960\) 33.4238 + 10.1853i 1.07875 + 0.328728i
\(961\) −0.906376 −0.0292379
\(962\) 27.0166 + 17.4274i 0.871050 + 0.561883i
\(963\) 8.80603 + 8.80603i 0.283770 + 0.283770i
\(964\) −9.95843 22.0034i −0.320739 0.708683i
\(965\) 4.89923 4.89923i 0.157712 0.157712i
\(966\) 0.790389 + 3.66331i 0.0254304 + 0.117865i
\(967\) 28.5983i 0.919660i −0.888007 0.459830i \(-0.847910\pi\)
0.888007 0.459830i \(-0.152090\pi\)
\(968\) −4.41444 0.657679i −0.141885 0.0211386i
\(969\) 11.3634i 0.365044i
\(970\) −20.2458 + 4.36820i −0.650053 + 0.140254i
\(971\) −32.7772 + 32.7772i −1.05187 + 1.05187i −0.0532921 + 0.998579i \(0.516971\pi\)
−0.998579 + 0.0532921i \(0.983029\pi\)
\(972\) 7.40546 19.6507i 0.237530 0.630295i
\(973\) 5.22421 + 5.22421i 0.167481 + 0.167481i
\(974\) −13.8965 + 21.5428i −0.445273 + 0.690277i
\(975\) 20.5307 0.657508
\(976\) −29.1497 + 1.88584i −0.933058 + 0.0603643i
\(977\) −15.8114 −0.505851 −0.252926 0.967486i \(-0.581393\pi\)
−0.252926 + 0.967486i \(0.581393\pi\)
\(978\) −4.14069 + 6.41904i −0.132405 + 0.205258i
\(979\) 23.4677 + 23.4677i 0.750032 + 0.750032i
\(980\) −39.5932 14.9209i −1.26476 0.476632i
\(981\) 13.7984 13.7984i 0.440551 0.440551i
\(982\) −48.4601 + 10.4557i −1.54642 + 0.333654i
\(983\) 22.0397i 0.702958i 0.936196 + 0.351479i \(0.114321\pi\)
−0.936196 + 0.351479i \(0.885679\pi\)
\(984\) 10.0248 + 13.5348i 0.319578 + 0.431472i
\(985\) 13.8823i 0.442328i
\(986\) 19.3419 + 89.6460i 0.615970 + 2.85491i
\(987\) −3.91685 + 3.91685i −0.124675 + 0.124675i
\(988\) 5.51808 2.49740i 0.175554 0.0794530i
\(989\) 19.8138 + 19.8138i 0.630041 + 0.630041i
\(990\) 14.1594 + 9.13370i 0.450014 + 0.290288i
\(991\) −13.5824 −0.431458 −0.215729 0.976453i \(-0.569213\pi\)
−0.215729 + 0.976453i \(0.569213\pi\)
\(992\) −29.8483 + 8.48957i −0.947686 + 0.269544i
\(993\) −13.8559 −0.439705
\(994\) −5.23455 3.37662i −0.166030 0.107100i
\(995\) 27.7458 + 27.7458i 0.879600 + 0.879600i
\(996\) 21.4996 9.73039i 0.681240 0.308319i
\(997\) 3.18735 3.18735i 0.100945 0.100945i −0.654831 0.755775i \(-0.727260\pi\)
0.755775 + 0.654831i \(0.227260\pi\)
\(998\) −0.162928 0.755139i −0.00515738 0.0239035i
\(999\) 42.4445i 1.34288i
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 304.2.k.b.77.8 68
4.3 odd 2 1216.2.k.b.913.12 68
16.5 even 4 inner 304.2.k.b.229.8 yes 68
16.11 odd 4 1216.2.k.b.305.12 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
304.2.k.b.77.8 68 1.1 even 1 trivial
304.2.k.b.229.8 yes 68 16.5 even 4 inner
1216.2.k.b.305.12 68 16.11 odd 4
1216.2.k.b.913.12 68 4.3 odd 2