Properties

Label 77.2.f.a.64.1
Level $77$
Weight $2$
Character 77.64
Analytic conductor $0.615$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [77,2,Mod(15,77)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(77, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("77.15");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.f (of order \(5\), 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: \(0.614848095564\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 64.1
Root \(-0.628998 - 0.456994i\) of defining polynomial
Character \(\chi\) \(=\) 77.64
Dual form 77.2.f.a.71.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.240256 + 0.739431i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(-0.0687611 - 0.211625i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} +O(q^{10})\) \(q+(-0.240256 + 0.739431i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(-0.0687611 - 0.211625i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} +0.173002 q^{10} +(0.660531 - 3.25018i) q^{11} -0.862478 q^{12} +(2.01774 - 6.20997i) q^{13} +(-0.628998 + 0.456994i) q^{14} +(0.111258 + 0.0808336i) q^{15} +(0.228211 + 0.702362i) q^{16} +(-1.33947 - 4.12246i) q^{17} +(-1.64674 - 1.19643i) q^{18} +(-2.35829 + 1.71340i) q^{19} +(0.0959574 - 0.295327i) q^{20} -0.618034 q^{21} +(2.24459 + 1.26929i) q^{22} -3.89796 q^{23} +(0.504188 - 1.55173i) q^{24} +(4.00503 - 2.90982i) q^{25} +(4.10707 + 2.98396i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(0.431239 + 1.32722i) q^{28} +(3.05322 + 2.21829i) q^{29} +(-0.0865012 + 0.0628468i) q^{30} +(-2.12900 + 6.55238i) q^{31} -5.85410 q^{32} +(0.850433 + 1.86504i) q^{33} +3.37009 q^{34} +(0.0687611 - 0.211625i) q^{35} +(-2.95576 + 2.14748i) q^{36} +(4.57379 + 3.32305i) q^{37} +(-0.700347 - 2.15545i) q^{38} +(1.24703 + 3.83797i) q^{39} +(0.475243 + 0.345285i) q^{40} +(-1.08255 + 0.786521i) q^{41} +(0.148486 - 0.456994i) q^{42} -4.70820 q^{43} +(3.41175 - 3.12764i) q^{44} +0.582554 q^{45} +(0.936507 - 2.88227i) q^{46} +(-4.89094 + 3.55348i) q^{47} +(-0.369254 - 0.268279i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.18938 + 3.66055i) q^{50} +(2.16731 + 1.57464i) q^{51} +(7.37184 - 5.35596i) q^{52} +(-0.530865 + 1.63383i) q^{53} +2.69953 q^{54} +(-0.733239 + 0.0837016i) q^{55} -2.63996 q^{56} +(0.556717 - 1.71340i) q^{57} +(-2.37383 + 1.72469i) q^{58} +(7.71239 + 5.60338i) q^{59} +(0.0593050 + 0.182522i) q^{60} +(-2.97566 - 9.15813i) q^{61} +(-4.33353 - 3.14850i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(0.950059 - 2.92398i) q^{64} -1.45293 q^{65} +(-1.58339 + 0.180749i) q^{66} +1.27155 q^{67} +(1.86925 - 5.75297i) q^{68} +(1.94898 - 1.41602i) q^{69} +(0.139962 + 0.101688i) q^{70} +(-2.87670 - 8.85357i) q^{71} +(-2.13577 - 6.57324i) q^{72} +(-4.52169 - 3.28520i) q^{73} +(-3.55605 + 2.58362i) q^{74} +(-0.945459 + 2.90982i) q^{75} -4.06794 q^{76} +(2.44479 - 2.24120i) q^{77} -3.13752 q^{78} +(-1.39971 + 4.30785i) q^{79} +(0.132945 - 0.0965905i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-0.321489 - 0.989441i) q^{82} +(3.48688 + 10.7315i) q^{83} +(-0.697759 - 0.506952i) q^{84} +(-0.780313 + 0.566931i) q^{85} +(1.13117 - 3.48139i) q^{86} -2.33245 q^{87} +(3.63267 + 7.96663i) q^{88} +7.92157 q^{89} +(-0.139962 + 0.430759i) q^{90} +(5.28251 - 3.83797i) q^{91} +(-4.40079 - 3.19736i) q^{92} +(-1.31579 - 4.04959i) q^{93} +(-1.45248 - 4.47026i) q^{94} +(0.524757 + 0.381258i) q^{95} +(2.92705 - 2.12663i) q^{96} +(-2.79781 + 8.61078i) q^{97} -0.777484 q^{98} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20} + 4 q^{21} - q^{22} - 16 q^{23} + 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} + 7 q^{28} - 9 q^{29} + 14 q^{30} - 11 q^{31} - 20 q^{32} + 10 q^{33} - 24 q^{34} - 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} - 5 q^{39} - 16 q^{40} - 22 q^{41} - 3 q^{42} + 16 q^{43} + 29 q^{44} + 18 q^{45} + 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} - 34 q^{50} + 3 q^{51} + 21 q^{52} + 2 q^{53} + 4 q^{54} + 26 q^{55} - 18 q^{56} - 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} + 7 q^{61} - 5 q^{62} - 8 q^{63} + q^{64} + 24 q^{65} + 18 q^{66} - 30 q^{67} + 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} + 3 q^{72} + 3 q^{73} - 9 q^{74} + 5 q^{75} - 52 q^{76} - 5 q^{77} - 18 q^{78} - 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} + 23 q^{83} + 4 q^{84} - 10 q^{85} - 17 q^{86} + 12 q^{87} - 7 q^{88} - 34 q^{89} + 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} - 30 q^{94} + 24 q^{95} + 10 q^{96} + 30 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.240256 + 0.739431i −0.169887 + 0.522857i −0.999363 0.0356845i \(-0.988639\pi\)
0.829477 + 0.558542i \(0.188639\pi\)
\(3\) −0.500000 + 0.363271i −0.288675 + 0.209735i −0.722692 0.691170i \(-0.757096\pi\)
0.434017 + 0.900905i \(0.357096\pi\)
\(4\) 1.12900 + 0.820265i 0.564499 + 0.410133i
\(5\) −0.0687611 0.211625i −0.0307509 0.0946416i 0.934503 0.355955i \(-0.115844\pi\)
−0.965254 + 0.261313i \(0.915844\pi\)
\(6\) −0.148486 0.456994i −0.0606193 0.186567i
\(7\) 0.809017 + 0.587785i 0.305780 + 0.222162i
\(8\) −2.13577 + 1.55173i −0.755110 + 0.548620i
\(9\) −0.809017 + 2.48990i −0.269672 + 0.829966i
\(10\) 0.173002 0.0547082
\(11\) 0.660531 3.25018i 0.199158 0.979967i
\(12\) −0.862478 −0.248976
\(13\) 2.01774 6.20997i 0.559620 1.72233i −0.123798 0.992307i \(-0.539507\pi\)
0.683418 0.730027i \(-0.260493\pi\)
\(14\) −0.628998 + 0.456994i −0.168107 + 0.122137i
\(15\) 0.111258 + 0.0808336i 0.0287267 + 0.0208711i
\(16\) 0.228211 + 0.702362i 0.0570529 + 0.175591i
\(17\) −1.33947 4.12246i −0.324869 0.999844i −0.971500 0.237041i \(-0.923822\pi\)
0.646631 0.762803i \(-0.276178\pi\)
\(18\) −1.64674 1.19643i −0.388140 0.282000i
\(19\) −2.35829 + 1.71340i −0.541029 + 0.393080i −0.824467 0.565910i \(-0.808525\pi\)
0.283438 + 0.958991i \(0.408525\pi\)
\(20\) 0.0959574 0.295327i 0.0214567 0.0660370i
\(21\) −0.618034 −0.134866
\(22\) 2.24459 + 1.26929i 0.478549 + 0.270614i
\(23\) −3.89796 −0.812780 −0.406390 0.913700i \(-0.633213\pi\)
−0.406390 + 0.913700i \(0.633213\pi\)
\(24\) 0.504188 1.55173i 0.102917 0.316746i
\(25\) 4.00503 2.90982i 0.801006 0.581965i
\(26\) 4.10707 + 2.98396i 0.805463 + 0.585203i
\(27\) −1.07295 3.30220i −0.206489 0.635508i
\(28\) 0.431239 + 1.32722i 0.0814965 + 0.250820i
\(29\) 3.05322 + 2.21829i 0.566969 + 0.411927i 0.834003 0.551760i \(-0.186044\pi\)
−0.267034 + 0.963687i \(0.586044\pi\)
\(30\) −0.0865012 + 0.0628468i −0.0157929 + 0.0114742i
\(31\) −2.12900 + 6.55238i −0.382379 + 1.17684i 0.555984 + 0.831193i \(0.312341\pi\)
−0.938364 + 0.345650i \(0.887659\pi\)
\(32\) −5.85410 −1.03487
\(33\) 0.850433 + 1.86504i 0.148041 + 0.324662i
\(34\) 3.37009 0.577966
\(35\) 0.0687611 0.211625i 0.0116228 0.0357712i
\(36\) −2.95576 + 2.14748i −0.492626 + 0.357914i
\(37\) 4.57379 + 3.32305i 0.751926 + 0.546306i 0.896423 0.443199i \(-0.146156\pi\)
−0.144497 + 0.989505i \(0.546156\pi\)
\(38\) −0.700347 2.15545i −0.113611 0.349660i
\(39\) 1.24703 + 3.83797i 0.199685 + 0.614567i
\(40\) 0.475243 + 0.345285i 0.0751426 + 0.0545943i
\(41\) −1.08255 + 0.786521i −0.169066 + 0.122834i −0.669101 0.743171i \(-0.733321\pi\)
0.500035 + 0.866005i \(0.333321\pi\)
\(42\) 0.148486 0.456994i 0.0229119 0.0705157i
\(43\) −4.70820 −0.717994 −0.358997 0.933339i \(-0.616881\pi\)
−0.358997 + 0.933339i \(0.616881\pi\)
\(44\) 3.41175 3.12764i 0.514341 0.471510i
\(45\) 0.582554 0.0868420
\(46\) 0.936507 2.88227i 0.138080 0.424968i
\(47\) −4.89094 + 3.55348i −0.713417 + 0.518328i −0.884274 0.466968i \(-0.845346\pi\)
0.170857 + 0.985296i \(0.445346\pi\)
\(48\) −0.369254 0.268279i −0.0532972 0.0387227i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) 1.18938 + 3.66055i 0.168204 + 0.517679i
\(51\) 2.16731 + 1.57464i 0.303484 + 0.220494i
\(52\) 7.37184 5.35596i 1.02229 0.742738i
\(53\) −0.530865 + 1.63383i −0.0729199 + 0.224424i −0.980873 0.194646i \(-0.937644\pi\)
0.907954 + 0.419071i \(0.137644\pi\)
\(54\) 2.69953 0.367360
\(55\) −0.733239 + 0.0837016i −0.0988700 + 0.0112863i
\(56\) −2.63996 −0.352780
\(57\) 0.556717 1.71340i 0.0737389 0.226945i
\(58\) −2.37383 + 1.72469i −0.311699 + 0.226463i
\(59\) 7.71239 + 5.60338i 1.00407 + 0.729498i 0.962957 0.269657i \(-0.0869102\pi\)
0.0411113 + 0.999155i \(0.486910\pi\)
\(60\) 0.0593050 + 0.182522i 0.00765624 + 0.0235635i
\(61\) −2.97566 9.15813i −0.380994 1.17258i −0.939345 0.342974i \(-0.888566\pi\)
0.558351 0.829605i \(-0.311434\pi\)
\(62\) −4.33353 3.14850i −0.550359 0.399859i
\(63\) −2.11803 + 1.53884i −0.266847 + 0.193876i
\(64\) 0.950059 2.92398i 0.118757 0.365498i
\(65\) −1.45293 −0.180213
\(66\) −1.58339 + 0.180749i −0.194902 + 0.0222487i
\(67\) 1.27155 0.155344 0.0776722 0.996979i \(-0.475251\pi\)
0.0776722 + 0.996979i \(0.475251\pi\)
\(68\) 1.86925 5.75297i 0.226680 0.697650i
\(69\) 1.94898 1.41602i 0.234629 0.170468i
\(70\) 0.139962 + 0.101688i 0.0167287 + 0.0121541i
\(71\) −2.87670 8.85357i −0.341401 1.05072i −0.963482 0.267772i \(-0.913713\pi\)
0.622081 0.782953i \(-0.286287\pi\)
\(72\) −2.13577 6.57324i −0.251703 0.774663i
\(73\) −4.52169 3.28520i −0.529223 0.384503i 0.290844 0.956771i \(-0.406064\pi\)
−0.820067 + 0.572267i \(0.806064\pi\)
\(74\) −3.55605 + 2.58362i −0.413382 + 0.300340i
\(75\) −0.945459 + 2.90982i −0.109172 + 0.335997i
\(76\) −4.06794 −0.466625
\(77\) 2.44479 2.24120i 0.278610 0.255409i
\(78\) −3.13752 −0.355254
\(79\) −1.39971 + 4.30785i −0.157479 + 0.484671i −0.998404 0.0564813i \(-0.982012\pi\)
0.840924 + 0.541153i \(0.182012\pi\)
\(80\) 0.132945 0.0965905i 0.0148638 0.0107991i
\(81\) −4.61803 3.35520i −0.513115 0.372800i
\(82\) −0.321489 0.989441i −0.0355025 0.109265i
\(83\) 3.48688 + 10.7315i 0.382734 + 1.17793i 0.938111 + 0.346336i \(0.112574\pi\)
−0.555376 + 0.831599i \(0.687426\pi\)
\(84\) −0.697759 0.506952i −0.0761318 0.0553130i
\(85\) −0.780313 + 0.566931i −0.0846368 + 0.0614922i
\(86\) 1.13117 3.48139i 0.121978 0.375408i
\(87\) −2.33245 −0.250065
\(88\) 3.63267 + 7.96663i 0.387244 + 0.849245i
\(89\) 7.92157 0.839684 0.419842 0.907597i \(-0.362085\pi\)
0.419842 + 0.907597i \(0.362085\pi\)
\(90\) −0.139962 + 0.430759i −0.0147533 + 0.0454059i
\(91\) 5.28251 3.83797i 0.553758 0.402329i
\(92\) −4.40079 3.19736i −0.458814 0.333348i
\(93\) −1.31579 4.04959i −0.136441 0.419923i
\(94\) −1.45248 4.47026i −0.149811 0.461072i
\(95\) 0.524757 + 0.381258i 0.0538389 + 0.0391162i
\(96\) 2.92705 2.12663i 0.298741 0.217048i
\(97\) −2.79781 + 8.61078i −0.284075 + 0.874292i 0.702600 + 0.711585i \(0.252023\pi\)
−0.986674 + 0.162707i \(0.947977\pi\)
\(98\) −0.777484 −0.0785378
\(99\) 7.55825 + 4.27411i 0.759633 + 0.429564i
\(100\) 6.90849 0.690849
\(101\) −5.93627 + 18.2700i −0.590681 + 1.81793i −0.0155316 + 0.999879i \(0.504944\pi\)
−0.575149 + 0.818049i \(0.695056\pi\)
\(102\) −1.68505 + 1.22426i −0.166845 + 0.121220i
\(103\) −13.1371 9.54464i −1.29443 0.940461i −0.294549 0.955636i \(-0.595169\pi\)
−0.999885 + 0.0151755i \(0.995169\pi\)
\(104\) 5.32676 + 16.3941i 0.522332 + 1.60757i
\(105\) 0.0424967 + 0.130791i 0.00414726 + 0.0127639i
\(106\) −1.08057 0.785077i −0.104954 0.0762534i
\(107\) 4.36332 3.17014i 0.421818 0.306469i −0.356551 0.934276i \(-0.616047\pi\)
0.778369 + 0.627807i \(0.216047\pi\)
\(108\) 1.49732 4.60828i 0.144080 0.443432i
\(109\) 5.39901 0.517132 0.258566 0.965994i \(-0.416750\pi\)
0.258566 + 0.965994i \(0.416750\pi\)
\(110\) 0.114273 0.562290i 0.0108955 0.0536122i
\(111\) −3.49406 −0.331642
\(112\) −0.228211 + 0.702362i −0.0215640 + 0.0663670i
\(113\) 13.3457 9.69624i 1.25546 0.912145i 0.256935 0.966429i \(-0.417287\pi\)
0.998526 + 0.0542834i \(0.0172875\pi\)
\(114\) 1.13319 + 0.823308i 0.106133 + 0.0771098i
\(115\) 0.268028 + 0.824906i 0.0249937 + 0.0769228i
\(116\) 1.62749 + 5.00890i 0.151109 + 0.465065i
\(117\) 13.8298 + 10.0479i 1.27857 + 0.928932i
\(118\) −5.99626 + 4.35654i −0.552001 + 0.401052i
\(119\) 1.33947 4.12246i 0.122789 0.377906i
\(120\) −0.363054 −0.0331421
\(121\) −10.1274 4.29369i −0.920673 0.390336i
\(122\) 7.48673 0.677816
\(123\) 0.255556 0.786521i 0.0230427 0.0709182i
\(124\) −7.77832 + 5.65128i −0.698514 + 0.507500i
\(125\) −1.79128 1.30144i −0.160217 0.116404i
\(126\) −0.628998 1.93586i −0.0560356 0.172460i
\(127\) 0.617194 + 1.89953i 0.0547671 + 0.168556i 0.974699 0.223523i \(-0.0717559\pi\)
−0.919931 + 0.392079i \(0.871756\pi\)
\(128\) −7.53831 5.47690i −0.666299 0.484094i
\(129\) 2.35410 1.71036i 0.207267 0.150588i
\(130\) 0.349074 1.07434i 0.0306158 0.0942258i
\(131\) 1.37009 0.119706 0.0598528 0.998207i \(-0.480937\pi\)
0.0598528 + 0.998207i \(0.480937\pi\)
\(132\) −0.569693 + 2.80321i −0.0495854 + 0.243988i
\(133\) −2.91501 −0.252763
\(134\) −0.305497 + 0.940223i −0.0263909 + 0.0812229i
\(135\) −0.625051 + 0.454126i −0.0537958 + 0.0390849i
\(136\) 9.25776 + 6.72615i 0.793846 + 0.576763i
\(137\) 0.772308 + 2.37692i 0.0659827 + 0.203074i 0.978612 0.205714i \(-0.0659516\pi\)
−0.912629 + 0.408788i \(0.865952\pi\)
\(138\) 0.578793 + 1.78134i 0.0492702 + 0.151638i
\(139\) 3.85302 + 2.79938i 0.326809 + 0.237441i 0.739075 0.673623i \(-0.235263\pi\)
−0.412266 + 0.911063i \(0.635263\pi\)
\(140\) 0.251220 0.182522i 0.0212320 0.0154259i
\(141\) 1.15459 3.55348i 0.0972344 0.299257i
\(142\) 7.23775 0.607378
\(143\) −18.8508 10.6599i −1.57638 0.891426i
\(144\) −1.93344 −0.161120
\(145\) 0.259504 0.798670i 0.0215506 0.0663260i
\(146\) 3.51554 2.55419i 0.290948 0.211386i
\(147\) −0.500000 0.363271i −0.0412393 0.0299621i
\(148\) 2.43801 + 7.50344i 0.200404 + 0.616779i
\(149\) −2.23415 6.87600i −0.183028 0.563304i 0.816880 0.576807i \(-0.195702\pi\)
−0.999909 + 0.0135034i \(0.995702\pi\)
\(150\) −1.92446 1.39820i −0.157132 0.114163i
\(151\) −6.58514 + 4.78439i −0.535891 + 0.389348i −0.822557 0.568683i \(-0.807453\pi\)
0.286666 + 0.958031i \(0.407453\pi\)
\(152\) 2.37804 7.31886i 0.192885 0.593638i
\(153\) 11.3482 0.917445
\(154\) 1.06984 + 2.34622i 0.0862103 + 0.189064i
\(155\) 1.53304 0.123137
\(156\) −1.74026 + 5.35596i −0.139332 + 0.428820i
\(157\) −16.3028 + 11.8447i −1.30111 + 0.945311i −0.999966 0.00826862i \(-0.997368\pi\)
−0.301143 + 0.953579i \(0.597368\pi\)
\(158\) −2.84907 2.06997i −0.226660 0.164678i
\(159\) −0.328093 1.00977i −0.0260194 0.0800796i
\(160\) 0.402535 + 1.23887i 0.0318232 + 0.0979416i
\(161\) −3.15351 2.29116i −0.248532 0.180569i
\(162\) 3.59045 2.60861i 0.282092 0.204952i
\(163\) 2.29739 7.07062i 0.179945 0.553814i −0.819880 0.572536i \(-0.805960\pi\)
0.999825 + 0.0187219i \(0.00595970\pi\)
\(164\) −1.86736 −0.145816
\(165\) 0.336213 0.308216i 0.0261742 0.0239945i
\(166\) −8.77295 −0.680913
\(167\) −0.683275 + 2.10290i −0.0528734 + 0.162728i −0.974006 0.226520i \(-0.927265\pi\)
0.921133 + 0.389248i \(0.127265\pi\)
\(168\) 1.31998 0.959022i 0.101839 0.0739902i
\(169\) −23.9752 17.4190i −1.84424 1.33992i
\(170\) −0.231732 0.713196i −0.0177730 0.0546997i
\(171\) −2.35829 7.25807i −0.180343 0.555038i
\(172\) −5.31555 3.86198i −0.405307 0.294473i
\(173\) 8.38320 6.09075i 0.637363 0.463071i −0.221581 0.975142i \(-0.571122\pi\)
0.858943 + 0.512071i \(0.171122\pi\)
\(174\) 0.560385 1.72469i 0.0424827 0.130748i
\(175\) 4.95049 0.374222
\(176\) 2.43355 0.277797i 0.183436 0.0209398i
\(177\) −5.89174 −0.442851
\(178\) −1.90320 + 5.85746i −0.142651 + 0.439035i
\(179\) 18.9386 13.7597i 1.41554 1.02845i 0.423051 0.906106i \(-0.360959\pi\)
0.992488 0.122343i \(-0.0390408\pi\)
\(180\) 0.657702 + 0.477849i 0.0490222 + 0.0356167i
\(181\) −4.23851 13.0448i −0.315046 0.969611i −0.975736 0.218952i \(-0.929736\pi\)
0.660690 0.750659i \(-0.270264\pi\)
\(182\) 1.56876 + 4.82815i 0.116284 + 0.357886i
\(183\) 4.81471 + 3.49809i 0.355914 + 0.258587i
\(184\) 8.32516 6.04858i 0.613739 0.445907i
\(185\) 0.388742 1.19643i 0.0285809 0.0879629i
\(186\) 3.31052 0.242739
\(187\) −14.2835 + 1.63051i −1.04451 + 0.119235i
\(188\) −8.43666 −0.615306
\(189\) 1.07295 3.30220i 0.0780456 0.240200i
\(190\) −0.407990 + 0.296422i −0.0295987 + 0.0215047i
\(191\) 9.72838 + 7.06808i 0.703921 + 0.511429i 0.881207 0.472731i \(-0.156732\pi\)
−0.177286 + 0.984159i \(0.556732\pi\)
\(192\) 0.587169 + 1.80712i 0.0423753 + 0.130418i
\(193\) 4.90840 + 15.1065i 0.353315 + 1.08739i 0.956980 + 0.290153i \(0.0937062\pi\)
−0.603666 + 0.797238i \(0.706294\pi\)
\(194\) −5.69489 4.13758i −0.408869 0.297061i
\(195\) 0.726463 0.527806i 0.0520231 0.0377970i
\(196\) −0.431239 + 1.32722i −0.0308028 + 0.0948012i
\(197\) 12.3035 0.876590 0.438295 0.898831i \(-0.355582\pi\)
0.438295 + 0.898831i \(0.355582\pi\)
\(198\) −4.97632 + 4.56193i −0.353652 + 0.324202i
\(199\) 15.2615 1.08186 0.540929 0.841068i \(-0.318073\pi\)
0.540929 + 0.841068i \(0.318073\pi\)
\(200\) −4.03857 + 12.4294i −0.285570 + 0.878895i
\(201\) −0.635774 + 0.461917i −0.0448440 + 0.0325811i
\(202\) −12.0832 8.77892i −0.850168 0.617683i
\(203\) 1.16623 + 3.58928i 0.0818530 + 0.251918i
\(204\) 1.15526 + 3.55553i 0.0808845 + 0.248937i
\(205\) 0.240885 + 0.175013i 0.0168242 + 0.0122235i
\(206\) 10.2139 7.42080i 0.711633 0.517032i
\(207\) 3.15351 9.70552i 0.219184 0.674580i
\(208\) 4.82212 0.334354
\(209\) 4.01114 + 8.79663i 0.277456 + 0.608476i
\(210\) −0.106921 −0.00737828
\(211\) 2.76058 8.49620i 0.190046 0.584903i −0.809952 0.586496i \(-0.800507\pi\)
0.999999 + 0.00159295i \(0.000507051\pi\)
\(212\) −1.93952 + 1.40915i −0.133207 + 0.0967805i
\(213\) 4.65459 + 3.38176i 0.318928 + 0.231714i
\(214\) 1.29579 + 3.98802i 0.0885781 + 0.272615i
\(215\) 0.323742 + 0.996374i 0.0220790 + 0.0679521i
\(216\) 7.41570 + 5.38782i 0.504574 + 0.366595i
\(217\) −5.57379 + 4.04959i −0.378373 + 0.274904i
\(218\) −1.29714 + 3.99220i −0.0878537 + 0.270386i
\(219\) 3.45426 0.233417
\(220\) −0.896483 0.506952i −0.0604409 0.0341787i
\(221\) −28.3031 −1.90387
\(222\) 0.839469 2.58362i 0.0563415 0.173401i
\(223\) −0.578645 + 0.420410i −0.0387489 + 0.0281527i −0.606991 0.794709i \(-0.707624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(224\) −4.73607 3.44095i −0.316442 0.229908i
\(225\) 4.00503 + 12.3262i 0.267002 + 0.821747i
\(226\) 3.96331 + 12.1978i 0.263636 + 0.811387i
\(227\) 4.30528 + 3.12797i 0.285751 + 0.207611i 0.721422 0.692496i \(-0.243489\pi\)
−0.435671 + 0.900106i \(0.643489\pi\)
\(228\) 2.03397 1.47777i 0.134703 0.0978675i
\(229\) −2.04208 + 6.28489i −0.134945 + 0.415317i −0.995581 0.0939024i \(-0.970066\pi\)
0.860637 + 0.509219i \(0.170066\pi\)
\(230\) −0.674356 −0.0444657
\(231\) −0.408230 + 2.00872i −0.0268596 + 0.132164i
\(232\) −9.96318 −0.654115
\(233\) −2.95332 + 9.08937i −0.193478 + 0.595464i 0.806513 + 0.591217i \(0.201352\pi\)
−0.999991 + 0.00424788i \(0.998648\pi\)
\(234\) −10.7524 + 7.81211i −0.702910 + 0.510694i
\(235\) 1.08831 + 0.790705i 0.0709936 + 0.0515799i
\(236\) 4.11102 + 12.6524i 0.267604 + 0.823602i
\(237\) −0.865066 2.66240i −0.0561921 0.172941i
\(238\) 2.72646 + 1.98089i 0.176730 + 0.128402i
\(239\) −21.7194 + 15.7801i −1.40491 + 1.02073i −0.410872 + 0.911693i \(0.634776\pi\)
−0.994038 + 0.109034i \(0.965224\pi\)
\(240\) −0.0313842 + 0.0965905i −0.00202584 + 0.00623489i
\(241\) 18.8663 1.21529 0.607643 0.794210i \(-0.292115\pi\)
0.607643 + 0.794210i \(0.292115\pi\)
\(242\) 5.60806 6.45693i 0.360500 0.415067i
\(243\) 13.9443 0.894525
\(244\) 4.15258 12.7803i 0.265842 0.818177i
\(245\) 0.180019 0.130791i 0.0115010 0.00835596i
\(246\) 0.520180 + 0.377933i 0.0331654 + 0.0240961i
\(247\) 5.88173 + 18.1021i 0.374245 + 1.15181i
\(248\) −5.62047 17.2980i −0.356900 1.09843i
\(249\) −5.64188 4.09907i −0.357540 0.259768i
\(250\) 1.39269 1.01185i 0.0880814 0.0639949i
\(251\) 9.07680 27.9355i 0.572923 1.76328i −0.0702229 0.997531i \(-0.522371\pi\)
0.643146 0.765744i \(-0.277629\pi\)
\(252\) −3.65351 −0.230150
\(253\) −2.57472 + 12.6691i −0.161871 + 0.796498i
\(254\) −1.55285 −0.0974348
\(255\) 0.184207 0.566931i 0.0115355 0.0355026i
\(256\) 10.8355 7.87245i 0.677218 0.492028i
\(257\) 13.6856 + 9.94320i 0.853687 + 0.620240i 0.926160 0.377130i \(-0.123089\pi\)
−0.0724730 + 0.997370i \(0.523089\pi\)
\(258\) 0.699104 + 2.15162i 0.0435243 + 0.133954i
\(259\) 1.74703 + 5.37681i 0.108555 + 0.334099i
\(260\) −1.64035 1.19178i −0.101730 0.0739114i
\(261\) −7.99343 + 5.80757i −0.494781 + 0.359480i
\(262\) −0.329173 + 1.01309i −0.0203364 + 0.0625889i
\(263\) −8.18034 −0.504421 −0.252211 0.967672i \(-0.581158\pi\)
−0.252211 + 0.967672i \(0.581158\pi\)
\(264\) −4.71038 2.66367i −0.289904 0.163938i
\(265\) 0.382263 0.0234822
\(266\) 0.700347 2.15545i 0.0429411 0.132159i
\(267\) −3.96078 + 2.87768i −0.242396 + 0.176111i
\(268\) 1.43558 + 1.04301i 0.0876917 + 0.0637118i
\(269\) −1.93048 5.94140i −0.117703 0.362254i 0.874798 0.484488i \(-0.160994\pi\)
−0.992501 + 0.122234i \(0.960994\pi\)
\(270\) −0.185623 0.571288i −0.0112966 0.0347675i
\(271\) −6.36444 4.62403i −0.386612 0.280890i 0.377454 0.926028i \(-0.376800\pi\)
−0.764066 + 0.645138i \(0.776800\pi\)
\(272\) 2.58978 1.88159i 0.157029 0.114088i
\(273\) −1.24703 + 3.83797i −0.0754738 + 0.232284i
\(274\) −1.94312 −0.117388
\(275\) −6.81202 14.9391i −0.410780 0.900862i
\(276\) 3.36190 0.202363
\(277\) 3.72293 11.4580i 0.223689 0.688444i −0.774733 0.632289i \(-0.782116\pi\)
0.998422 0.0561556i \(-0.0178843\pi\)
\(278\) −2.99566 + 2.17648i −0.179668 + 0.130536i
\(279\) −14.5924 10.6020i −0.873622 0.634724i
\(280\) 0.181527 + 0.558682i 0.0108483 + 0.0333876i
\(281\) 6.53723 + 20.1195i 0.389978 + 1.20023i 0.932804 + 0.360384i \(0.117354\pi\)
−0.542826 + 0.839846i \(0.682646\pi\)
\(282\) 2.35015 + 1.70749i 0.139950 + 0.101679i
\(283\) 20.2281 14.6966i 1.20244 0.873623i 0.207916 0.978147i \(-0.433332\pi\)
0.994522 + 0.104524i \(0.0333319\pi\)
\(284\) 4.01448 12.3553i 0.238216 0.733153i
\(285\) −0.400878 −0.0237460
\(286\) 12.4113 11.3777i 0.733894 0.672780i
\(287\) −1.33811 −0.0789861
\(288\) 4.73607 14.5761i 0.279075 0.858906i
\(289\) −1.44723 + 1.05147i −0.0851312 + 0.0618515i
\(290\) 0.528215 + 0.383770i 0.0310178 + 0.0225358i
\(291\) −1.72914 5.32176i −0.101364 0.311967i
\(292\) −2.41024 7.41796i −0.141049 0.434104i
\(293\) 0.368173 + 0.267494i 0.0215089 + 0.0156271i 0.598488 0.801132i \(-0.295769\pi\)
−0.576979 + 0.816759i \(0.695769\pi\)
\(294\) 0.388742 0.282438i 0.0226719 0.0164721i
\(295\) 0.655503 2.01743i 0.0381648 0.117459i
\(296\) −14.9251 −0.867502
\(297\) −11.4415 + 1.30608i −0.663901 + 0.0757864i
\(298\) 5.62110 0.325621
\(299\) −7.86507 + 24.2062i −0.454849 + 1.39988i
\(300\) −3.45425 + 2.50966i −0.199431 + 0.144895i
\(301\) −3.80902 2.76741i −0.219548 0.159511i
\(302\) −1.95561 6.01874i −0.112533 0.346339i
\(303\) −3.66881 11.2915i −0.210768 0.648677i
\(304\) −1.74162 1.26536i −0.0998885 0.0725732i
\(305\) −1.73348 + 1.25945i −0.0992588 + 0.0721157i
\(306\) −2.72646 + 8.39119i −0.155862 + 0.479692i
\(307\) −8.03578 −0.458626 −0.229313 0.973353i \(-0.573648\pi\)
−0.229313 + 0.973353i \(0.573648\pi\)
\(308\) 4.59855 0.524938i 0.262026 0.0299111i
\(309\) 10.0358 0.570918
\(310\) −0.368322 + 1.13358i −0.0209193 + 0.0643829i
\(311\) −0.110807 + 0.0805059i −0.00628328 + 0.00456507i −0.590922 0.806728i \(-0.701236\pi\)
0.584639 + 0.811293i \(0.301236\pi\)
\(312\) −8.61887 6.26198i −0.487948 0.354515i
\(313\) −4.72485 14.5416i −0.267064 0.821939i −0.991211 0.132293i \(-0.957766\pi\)
0.724146 0.689646i \(-0.242234\pi\)
\(314\) −4.84150 14.9006i −0.273221 0.840889i
\(315\) 0.471296 + 0.342417i 0.0265545 + 0.0192930i
\(316\) −5.11385 + 3.71543i −0.287676 + 0.209009i
\(317\) −10.1953 + 31.3778i −0.572622 + 1.76235i 0.0715138 + 0.997440i \(0.477217\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(318\) 0.825478 0.0462905
\(319\) 9.22661 8.45828i 0.516591 0.473573i
\(320\) −0.684115 −0.0382432
\(321\) −1.03004 + 3.17014i −0.0574912 + 0.176940i
\(322\) 2.45181 1.78134i 0.136634 0.0992703i
\(323\) 10.2223 + 7.42692i 0.568783 + 0.413245i
\(324\) −2.46160 7.57602i −0.136756 0.420890i
\(325\) −9.98880 30.7424i −0.554079 1.70528i
\(326\) 4.67628 + 3.39752i 0.258995 + 0.188171i
\(327\) −2.69951 + 1.96131i −0.149283 + 0.108461i
\(328\) 1.09162 3.35966i 0.0602747 0.185506i
\(329\) −6.04554 −0.333301
\(330\) 0.147127 + 0.322657i 0.00809908 + 0.0177617i
\(331\) 29.5335 1.62331 0.811653 0.584140i \(-0.198568\pi\)
0.811653 + 0.584140i \(0.198568\pi\)
\(332\) −4.86600 + 14.9760i −0.267056 + 0.821915i
\(333\) −11.9743 + 8.69986i −0.656190 + 0.476750i
\(334\) −1.39079 1.01047i −0.0761008 0.0552905i
\(335\) −0.0874331 0.269091i −0.00477698 0.0147020i
\(336\) −0.141042 0.434084i −0.00769449 0.0236812i
\(337\) −4.55497 3.30938i −0.248125 0.180273i 0.456770 0.889585i \(-0.349006\pi\)
−0.704895 + 0.709311i \(0.749006\pi\)
\(338\) 18.6403 13.5430i 1.01390 0.736641i
\(339\) −3.15050 + 9.69624i −0.171112 + 0.526627i
\(340\) −1.34600 −0.0729974
\(341\) 19.8902 + 11.2477i 1.07711 + 0.609096i
\(342\) 5.93344 0.320844
\(343\) −0.309017 + 0.951057i −0.0166853 + 0.0513522i
\(344\) 10.0557 7.30586i 0.542165 0.393906i
\(345\) −0.433679 0.315086i −0.0233485 0.0169637i
\(346\) 2.48958 + 7.66214i 0.133841 + 0.411919i
\(347\) 2.69791 + 8.30331i 0.144831 + 0.445745i 0.996989 0.0775398i \(-0.0247065\pi\)
−0.852158 + 0.523285i \(0.824706\pi\)
\(348\) −2.63333 1.91323i −0.141162 0.102560i
\(349\) −14.9401 + 10.8546i −0.799724 + 0.581034i −0.910833 0.412774i \(-0.864560\pi\)
0.111109 + 0.993808i \(0.464560\pi\)
\(350\) −1.18938 + 3.66055i −0.0635752 + 0.195664i
\(351\) −22.6715 −1.21011
\(352\) −3.86681 + 19.0269i −0.206102 + 1.01414i
\(353\) −23.4857 −1.25002 −0.625009 0.780618i \(-0.714905\pi\)
−0.625009 + 0.780618i \(0.714905\pi\)
\(354\) 1.41553 4.35654i 0.0752343 0.231547i
\(355\) −1.67583 + 1.21756i −0.0889439 + 0.0646215i
\(356\) 8.94343 + 6.49778i 0.474001 + 0.344382i
\(357\) 0.827838 + 2.54782i 0.0438138 + 0.134845i
\(358\) 5.62425 + 17.3097i 0.297251 + 0.914844i
\(359\) −12.0391 8.74695i −0.635402 0.461647i 0.222865 0.974849i \(-0.428459\pi\)
−0.858267 + 0.513203i \(0.828459\pi\)
\(360\) −1.24420 + 0.903967i −0.0655753 + 0.0476432i
\(361\) −3.24552 + 9.98870i −0.170817 + 0.525721i
\(362\) 10.6641 0.560490
\(363\) 6.62347 1.53215i 0.347642 0.0804168i
\(364\) 9.11210 0.477604
\(365\) −0.384314 + 1.18280i −0.0201159 + 0.0619104i
\(366\) −3.74336 + 2.71971i −0.195669 + 0.142162i
\(367\) 27.6894 + 20.1175i 1.44537 + 1.05012i 0.986885 + 0.161424i \(0.0516085\pi\)
0.458487 + 0.888701i \(0.348391\pi\)
\(368\) −0.889558 2.73778i −0.0463714 0.142717i
\(369\) −1.08255 3.33176i −0.0563555 0.173444i
\(370\) 0.791277 + 0.574896i 0.0411365 + 0.0298874i
\(371\) −1.38982 + 1.00977i −0.0721560 + 0.0524244i
\(372\) 1.83621 5.65128i 0.0952032 0.293005i
\(373\) 3.01739 0.156235 0.0781173 0.996944i \(-0.475109\pi\)
0.0781173 + 0.996944i \(0.475109\pi\)
\(374\) 2.22605 10.9534i 0.115106 0.566388i
\(375\) 1.36841 0.0706646
\(376\) 4.93191 15.1788i 0.254344 0.782789i
\(377\) 19.9361 14.4845i 1.02676 0.745987i
\(378\) 2.18397 + 1.58674i 0.112331 + 0.0816133i
\(379\) −1.89252 5.82457i −0.0972121 0.299188i 0.890612 0.454764i \(-0.150277\pi\)
−0.987824 + 0.155576i \(0.950277\pi\)
\(380\) 0.279717 + 0.860879i 0.0143492 + 0.0441622i
\(381\) −0.998641 0.725555i −0.0511619 0.0371713i
\(382\) −7.56367 + 5.49532i −0.386991 + 0.281165i
\(383\) 1.35689 4.17607i 0.0693338 0.213387i −0.910386 0.413760i \(-0.864215\pi\)
0.979720 + 0.200373i \(0.0642153\pi\)
\(384\) 5.75876 0.293875
\(385\) −0.642402 0.363271i −0.0327398 0.0185140i
\(386\) −12.3495 −0.628573
\(387\) 3.80902 11.7229i 0.193623 0.595911i
\(388\) −10.2218 + 7.42661i −0.518936 + 0.377029i
\(389\) −8.49145 6.16940i −0.430533 0.312801i 0.351329 0.936252i \(-0.385730\pi\)
−0.781862 + 0.623451i \(0.785730\pi\)
\(390\) 0.215740 + 0.663978i 0.0109244 + 0.0336218i
\(391\) 5.22119 + 16.0692i 0.264047 + 0.812654i
\(392\) −2.13577 1.55173i −0.107873 0.0783742i
\(393\) −0.685047 + 0.497716i −0.0345560 + 0.0251064i
\(394\) −2.95600 + 9.09762i −0.148921 + 0.458331i
\(395\) 1.00789 0.0507127
\(396\) 5.02734 + 11.0252i 0.252634 + 0.554038i
\(397\) 11.3888 0.571589 0.285794 0.958291i \(-0.407743\pi\)
0.285794 + 0.958291i \(0.407743\pi\)
\(398\) −3.66666 + 11.2848i −0.183793 + 0.565657i
\(399\) 1.45750 1.05894i 0.0729664 0.0530132i
\(400\) 2.95774 + 2.14893i 0.147887 + 0.107446i
\(401\) −1.46009 4.49370i −0.0729135 0.224405i 0.907958 0.419061i \(-0.137641\pi\)
−0.980871 + 0.194657i \(0.937641\pi\)
\(402\) −0.188807 0.581090i −0.00941686 0.0289821i
\(403\) 36.3943 + 26.4420i 1.81293 + 1.31717i
\(404\) −21.6882 + 15.7574i −1.07903 + 0.783961i
\(405\) −0.392503 + 1.20800i −0.0195036 + 0.0600260i
\(406\) −2.93422 −0.145623
\(407\) 13.8217 12.6707i 0.685114 0.628062i
\(408\) −7.07230 −0.350131
\(409\) 0.761863 2.34477i 0.0376717 0.115942i −0.930452 0.366413i \(-0.880586\pi\)
0.968124 + 0.250472i \(0.0805857\pi\)
\(410\) −0.187285 + 0.136070i −0.00924932 + 0.00672003i
\(411\) −1.24962 0.907902i −0.0616392 0.0447835i
\(412\) −7.00259 21.5518i −0.344993 1.06178i
\(413\) 2.94587 + 9.06646i 0.144957 + 0.446131i
\(414\) 6.41892 + 4.66362i 0.315472 + 0.229204i
\(415\) 2.03129 1.47582i 0.0997122 0.0724452i
\(416\) −11.8121 + 36.3538i −0.579134 + 1.78239i
\(417\) −2.94345 −0.144141
\(418\) −7.46820 + 0.852519i −0.365282 + 0.0416981i
\(419\) −14.3399 −0.700548 −0.350274 0.936647i \(-0.613912\pi\)
−0.350274 + 0.936647i \(0.613912\pi\)
\(420\) −0.0593050 + 0.182522i −0.00289379 + 0.00890616i
\(421\) 14.0087 10.1779i 0.682744 0.496043i −0.191523 0.981488i \(-0.561343\pi\)
0.874267 + 0.485446i \(0.161343\pi\)
\(422\) 5.61911 + 4.08253i 0.273534 + 0.198734i
\(423\) −4.89094 15.0528i −0.237806 0.731891i
\(424\) −1.40146 4.31326i −0.0680611 0.209470i
\(425\) −17.3602 12.6130i −0.842096 0.611818i
\(426\) −3.61887 + 2.62927i −0.175335 + 0.127388i
\(427\) 2.97566 9.15813i 0.144002 0.443193i
\(428\) 7.52653 0.363808
\(429\) 13.2978 1.51799i 0.642024 0.0732891i
\(430\) −0.814531 −0.0392802
\(431\) 8.61919 26.5272i 0.415172 1.27777i −0.496925 0.867794i \(-0.665538\pi\)
0.912097 0.409975i \(-0.134462\pi\)
\(432\) 2.07448 1.50720i 0.0998085 0.0725151i
\(433\) 23.9040 + 17.3673i 1.14875 + 0.834619i 0.988315 0.152426i \(-0.0487087\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(434\) −1.65526 5.09437i −0.0794551 0.244538i
\(435\) 0.160382 + 0.493605i 0.00768973 + 0.0236666i
\(436\) 6.09548 + 4.42862i 0.291920 + 0.212093i
\(437\) 9.19251 6.67875i 0.439738 0.319488i
\(438\) −0.829907 + 2.55419i −0.0396545 + 0.122044i
\(439\) −33.6655 −1.60677 −0.803384 0.595461i \(-0.796970\pi\)
−0.803384 + 0.595461i \(0.796970\pi\)
\(440\) 1.43615 1.31656i 0.0684658 0.0627644i
\(441\) −2.61803 −0.124668
\(442\) 6.79997 20.9282i 0.323442 0.995451i
\(443\) −8.35449 + 6.06989i −0.396934 + 0.288389i −0.768291 0.640101i \(-0.778893\pi\)
0.371357 + 0.928490i \(0.378893\pi\)
\(444\) −3.94479 2.86606i −0.187211 0.136017i
\(445\) −0.544696 1.67640i −0.0258211 0.0794691i
\(446\) −0.171842 0.528874i −0.00813694 0.0250429i
\(447\) 3.61493 + 2.62640i 0.170980 + 0.124224i
\(448\) 2.48729 1.80712i 0.117513 0.0853784i
\(449\) −0.852224 + 2.62287i −0.0402189 + 0.123781i −0.969150 0.246471i \(-0.920729\pi\)
0.928931 + 0.370253i \(0.120729\pi\)
\(450\) −10.0766 −0.475016
\(451\) 1.84128 + 4.03802i 0.0867025 + 0.190143i
\(452\) 23.0208 1.08281
\(453\) 1.55454 4.78439i 0.0730387 0.224790i
\(454\) −3.34729 + 2.43195i −0.157096 + 0.114137i
\(455\) −1.17544 0.854009i −0.0551056 0.0400365i
\(456\) 1.46971 + 4.52331i 0.0688255 + 0.211823i
\(457\) −12.4628 38.3566i −0.582986 1.79425i −0.607213 0.794539i \(-0.707713\pi\)
0.0242276 0.999706i \(-0.492287\pi\)
\(458\) −4.15662 3.01996i −0.194226 0.141114i
\(459\) −12.1760 + 8.84638i −0.568327 + 0.412914i
\(460\) −0.374038 + 1.15117i −0.0174396 + 0.0536736i
\(461\) −34.2251 −1.59402 −0.797011 0.603965i \(-0.793587\pi\)
−0.797011 + 0.603965i \(0.793587\pi\)
\(462\) −1.38723 0.784466i −0.0645400 0.0364967i
\(463\) 0.707349 0.0328733 0.0164367 0.999865i \(-0.494768\pi\)
0.0164367 + 0.999865i \(0.494768\pi\)
\(464\) −0.861267 + 2.65071i −0.0399833 + 0.123056i
\(465\) −0.766520 + 0.556910i −0.0355465 + 0.0258261i
\(466\) −6.01142 4.36755i −0.278473 0.202323i
\(467\) −8.83555 27.1930i −0.408860 1.25834i −0.917629 0.397439i \(-0.869899\pi\)
0.508768 0.860904i \(-0.330101\pi\)
\(468\) 7.37184 + 22.6882i 0.340764 + 1.04876i
\(469\) 1.02870 + 0.747397i 0.0475011 + 0.0345116i
\(470\) −0.846145 + 0.614760i −0.0390298 + 0.0283568i
\(471\) 3.84858 11.8447i 0.177333 0.545775i
\(472\) −25.1669 −1.15840
\(473\) −3.10991 + 15.3025i −0.142994 + 0.703611i
\(474\) 2.17650 0.0999699
\(475\) −4.45933 + 13.7244i −0.204608 + 0.629719i
\(476\) 4.89377 3.55553i 0.224306 0.162968i
\(477\) −3.63860 2.64360i −0.166600 0.121042i
\(478\) −6.45006 19.8512i −0.295019 0.907975i
\(479\) −1.57511 4.84769i −0.0719686 0.221497i 0.908602 0.417663i \(-0.137151\pi\)
−0.980571 + 0.196166i \(0.937151\pi\)
\(480\) −0.651315 0.473208i −0.0297283 0.0215989i
\(481\) 29.8648 21.6980i 1.36172 0.989344i
\(482\) −4.53274 + 13.9503i −0.206461 + 0.635421i
\(483\) 2.40907 0.109617
\(484\) −7.91185 13.1547i −0.359629 0.597942i
\(485\) 2.01464 0.0914800
\(486\) −3.35019 + 10.3108i −0.151968 + 0.467709i
\(487\) −23.6138 + 17.1564i −1.07004 + 0.777433i −0.975920 0.218128i \(-0.930005\pi\)
−0.0941240 + 0.995560i \(0.530005\pi\)
\(488\) 20.5663 + 14.9423i 0.930992 + 0.676405i
\(489\) 1.41986 + 4.36989i 0.0642084 + 0.197613i
\(490\) 0.0534607 + 0.164535i 0.00241511 + 0.00743294i
\(491\) −24.3870 17.7182i −1.10057 0.799610i −0.119416 0.992844i \(-0.538102\pi\)
−0.981153 + 0.193235i \(0.938102\pi\)
\(492\) 0.933679 0.678357i 0.0420935 0.0305827i
\(493\) 5.05514 15.5581i 0.227672 0.700703i
\(494\) −14.7984 −0.665810
\(495\) 0.384795 1.89341i 0.0172952 0.0851023i
\(496\) −5.08801 −0.228458
\(497\) 2.87670 8.85357i 0.129038 0.397137i
\(498\) 4.38647 3.18696i 0.196563 0.142811i
\(499\) −4.81450 3.49794i −0.215526 0.156589i 0.474784 0.880102i \(-0.342526\pi\)
−0.690311 + 0.723513i \(0.742526\pi\)
\(500\) −0.954823 2.93864i −0.0427010 0.131420i
\(501\) −0.422287 1.29967i −0.0188664 0.0580648i
\(502\) 18.4757 + 13.4233i 0.824609 + 0.599113i
\(503\) 4.02773 2.92632i 0.179588 0.130478i −0.494360 0.869257i \(-0.664597\pi\)
0.673947 + 0.738779i \(0.264597\pi\)
\(504\) 2.13577 6.57324i 0.0951349 0.292795i
\(505\) 4.27456 0.190216
\(506\) −8.74933 4.94765i −0.388955 0.219950i
\(507\) 18.3154 0.813416
\(508\) −0.861305 + 2.65083i −0.0382142 + 0.117611i
\(509\) 17.2551 12.5366i 0.764821 0.555675i −0.135565 0.990769i \(-0.543285\pi\)
0.900385 + 0.435094i \(0.143285\pi\)
\(510\) 0.374949 + 0.272417i 0.0166030 + 0.0120628i
\(511\) −1.72713 5.31556i −0.0764038 0.235147i
\(512\) −2.54091 7.82012i −0.112293 0.345604i
\(513\) 8.18830 + 5.94915i 0.361522 + 0.262661i
\(514\) −10.6404 + 7.73068i −0.469327 + 0.340986i
\(515\) −1.11656 + 3.43643i −0.0492017 + 0.151427i
\(516\) 4.06072 0.178763
\(517\) 8.31884 + 18.2436i 0.365862 + 0.802354i
\(518\) −4.39552 −0.193128
\(519\) −1.97900 + 6.09075i −0.0868686 + 0.267354i
\(520\) 3.10312 2.25455i 0.136081 0.0988686i
\(521\) 17.9103 + 13.0126i 0.784664 + 0.570092i 0.906375 0.422473i \(-0.138838\pi\)
−0.121711 + 0.992566i \(0.538838\pi\)
\(522\) −2.37383 7.30590i −0.103900 0.319771i
\(523\) 1.51773 + 4.67108i 0.0663655 + 0.204252i 0.978740 0.205104i \(-0.0657533\pi\)
−0.912375 + 0.409356i \(0.865753\pi\)
\(524\) 1.54683 + 1.12384i 0.0675737 + 0.0490952i
\(525\) −2.47524 + 1.79837i −0.108028 + 0.0784873i
\(526\) 1.96537 6.04880i 0.0856944 0.263740i
\(527\) 29.8637 1.30088
\(528\) −1.11586 + 1.02294i −0.0485615 + 0.0445176i
\(529\) −7.80592 −0.339388
\(530\) −0.0918410 + 0.282657i −0.00398932 + 0.0122779i
\(531\) −20.1913 + 14.6698i −0.876228 + 0.636617i
\(532\) −3.29104 2.39108i −0.142685 0.103666i
\(533\) 2.69996 + 8.30962i 0.116948 + 0.359929i
\(534\) −1.17624 3.62011i −0.0509010 0.156657i
\(535\) −0.970907 0.705405i −0.0419760 0.0304973i
\(536\) −2.71574 + 1.97310i −0.117302 + 0.0852250i
\(537\) −4.47080 + 13.7597i −0.192929 + 0.593775i
\(538\) 4.85707 0.209403
\(539\) 3.29522 0.376160i 0.141935 0.0162024i
\(540\) −1.07818 −0.0463977
\(541\) 5.99013 18.4357i 0.257536 0.792614i −0.735784 0.677217i \(-0.763186\pi\)
0.993319 0.115397i \(-0.0368141\pi\)
\(542\) 4.94825 3.59511i 0.212546 0.154423i
\(543\) 6.85805 + 4.98266i 0.294307 + 0.213827i
\(544\) 7.84139 + 24.1333i 0.336197 + 1.03471i
\(545\) −0.371242 1.14257i −0.0159023 0.0489422i
\(546\) −2.53831 1.84419i −0.108630 0.0789240i
\(547\) −11.6904 + 8.49354i −0.499843 + 0.363158i −0.808957 0.587868i \(-0.799968\pi\)
0.309114 + 0.951025i \(0.399968\pi\)
\(548\) −1.07777 + 3.31703i −0.0460400 + 0.141697i
\(549\) 25.2102 1.07594
\(550\) 12.6831 1.44781i 0.540808 0.0617349i
\(551\) −11.0012 −0.468667
\(552\) −1.96530 + 6.04858i −0.0836489 + 0.257445i
\(553\) −3.66448 + 2.66240i −0.155829 + 0.113217i
\(554\) 7.57795 + 5.50570i 0.321956 + 0.233915i
\(555\) 0.240256 + 0.739431i 0.0101983 + 0.0313871i
\(556\) 2.05382 + 6.32100i 0.0871012 + 0.268070i
\(557\) −14.9432 10.8569i −0.633164 0.460021i 0.224331 0.974513i \(-0.427980\pi\)
−0.857495 + 0.514492i \(0.827980\pi\)
\(558\) 11.3453 8.24287i 0.480286 0.348949i
\(559\) −9.49993 + 29.2378i −0.401804 + 1.23663i
\(560\) 0.164330 0.00694419
\(561\) 6.54945 6.00405i 0.276518 0.253491i
\(562\) −16.4476 −0.693801
\(563\) 9.66724 29.7527i 0.407426 1.25393i −0.511427 0.859327i \(-0.670883\pi\)
0.918853 0.394600i \(-0.129117\pi\)
\(564\) 4.21833 3.06479i 0.177624 0.129051i
\(565\) −2.96963 2.15757i −0.124933 0.0907695i
\(566\) 6.00720 + 18.4883i 0.252502 + 0.777120i
\(567\) −1.76393 5.42882i −0.0740782 0.227989i
\(568\) 19.8823 + 14.4454i 0.834244 + 0.606114i
\(569\) −1.40449 + 1.02042i −0.0588794 + 0.0427784i −0.616836 0.787092i \(-0.711586\pi\)
0.557956 + 0.829870i \(0.311586\pi\)
\(570\) 0.0963134 0.296422i 0.00403412 0.0124158i
\(571\) 12.5309 0.524403 0.262201 0.965013i \(-0.415551\pi\)
0.262201 + 0.965013i \(0.415551\pi\)
\(572\) −12.5385 27.4976i −0.524262 1.14973i
\(573\) −7.43182 −0.310469
\(574\) 0.321489 0.989441i 0.0134187 0.0412985i
\(575\) −15.6114 + 11.3424i −0.651042 + 0.473009i
\(576\) 6.51180 + 4.73110i 0.271325 + 0.197129i
\(577\) 6.23893 + 19.2015i 0.259730 + 0.799368i 0.992861 + 0.119280i \(0.0380585\pi\)
−0.733130 + 0.680088i \(0.761942\pi\)
\(578\) −0.429788 1.32275i −0.0178768 0.0550192i
\(579\) −7.94196 5.77017i −0.330057 0.239800i
\(580\) 0.948101 0.688835i 0.0393677 0.0286023i
\(581\) −3.48688 + 10.7315i −0.144660 + 0.445218i
\(582\) 4.35051 0.180334
\(583\) 4.95961 + 2.80461i 0.205406 + 0.116155i
\(584\) 14.7550 0.610568
\(585\) 1.17544 3.61764i 0.0485986 0.149571i
\(586\) −0.286249 + 0.207972i −0.0118248 + 0.00859125i
\(587\) 0.00677611 + 0.00492314i 0.000279680 + 0.000203200i 0.587925 0.808915i \(-0.299945\pi\)
−0.587645 + 0.809119i \(0.699945\pi\)
\(588\) −0.266520 0.820265i −0.0109911 0.0338272i
\(589\) −6.20604 19.1002i −0.255716 0.787012i
\(590\) 1.33426 + 0.969399i 0.0549307 + 0.0399095i
\(591\) −6.15177 + 4.46952i −0.253050 + 0.183851i
\(592\) −1.29020 + 3.97082i −0.0530267 + 0.163200i
\(593\) −0.439298 −0.0180398 −0.00901989 0.999959i \(-0.502871\pi\)
−0.00901989 + 0.999959i \(0.502871\pi\)
\(594\) 1.78312 8.77397i 0.0731624 0.360001i
\(595\) −0.964520 −0.0395415
\(596\) 3.11779 9.59558i 0.127710 0.393050i
\(597\) −7.63075 + 5.54406i −0.312306 + 0.226903i
\(598\) −16.0092 11.6314i −0.654664 0.475641i
\(599\) 13.9572 + 42.9558i 0.570275 + 1.75512i 0.651734 + 0.758448i \(0.274042\pi\)
−0.0814591 + 0.996677i \(0.525958\pi\)
\(600\) −2.49598 7.68182i −0.101898 0.313609i
\(601\) −9.01541 6.55008i −0.367746 0.267183i 0.388529 0.921436i \(-0.372983\pi\)
−0.756276 + 0.654253i \(0.772983\pi\)
\(602\) 2.96145 2.15162i 0.120700 0.0876935i
\(603\) −1.02870 + 3.16603i −0.0418921 + 0.128931i
\(604\) −11.3591 −0.462194
\(605\) −0.212282 + 2.43845i −0.00863047 + 0.0991371i
\(606\) 9.23071 0.374972
\(607\) −11.0318 + 33.9525i −0.447768 + 1.37809i 0.431651 + 0.902041i \(0.357931\pi\)
−0.879419 + 0.476049i \(0.842069\pi\)
\(608\) 13.8057 10.0304i 0.559894 0.406787i
\(609\) −1.88699 1.37098i −0.0764649 0.0555550i
\(610\) −0.514796 1.58438i −0.0208435 0.0641496i
\(611\) 12.1983 + 37.5426i 0.493491 + 1.51881i
\(612\) 12.8121 + 9.30850i 0.517897 + 0.376274i
\(613\) −13.9135 + 10.1087i −0.561960 + 0.408288i −0.832176 0.554512i \(-0.812905\pi\)
0.270216 + 0.962800i \(0.412905\pi\)
\(614\) 1.93064 5.94191i 0.0779144 0.239796i
\(615\) −0.184020 −0.00742040
\(616\) −1.74378 + 8.58036i −0.0702587 + 0.345713i
\(617\) −16.8852 −0.679774 −0.339887 0.940466i \(-0.610389\pi\)
−0.339887 + 0.940466i \(0.610389\pi\)
\(618\) −2.41117 + 7.42080i −0.0969913 + 0.298509i
\(619\) −25.1355 + 18.2620i −1.01028 + 0.734013i −0.964268 0.264928i \(-0.914652\pi\)
−0.0460139 + 0.998941i \(0.514652\pi\)
\(620\) 1.73080 + 1.25750i 0.0695106 + 0.0505024i
\(621\) 4.18231 + 12.8718i 0.167830 + 0.516529i
\(622\) −0.0329066 0.101276i −0.00131943 0.00406080i
\(623\) 6.40868 + 4.65618i 0.256758 + 0.186546i
\(624\) −2.41106 + 1.75174i −0.0965196 + 0.0701256i
\(625\) 7.49668 23.0724i 0.299867 0.922896i
\(626\) 11.8877 0.475127
\(627\) −5.20113 2.94118i −0.207713 0.117460i
\(628\) −28.1217 −1.12218
\(629\) 7.57271 23.3064i 0.301944 0.929287i
\(630\) −0.366425 + 0.266223i −0.0145987 + 0.0106066i
\(631\) −5.86832 4.26359i −0.233614 0.169731i 0.464819 0.885406i \(-0.346119\pi\)
−0.698434 + 0.715675i \(0.746119\pi\)
\(632\) −3.69517 11.3726i −0.146986 0.452376i
\(633\) 1.70613 + 5.25094i 0.0678128 + 0.208706i
\(634\) −20.7522 15.0774i −0.824176 0.598799i
\(635\) 0.359549 0.261227i 0.0142683 0.0103665i
\(636\) 0.457859 1.40915i 0.0181553 0.0558763i
\(637\) 6.52954 0.258710
\(638\) 4.03757 + 8.85460i 0.159849 + 0.350557i
\(639\) 24.3718 0.964132
\(640\) −0.640707 + 1.97189i −0.0253262 + 0.0779459i
\(641\) 16.7870 12.1965i 0.663047 0.481732i −0.204643 0.978837i \(-0.565603\pi\)
0.867691 + 0.497104i \(0.165603\pi\)
\(642\) −2.09663 1.52329i −0.0827472 0.0601194i
\(643\) 2.19750 + 6.76322i 0.0866611 + 0.266715i 0.984991 0.172606i \(-0.0552188\pi\)
−0.898330 + 0.439322i \(0.855219\pi\)
\(644\) −1.68095 5.17343i −0.0662387 0.203862i
\(645\) −0.523825 0.380581i −0.0206256 0.0149854i
\(646\) −7.94766 + 5.77431i −0.312696 + 0.227187i
\(647\) 8.52234 26.2291i 0.335048 1.03117i −0.631651 0.775253i \(-0.717622\pi\)
0.966699 0.255918i \(-0.0823777\pi\)
\(648\) 15.0694 0.591984
\(649\) 23.3063 21.3655i 0.914852 0.838669i
\(650\) 25.1317 0.985748
\(651\) 1.31579 4.04959i 0.0515700 0.158716i
\(652\) 8.39353 6.09826i 0.328716 0.238826i
\(653\) −13.0690 9.49516i −0.511428 0.371574i 0.301937 0.953328i \(-0.402367\pi\)
−0.813365 + 0.581753i \(0.802367\pi\)
\(654\) −0.801680 2.46732i −0.0313482 0.0964797i
\(655\) −0.0942092 0.289946i −0.00368106 0.0113291i
\(656\) −0.799474 0.580852i −0.0312142 0.0226785i
\(657\) 11.8379 8.60076i 0.461842 0.335548i
\(658\) 1.45248 4.47026i 0.0566234 0.174269i
\(659\) −13.2085 −0.514531 −0.257266 0.966341i \(-0.582822\pi\)
−0.257266 + 0.966341i \(0.582822\pi\)
\(660\) 0.632403 0.0721907i 0.0246162 0.00281002i
\(661\) −4.90660 −0.190845 −0.0954223 0.995437i \(-0.530420\pi\)
−0.0954223 + 0.995437i \(0.530420\pi\)
\(662\) −7.09559 + 21.8380i −0.275778 + 0.848757i
\(663\) 14.1515 10.2817i 0.549600 0.399308i
\(664\) −24.0996 17.5094i −0.935245 0.679495i
\(665\) 0.200439 + 0.616888i 0.00777270 + 0.0239219i
\(666\) −3.55605 10.9444i −0.137794 0.424087i
\(667\) −11.9013 8.64682i −0.460821 0.334806i
\(668\) −2.49635 + 1.81371i −0.0965869 + 0.0701745i
\(669\) 0.136599 0.420410i 0.00528124 0.0162540i
\(670\) 0.219981 0.00849861
\(671\) −31.7311 + 3.62221i −1.22497 + 0.139834i
\(672\) 3.61803 0.139569
\(673\) −9.26654 + 28.5195i −0.357199 + 1.09935i 0.597524 + 0.801851i \(0.296151\pi\)
−0.954723 + 0.297495i \(0.903849\pi\)
\(674\) 3.54142 2.57299i 0.136410 0.0991079i
\(675\) −13.9060 10.1033i −0.535242 0.388876i
\(676\) −12.7797 39.3320i −0.491528 1.51277i
\(677\) 3.89019 + 11.9728i 0.149512 + 0.460151i 0.997564 0.0697626i \(-0.0222242\pi\)
−0.848051 + 0.529914i \(0.822224\pi\)
\(678\) −6.41278 4.65916i −0.246281 0.178934i
\(679\) −7.32477 + 5.32176i −0.281099 + 0.204230i
\(680\) 0.786849 2.42167i 0.0301743 0.0928668i
\(681\) −3.28894 −0.126033
\(682\) −13.0956 + 12.0051i −0.501457 + 0.459699i
\(683\) −28.5342 −1.09183 −0.545916 0.837840i \(-0.683818\pi\)
−0.545916 + 0.837840i \(0.683818\pi\)
\(684\) 3.29104 10.1288i 0.125836 0.387283i
\(685\) 0.449911 0.326879i 0.0171902 0.0124894i
\(686\) −0.628998 0.456994i −0.0240153 0.0174481i
\(687\) −1.26208 3.88427i −0.0481513 0.148194i
\(688\) −1.07447 3.30687i −0.0409636 0.126073i
\(689\) 9.07491 + 6.59331i 0.345726 + 0.251185i
\(690\) 0.337178 0.244974i 0.0128362 0.00932601i
\(691\) 7.84107 24.1323i 0.298288 0.918037i −0.683809 0.729661i \(-0.739678\pi\)
0.982097 0.188376i \(-0.0603223\pi\)
\(692\) 14.4606 0.549711
\(693\) 3.60249 + 7.90045i 0.136847 + 0.300113i
\(694\) −6.78791 −0.257666
\(695\) 0.327482 1.00788i 0.0124221 0.0382312i
\(696\) 4.98159 3.61934i 0.188827 0.137191i
\(697\) 4.69245 + 3.40927i 0.177739 + 0.129135i
\(698\) −4.43679 13.6551i −0.167935 0.516851i
\(699\) −1.82525 5.61754i −0.0690373 0.212475i
\(700\) 5.58909 + 4.06071i 0.211248 + 0.153480i
\(701\) 36.9738 26.8630i 1.39648 1.01460i 0.401363 0.915919i \(-0.368537\pi\)
0.995119 0.0986843i \(-0.0314634\pi\)
\(702\) 5.44695 16.7640i 0.205582 0.632716i
\(703\) −16.4800 −0.621556
\(704\) −8.87594 5.01925i −0.334525 0.189170i
\(705\) −0.831396 −0.0313122
\(706\) 5.64257 17.3661i 0.212361 0.653580i
\(707\) −15.5413 + 11.2915i −0.584493 + 0.424659i
\(708\) −6.65177 4.83279i −0.249989 0.181627i
\(709\) 11.9065 + 36.6446i 0.447160 + 1.37622i 0.880098 + 0.474793i \(0.157477\pi\)
−0.432938 + 0.901424i \(0.642523\pi\)
\(710\) −0.497676 1.53169i −0.0186774 0.0574833i
\(711\) −9.59373 6.97025i −0.359793 0.261405i
\(712\) −16.9187 + 12.2921i −0.634054 + 0.460667i
\(713\) 8.29874 25.5409i 0.310790 0.956515i
\(714\) −2.08283 −0.0779480
\(715\) −0.959703 + 4.72228i −0.0358908 + 0.176603i
\(716\) 32.6683 1.22087
\(717\) 5.12725 15.7801i 0.191481 0.589317i
\(718\) 9.36025 6.80062i 0.349321 0.253797i
\(719\) −4.61312 3.35163i −0.172040 0.124995i 0.498433 0.866928i \(-0.333909\pi\)
−0.670473 + 0.741934i \(0.733909\pi\)
\(720\) 0.132945 + 0.409164i 0.00495458 + 0.0152486i
\(721\) −5.01791 15.4435i −0.186877 0.575148i
\(722\) −6.60620 4.79969i −0.245857 0.178626i
\(723\) −9.43316 + 6.85359i −0.350823 + 0.254888i
\(724\) 5.91491 18.2042i 0.219826 0.676555i
\(725\) 18.6831 0.693872
\(726\) −0.458411 + 5.26571i −0.0170132 + 0.195429i
\(727\) 11.8221 0.438458 0.219229 0.975673i \(-0.429646\pi\)
0.219229 + 0.975673i \(0.429646\pi\)
\(728\) −5.32676 + 16.3941i −0.197423 + 0.607605i
\(729\) 6.88197 5.00004i 0.254888 0.185187i
\(730\) −0.782263 0.568347i −0.0289529 0.0210355i
\(731\) 6.30649 + 19.4094i 0.233254 + 0.717882i
\(732\) 2.56644 + 7.89868i 0.0948582 + 0.291944i
\(733\) −7.12900 5.17952i −0.263316 0.191310i 0.448292 0.893887i \(-0.352033\pi\)
−0.711607 + 0.702577i \(0.752033\pi\)
\(734\) −21.5280 + 15.6410i −0.794614 + 0.577321i
\(735\) −0.0424967 + 0.130791i −0.00156752 + 0.00482432i
\(736\) 22.8190 0.841121
\(737\) 0.839897 4.13277i 0.0309380 0.152232i
\(738\) 2.72370 0.100261
\(739\) 0.148578 0.457276i 0.00546553 0.0168212i −0.948287 0.317416i \(-0.897185\pi\)
0.953752 + 0.300594i \(0.0971850\pi\)
\(740\) 1.42027 1.03189i 0.0522103 0.0379330i
\(741\) −9.51683 6.91438i −0.349610 0.254006i
\(742\) −0.412739 1.27028i −0.0151521 0.0466335i
\(743\) 10.2730 + 31.6172i 0.376881 + 1.15992i 0.942201 + 0.335049i \(0.108753\pi\)
−0.565319 + 0.824872i \(0.691247\pi\)
\(744\) 9.09412 + 6.60726i 0.333407 + 0.242234i
\(745\) −1.30151 + 0.945603i −0.0476837 + 0.0346442i
\(746\) −0.724946 + 2.23116i −0.0265422 + 0.0816884i
\(747\) −29.5413 −1.08086
\(748\) −17.4635 9.87543i −0.638530 0.361082i
\(749\) 5.39336 0.197069
\(750\) −0.328769 + 1.01185i −0.0120050 + 0.0369475i
\(751\) −22.6578 + 16.4619i −0.826796 + 0.600703i −0.918651 0.395070i \(-0.870720\pi\)
0.0918547 + 0.995772i \(0.470720\pi\)
\(752\) −3.61200 2.62427i −0.131716 0.0956973i
\(753\) 5.60977 + 17.2651i 0.204432 + 0.629176i
\(754\) 5.92049 + 18.2214i 0.215611 + 0.663584i
\(755\) 1.46530 + 1.06460i 0.0533276 + 0.0387448i
\(756\) 3.92003 2.84807i 0.142570 0.103583i
\(757\) −6.87465 + 21.1580i −0.249863 + 0.769001i 0.744935 + 0.667137i \(0.232481\pi\)
−0.994798 + 0.101864i \(0.967519\pi\)
\(758\) 4.76156 0.172948
\(759\) −3.31495 7.26986i −0.120325 0.263879i
\(760\) −1.71237 −0.0621142
\(761\) −14.9025 + 45.8651i −0.540214 + 1.66261i 0.191891 + 0.981416i \(0.438538\pi\)
−0.732105 + 0.681192i \(0.761462\pi\)
\(762\) 0.776427 0.564108i 0.0281270 0.0204355i
\(763\) 4.36789 + 3.17346i 0.158128 + 0.114887i
\(764\) 5.18562 + 15.9597i 0.187609 + 0.577402i
\(765\) −0.780313 2.40156i −0.0282123 0.0868284i
\(766\) 2.76192 + 2.00665i 0.0997922 + 0.0725033i
\(767\) 50.3584 36.5875i 1.81834 1.32110i
\(768\) −2.55791 + 7.87245i −0.0923007 + 0.284072i
\(769\) 43.6883 1.57544 0.787721 0.616032i \(-0.211261\pi\)
0.787721 + 0.616032i \(0.211261\pi\)
\(770\) 0.422955 0.387734i 0.0152422 0.0139730i
\(771\) −10.4549 −0.376524
\(772\) −6.84977 + 21.0814i −0.246528 + 0.758737i
\(773\) 0.473736 0.344189i 0.0170391 0.0123796i −0.579233 0.815162i \(-0.696648\pi\)
0.596272 + 0.802782i \(0.296648\pi\)
\(774\) 7.75318 + 5.63301i 0.278682 + 0.202475i
\(775\) 10.5396 + 32.4375i 0.378593 + 1.16519i
\(776\) −7.38612 22.7321i −0.265146 0.816036i
\(777\) −2.82676 2.05376i −0.101409 0.0736782i
\(778\) 6.60197 4.79661i 0.236692 0.171967i
\(779\) 1.20535 3.70969i 0.0431862 0.132913i
\(780\) 1.25312 0.0448688
\(781\) −30.6759 + 3.50175i −1.09767 + 0.125302i
\(782\) −13.1365 −0.469760
\(783\) 4.04930 12.4625i 0.144710 0.445372i
\(784\) −0.597465 + 0.434084i −0.0213380 + 0.0155030i
\(785\) 3.62764 + 2.63563i 0.129476 + 0.0940698i
\(786\) −0.203440 0.626124i −0.00725647 0.0223331i
\(787\) 9.49195 + 29.2132i 0.338351 + 1.04134i 0.965048 + 0.262075i \(0.0844067\pi\)
−0.626696 + 0.779264i \(0.715593\pi\)
\(788\) 13.8907 + 10.0922i 0.494834 + 0.359518i
\(789\) 4.09017 2.97168i 0.145614 0.105795i
\(790\) −0.242153 + 0.745269i −0.00861540 + 0.0265155i
\(791\) 16.4962 0.586538
\(792\) −22.7750 + 2.59984i −0.809274 + 0.0923811i
\(793\) −62.8758 −2.23278
\(794\) −2.73623 + 8.42125i −0.0971052 + 0.298859i
\(795\) −0.191132 + 0.138865i −0.00677874 + 0.00492504i
\(796\) 17.2302 + 12.5185i 0.610708 + 0.443705i
\(797\) −3.34767 10.3031i −0.118581 0.364953i 0.874096 0.485752i \(-0.161454\pi\)
−0.992677 + 0.120799i \(0.961454\pi\)
\(798\) 0.432838 + 1.33214i 0.0153223 + 0.0471572i
\(799\) 21.2003 + 15.4029i 0.750014 + 0.544917i
\(800\) −23.4458 + 17.0344i −0.828936 + 0.602257i
\(801\) −6.40868 + 19.7239i −0.226440 + 0.696910i
\(802\) 3.67358 0.129719
\(803\) −13.6642 + 12.5263i −0.482200 + 0.442045i
\(804\) −1.09668 −0.0386770
\(805\) −0.268028 + 0.824906i −0.00944675 + 0.0290741i
\(806\) −28.2960 + 20.5582i −0.996684 + 0.724133i
\(807\) 3.12358 + 2.26941i 0.109955 + 0.0798872i
\(808\) −15.6715 48.2320i −0.551322 1.69679i
\(809\) −11.9250 36.7013i −0.419260 1.29035i −0.908385 0.418136i \(-0.862684\pi\)
0.489125 0.872214i \(-0.337316\pi\)
\(810\) −0.798931 0.580458i −0.0280716 0.0203952i
\(811\) 41.1737 29.9144i 1.44580 1.05044i 0.459015 0.888428i \(-0.348202\pi\)
0.986789 0.162010i \(-0.0517977\pi\)
\(812\) −1.62749 + 5.00890i −0.0571137 + 0.175778i
\(813\) 4.86200 0.170518
\(814\) 6.04836 + 13.2644i 0.211995 + 0.464916i
\(815\) −1.65429 −0.0579473
\(816\) −0.611364 + 1.88159i −0.0214020 + 0.0658687i
\(817\) 11.1033 8.06703i 0.388456 0.282230i
\(818\) 1.55076 + 1.12669i 0.0542209 + 0.0393938i
\(819\) 5.28251 + 16.2579i 0.184586 + 0.568097i
\(820\) 0.128402 + 0.395180i 0.00448398 + 0.0138003i
\(821\) 32.6110 + 23.6933i 1.13813 + 0.826901i 0.986858 0.161590i \(-0.0516623\pi\)
0.151274 + 0.988492i \(0.451662\pi\)
\(822\) 0.971560 0.705880i 0.0338870 0.0246204i
\(823\) 7.93609 24.4248i 0.276635 0.851395i −0.712147 0.702030i \(-0.752277\pi\)
0.988782 0.149365i \(-0.0477228\pi\)
\(824\) 42.8685 1.49340
\(825\) 8.83296 + 4.99494i 0.307524 + 0.173902i
\(826\) −7.41179 −0.257889
\(827\) −9.87486 + 30.3917i −0.343382 + 1.05682i 0.619062 + 0.785342i \(0.287513\pi\)
−0.962444 + 0.271480i \(0.912487\pi\)
\(828\) 11.5214 8.37079i 0.400397 0.290905i
\(829\) −39.1566 28.4489i −1.35996 0.988072i −0.998447 0.0557070i \(-0.982259\pi\)
−0.361518 0.932365i \(-0.617741\pi\)
\(830\) 0.603238 + 1.85658i 0.0209387 + 0.0644427i
\(831\) 2.30090 + 7.08143i 0.0798172 + 0.245652i
\(832\) −16.2409 11.7997i −0.563050 0.409080i
\(833\) 3.50678 2.54782i 0.121503 0.0882768i
\(834\) 0.707180 2.17648i 0.0244876 0.0753652i
\(835\) 0.492010 0.0170267
\(836\) −2.68700 + 13.2216i −0.0929319 + 0.457278i
\(837\) 23.9216 0.826850
\(838\) 3.44524 10.6033i 0.119014 0.366287i
\(839\) 30.5133 22.1692i 1.05344 0.765366i 0.0805734 0.996749i \(-0.474325\pi\)
0.972863 + 0.231382i \(0.0743249\pi\)
\(840\) −0.293717 0.213398i −0.0101342 0.00736292i
\(841\) −4.56017 14.0348i −0.157247 0.483957i
\(842\) 4.16021 + 12.8038i 0.143370 + 0.441248i
\(843\) −10.5775 7.68497i −0.364307 0.264685i
\(844\) 10.0858 7.32779i 0.347169 0.252233i
\(845\) −2.03773 + 6.27150i −0.0701001 + 0.215746i
\(846\) 12.3056 0.423074
\(847\) −5.66947 9.42641i −0.194805 0.323895i
\(848\) −1.26869 −0.0435671
\(849\) −4.77522 + 14.6966i −0.163885 + 0.504386i
\(850\) 13.4973 9.80638i 0.462954 0.336356i
\(851\) −17.8284 12.9531i −0.611151 0.444027i
\(852\) 2.48109 + 7.63600i 0.0850007 + 0.261605i
\(853\) 2.87035 + 8.83403i 0.0982789 + 0.302471i 0.988094 0.153849i \(-0.0491670\pi\)
−0.889815 + 0.456321i \(0.849167\pi\)
\(854\) 6.05689 + 4.40059i 0.207262 + 0.150585i
\(855\) −1.37383 + 0.998146i −0.0469840 + 0.0341359i
\(856\) −4.39986 + 13.5414i −0.150384 + 0.462835i
\(857\) −29.7644 −1.01673 −0.508365 0.861141i \(-0.669750\pi\)
−0.508365 + 0.861141i \(0.669750\pi\)
\(858\) −2.07243 + 10.1975i −0.0707516 + 0.348138i
\(859\) 33.2611 1.13485 0.567427 0.823424i \(-0.307939\pi\)
0.567427 + 0.823424i \(0.307939\pi\)
\(860\) −0.451787 + 1.39046i −0.0154058 + 0.0474142i
\(861\) 0.669055 0.486097i 0.0228013 0.0165661i
\(862\) 17.5442 + 12.7466i 0.597558 + 0.434151i
\(863\) −5.73772 17.6589i −0.195314 0.601116i −0.999973 0.00737787i \(-0.997652\pi\)
0.804658 0.593738i \(-0.202348\pi\)
\(864\) 6.28115 + 19.3314i 0.213689 + 0.657668i
\(865\) −1.86539 1.35529i −0.0634253 0.0460812i
\(866\) −18.5850 + 13.5028i −0.631544 + 0.458844i
\(867\) 0.341645 1.05147i 0.0116029 0.0357100i
\(868\) −9.61454 −0.326339
\(869\) 13.0768 + 7.39477i 0.443599 + 0.250850i
\(870\) −0.403520 −0.0136806
\(871\) 2.56565 7.89627i 0.0869339 0.267555i
\(872\) −11.5311 + 8.37782i −0.390491 + 0.283709i
\(873\) −19.1765 13.9325i −0.649026 0.471545i
\(874\) 2.72992 + 8.40184i 0.0923411 + 0.284197i
\(875\) −0.684207 2.10577i −0.0231304 0.0711881i
\(876\) 3.89985 + 2.83341i 0.131764 + 0.0957321i
\(877\) 18.1965 13.2205i 0.614452 0.446426i −0.236527 0.971625i \(-0.576009\pi\)
0.850979 + 0.525199i \(0.176009\pi\)
\(878\) 8.08834 24.8934i 0.272968 0.840110i
\(879\) −0.281259 −0.00948664
\(880\) −0.226122 0.495898i −0.00762259 0.0167167i
\(881\) 7.06565 0.238048 0.119024 0.992891i \(-0.462023\pi\)
0.119024 + 0.992891i \(0.462023\pi\)
\(882\) 0.628998 1.93586i 0.0211795 0.0651837i
\(883\) 16.1304 11.7194i 0.542830 0.394389i −0.282305 0.959325i \(-0.591099\pi\)
0.825135 + 0.564936i \(0.191099\pi\)
\(884\) −31.9541 23.2160i −1.07473 0.780839i
\(885\) 0.405123 + 1.24684i 0.0136181 + 0.0419121i
\(886\) −2.48105 7.63590i −0.0833527 0.256533i
\(887\) −5.62656 4.08793i −0.188921 0.137259i 0.489304 0.872113i \(-0.337251\pi\)
−0.678226 + 0.734854i \(0.737251\pi\)
\(888\) 7.46253 5.42185i 0.250426 0.181945i
\(889\) −0.617194 + 1.89953i −0.0207000 + 0.0637081i
\(890\) 1.37045 0.0459376
\(891\) −13.9554 + 12.7933i −0.467522 + 0.428590i
\(892\) −0.998136 −0.0334201
\(893\) 5.44574 16.7603i 0.182235 0.560861i
\(894\) −2.81055 + 2.04198i −0.0939988 + 0.0682941i
\(895\) −4.21414 3.06175i −0.140863 0.102343i
\(896\) −2.87938 8.86181i −0.0961933 0.296052i
\(897\) −4.86088 14.9602i −0.162300 0.499508i
\(898\) −1.73468 1.26032i −0.0578872 0.0420575i
\(899\) −21.0354 + 15.2831i −0.701570 + 0.509721i
\(900\) −5.58909 + 17.2014i −0.186303 + 0.573382i
\(901\) 7.44650 0.248079
\(902\) −3.42822 + 0.391342i −0.114147 + 0.0130303i
\(903\) 2.90983 0.0968331
\(904\) −13.4575 + 41.4179i −0.447590 + 1.37754i
\(905\) −2.46916 + 1.79395i −0.0820776 + 0.0596329i
\(906\) 3.16424 + 2.29895i 0.105125 + 0.0763776i
\(907\) −7.24340 22.2929i −0.240513 0.740224i −0.996342 0.0854543i \(-0.972766\pi\)
0.755829 0.654769i \(-0.227234\pi\)
\(908\) 2.29489 + 7.06294i 0.0761586 + 0.234392i
\(909\) −40.6878 29.5614i −1.34953 0.980490i
\(910\) 0.913888 0.663978i 0.0302951 0.0220107i
\(911\) 14.4650 44.5186i 0.479246 1.47497i −0.360899 0.932605i \(-0.617530\pi\)
0.840145 0.542362i \(-0.182470\pi\)
\(912\) 1.33048 0.0440564
\(913\) 37.1825 4.24450i 1.23056 0.140473i
\(914\) 31.3563 1.03718
\(915\) 0.409219 1.25945i 0.0135284 0.0416360i
\(916\) −7.46078 + 5.42058i −0.246511 + 0.179101i
\(917\) 1.10843 + 0.805321i 0.0366036 + 0.0265940i
\(918\) −3.61594 11.1287i −0.119344 0.367302i
\(919\) 3.28402 + 10.1072i 0.108330 + 0.333405i 0.990498 0.137530i \(-0.0439165\pi\)
−0.882168 + 0.470935i \(0.843916\pi\)
\(920\) −1.85248 1.34590i −0.0610744 0.0443732i
\(921\) 4.01789 2.91917i 0.132394 0.0961898i
\(922\) 8.22278 25.3071i 0.270803 0.833445i
\(923\) −60.7848 −2.00075
\(924\) −2.10858 + 1.93299i −0.0693671 + 0.0635907i
\(925\) 27.9876 0.920228
\(926\) −0.169945 + 0.523036i −0.00558473 + 0.0171880i
\(927\) 34.3933 24.9882i 1.12962 0.820720i
\(928\) −17.8739 12.9861i −0.586738 0.426290i
\(929\) −11.3319 34.8762i −0.371789 1.14425i −0.945619 0.325275i \(-0.894543\pi\)
0.573830 0.818974i \(-0.305457\pi\)
\(930\) −0.227635 0.700590i −0.00746446 0.0229733i
\(931\) −2.35829 1.71340i −0.0772898 0.0561543i
\(932\) −10.7900 + 7.83938i −0.353438 + 0.256787i
\(933\) 0.0261579 0.0805059i 0.000856373 0.00263564i
\(934\) 22.2302 0.727393
\(935\) 1.32721 + 2.91064i 0.0434043 + 0.0951880i
\(936\) −45.1290 −1.47509
\(937\) −12.4278 + 38.2490i −0.406000 + 1.24954i 0.514057 + 0.857756i \(0.328142\pi\)
−0.920057 + 0.391784i \(0.871858\pi\)
\(938\) −0.799801 + 0.581090i −0.0261144 + 0.0189732i
\(939\) 7.64497 + 5.55439i 0.249484 + 0.181261i
\(940\) 0.580114 + 1.78541i 0.0189212 + 0.0582336i
\(941\) 7.69751 + 23.6905i 0.250932 + 0.772288i 0.994604 + 0.103744i \(0.0330823\pi\)
−0.743672 + 0.668544i \(0.766918\pi\)
\(942\) 7.83371 + 5.69152i 0.255236 + 0.185440i
\(943\) 4.21975 3.06583i 0.137414 0.0998371i
\(944\) −2.17555 + 6.69565i −0.0708081 + 0.217925i
\(945\) −0.772605 −0.0251328
\(946\) −10.5680 5.97609i −0.343595 0.194299i
\(947\) −32.2061 −1.04656 −0.523279 0.852161i \(-0.675292\pi\)
−0.523279 + 0.852161i \(0.675292\pi\)
\(948\) 1.20722 3.71543i 0.0392085 0.120671i
\(949\) −29.5246 + 21.4508i −0.958408 + 0.696324i
\(950\) −9.07688 6.59474i −0.294493 0.213962i
\(951\) −6.30101 19.3925i −0.204324 0.628846i
\(952\) 3.53615 + 10.8831i 0.114607 + 0.352725i
\(953\) −36.4552 26.4863i −1.18090 0.857975i −0.188628 0.982049i \(-0.560404\pi\)
−0.992273 + 0.124074i \(0.960404\pi\)
\(954\) 2.82896 2.05536i 0.0915908 0.0665446i
\(955\) 0.826849 2.54478i 0.0267562 0.0823471i
\(956\) −37.4650 −1.21170
\(957\) −1.54066 + 7.58090i −0.0498024 + 0.245056i
\(958\) 3.96296 0.128038
\(959\) −0.772308 + 2.37692i −0.0249391 + 0.0767547i
\(960\) 0.342058 0.248519i 0.0110399 0.00802093i
\(961\) −13.3216 9.67867i −0.429727 0.312215i
\(962\) 8.86901 + 27.2960i 0.285948 + 0.880059i
\(963\) 4.36332 + 13.4289i 0.140606 + 0.432741i
\(964\) 21.3000 + 15.4754i 0.686028 + 0.498428i
\(965\) 2.85941 2.07748i 0.0920476 0.0668765i
\(966\) −0.578793 + 1.78134i −0.0186224 + 0.0573138i
\(967\) 1.81387 0.0583300 0.0291650 0.999575i \(-0.490715\pi\)
0.0291650 + 0.999575i \(0.490715\pi\)
\(968\) 28.2925 6.54464i 0.909355 0.210353i
\(969\) −7.80912 −0.250865
\(970\) −0.484029 + 1.48969i −0.0155412 + 0.0478310i
\(971\) −18.6510 + 13.5507i −0.598539 + 0.434864i −0.845360 0.534197i \(-0.820614\pi\)
0.246821 + 0.969061i \(0.420614\pi\)
\(972\) 15.7431 + 11.4380i 0.504959 + 0.366874i
\(973\) 1.47172 + 4.52950i 0.0471813 + 0.145209i
\(974\) −7.01266 21.5827i −0.224700 0.691555i
\(975\) 16.1622 + 11.7425i 0.517605 + 0.376062i
\(976\) 5.75325 4.17998i 0.184157 0.133798i
\(977\) −2.19232 + 6.74726i −0.0701385 + 0.215864i −0.979981 0.199089i \(-0.936202\pi\)
0.909843 + 0.414953i \(0.136202\pi\)
\(978\) −3.57236 −0.114232
\(979\) 5.23244 25.7466i 0.167229 0.822863i
\(980\) 0.310525 0.00991935
\(981\) −4.36789 + 13.4430i −0.139456 + 0.429202i
\(982\) 18.9605 13.7756i 0.605053 0.439597i
\(983\) −31.0260 22.5417i −0.989576 0.718969i −0.0297474 0.999557i \(-0.509470\pi\)
−0.959828 + 0.280589i \(0.909470\pi\)
\(984\) 0.674659 + 2.07639i 0.0215073 + 0.0661928i
\(985\) −0.846005 2.60374i −0.0269560 0.0829619i
\(986\) 10.2896 + 7.47586i 0.327689 + 0.238080i
\(987\) 3.02277 2.19617i 0.0962158 0.0699048i
\(988\) −8.20806 + 25.2618i −0.261133 + 0.803685i
\(989\) 18.3524 0.583572
\(990\) 1.30760 + 0.739431i 0.0415581 + 0.0235007i
\(991\) 20.2722 0.643967 0.321984 0.946745i \(-0.395650\pi\)
0.321984 + 0.946745i \(0.395650\pi\)
\(992\) 12.4634 38.3583i 0.395712 1.21788i
\(993\) −14.7667 + 10.7287i −0.468608 + 0.340464i
\(994\) 5.85546 + 4.25424i 0.185724 + 0.134936i
\(995\) −1.04940 3.22971i −0.0332681 0.102389i
\(996\) −3.00735 9.25568i −0.0952916 0.293277i
\(997\) −12.4675 9.05819i −0.394851 0.286876i 0.372590 0.927996i \(-0.378470\pi\)
−0.767440 + 0.641120i \(0.778470\pi\)
\(998\) 3.74319 2.71959i 0.118489 0.0860871i
\(999\) 6.06593 18.6690i 0.191918 0.590662i
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 77.2.f.a.64.1 8
3.2 odd 2 693.2.m.g.64.2 8
7.2 even 3 539.2.q.c.361.2 16
7.3 odd 6 539.2.q.b.471.1 16
7.4 even 3 539.2.q.c.471.1 16
7.5 odd 6 539.2.q.b.361.2 16
7.6 odd 2 539.2.f.d.295.1 8
11.2 odd 10 847.2.f.s.729.1 8
11.3 even 5 847.2.f.p.323.2 8
11.4 even 5 847.2.a.l.1.2 4
11.5 even 5 inner 77.2.f.a.71.1 yes 8
11.6 odd 10 847.2.f.q.148.2 8
11.7 odd 10 847.2.a.k.1.3 4
11.8 odd 10 847.2.f.s.323.1 8
11.9 even 5 847.2.f.p.729.2 8
11.10 odd 2 847.2.f.q.372.2 8
33.5 odd 10 693.2.m.g.379.2 8
33.26 odd 10 7623.2.a.ch.1.3 4
33.29 even 10 7623.2.a.co.1.2 4
77.5 odd 30 539.2.q.b.214.1 16
77.16 even 15 539.2.q.c.214.1 16
77.27 odd 10 539.2.f.d.148.1 8
77.38 odd 30 539.2.q.b.324.2 16
77.48 odd 10 5929.2.a.bi.1.2 4
77.60 even 15 539.2.q.c.324.2 16
77.62 even 10 5929.2.a.bb.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.f.a.64.1 8 1.1 even 1 trivial
77.2.f.a.71.1 yes 8 11.5 even 5 inner
539.2.f.d.148.1 8 77.27 odd 10
539.2.f.d.295.1 8 7.6 odd 2
539.2.q.b.214.1 16 77.5 odd 30
539.2.q.b.324.2 16 77.38 odd 30
539.2.q.b.361.2 16 7.5 odd 6
539.2.q.b.471.1 16 7.3 odd 6
539.2.q.c.214.1 16 77.16 even 15
539.2.q.c.324.2 16 77.60 even 15
539.2.q.c.361.2 16 7.2 even 3
539.2.q.c.471.1 16 7.4 even 3
693.2.m.g.64.2 8 3.2 odd 2
693.2.m.g.379.2 8 33.5 odd 10
847.2.a.k.1.3 4 11.7 odd 10
847.2.a.l.1.2 4 11.4 even 5
847.2.f.p.323.2 8 11.3 even 5
847.2.f.p.729.2 8 11.9 even 5
847.2.f.q.148.2 8 11.6 odd 10
847.2.f.q.372.2 8 11.10 odd 2
847.2.f.s.323.1 8 11.8 odd 10
847.2.f.s.729.1 8 11.2 odd 10
5929.2.a.bb.1.3 4 77.62 even 10
5929.2.a.bi.1.2 4 77.48 odd 10
7623.2.a.ch.1.3 4 33.26 odd 10
7623.2.a.co.1.2 4 33.29 even 10