Properties

Label 930.2.bg.g.541.1
Level $930$
Weight $2$
Character 930.541
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
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] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), degree \(8\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 541.1
Character \(\chi\) \(=\) 930.541
Dual form 930.2.bg.g.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.272387 + 2.59159i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.272387 + 2.59159i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-4.40434 + 1.96094i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(-1.10502 - 0.234879i) q^{13} +(2.38057 + 1.05990i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.16953 - 1.85640i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-3.63266 + 0.772145i) q^{19} +(0.913545 - 0.406737i) q^{20} +(1.74366 + 1.93653i) q^{21} +(0.503948 + 4.79474i) q^{22} +(-3.62530 + 2.63393i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.564853 + 0.978355i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.74366 - 1.93653i) q^{28} +(0.109322 - 0.336457i) q^{29} +1.00000 q^{30} +(-3.55116 + 4.28827i) q^{31} +1.00000 q^{32} +(-1.48982 + 4.58519i) q^{33} +(-3.05399 + 3.39180i) q^{34} +(-2.10819 - 1.53169i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.47405 - 4.28518i) q^{37} +(-0.388199 + 3.69347i) q^{38} +(-0.913952 + 0.664025i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-4.05295 - 4.50126i) q^{41} +(2.38057 - 1.05990i) q^{42} +(8.37667 - 1.78052i) q^{43} +(4.71580 + 1.00237i) q^{44} +(0.913545 + 0.406737i) q^{45} +(1.38474 + 4.26179i) q^{46} +(1.56658 + 4.82145i) q^{47} +(0.913545 + 0.406737i) q^{48} +(0.204908 + 0.0435545i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(-4.16953 + 1.85640i) q^{51} +(0.755921 + 0.839536i) q^{52} +(0.656704 + 6.24812i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(0.503948 - 4.79474i) q^{55} +(-1.30293 - 2.25674i) q^{56} +(-1.85691 + 3.21626i) q^{57} +(-0.286207 - 0.207942i) q^{58} +(0.787413 - 0.874510i) q^{59} +(0.309017 - 0.951057i) q^{60} +9.97448 q^{61} +(2.98102 + 4.70250i) q^{62} +2.60586 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.755921 - 0.839536i) q^{65} +(3.90040 + 2.83380i) q^{66} +(-0.256055 + 0.443500i) q^{67} +(2.28206 + 3.95264i) q^{68} +(-0.468404 + 4.45657i) q^{69} +(-2.10819 + 1.53169i) q^{70} +(-1.17136 - 11.1448i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-0.837072 + 0.372688i) q^{73} +(-4.83998 + 1.02877i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(3.39274 + 1.51054i) q^{76} +(-3.88226 - 11.9484i) q^{77} +(0.349099 + 1.07442i) q^{78} +(7.45987 + 3.32135i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-5.53338 + 2.46362i) q^{82} +(6.59577 + 7.32534i) q^{83} +(-0.272387 - 2.59159i) q^{84} +(3.69245 - 2.68272i) q^{85} +(0.895161 - 8.51689i) q^{86} +(-0.176886 - 0.306375i) q^{87} +(2.41058 - 4.17524i) q^{88} +(3.79884 + 2.76002i) q^{89} +(0.669131 - 0.743145i) q^{90} +(0.909703 - 2.79978i) q^{91} +4.48112 q^{92} +(0.810617 + 5.50844i) q^{93} +5.06957 q^{94} +(1.14763 - 3.53205i) q^{95} +(0.669131 - 0.743145i) q^{96} +(-14.6203 - 10.6223i) q^{97} +(0.104743 - 0.181420i) q^{98} +(2.41058 + 4.17524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{11}{15}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) 0.669131 0.743145i 0.386323 0.429055i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −0.272387 + 2.59159i −0.102952 + 0.979528i 0.814090 + 0.580738i \(0.197236\pi\)
−0.917043 + 0.398789i \(0.869431\pi\)
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) −0.104528 0.994522i −0.0348428 0.331507i
\(10\) 0.669131 + 0.743145i 0.211598 + 0.235003i
\(11\) −4.40434 + 1.96094i −1.32796 + 0.591246i −0.943339 0.331829i \(-0.892334\pi\)
−0.384620 + 0.923075i \(0.625668\pi\)
\(12\) −0.978148 + 0.207912i −0.282367 + 0.0600189i
\(13\) −1.10502 0.234879i −0.306477 0.0651438i 0.0521057 0.998642i \(-0.483407\pi\)
−0.358583 + 0.933498i \(0.616740\pi\)
\(14\) 2.38057 + 1.05990i 0.636235 + 0.283270i
\(15\) 0.309017 + 0.951057i 0.0797878 + 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −4.16953 1.85640i −1.01126 0.450242i −0.166875 0.985978i \(-0.553367\pi\)
−0.844385 + 0.535736i \(0.820034\pi\)
\(18\) −0.978148 0.207912i −0.230552 0.0490053i
\(19\) −3.63266 + 0.772145i −0.833389 + 0.177142i −0.604797 0.796380i \(-0.706746\pi\)
−0.228592 + 0.973522i \(0.573412\pi\)
\(20\) 0.913545 0.406737i 0.204275 0.0909491i
\(21\) 1.74366 + 1.93653i 0.380498 + 0.422586i
\(22\) 0.503948 + 4.79474i 0.107442 + 1.02224i
\(23\) −3.62530 + 2.63393i −0.755927 + 0.549213i −0.897658 0.440692i \(-0.854733\pi\)
0.141731 + 0.989905i \(0.454733\pi\)
\(24\) −0.104528 + 0.994522i −0.0213368 + 0.203006i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −0.564853 + 0.978355i −0.110777 + 0.191871i
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 1.74366 1.93653i 0.329521 0.365970i
\(29\) 0.109322 0.336457i 0.0203005 0.0624785i −0.940393 0.340089i \(-0.889543\pi\)
0.960694 + 0.277611i \(0.0895426\pi\)
\(30\) 1.00000 0.182574
\(31\) −3.55116 + 4.28827i −0.637807 + 0.770196i
\(32\) 1.00000 0.176777
\(33\) −1.48982 + 4.58519i −0.259344 + 0.798179i
\(34\) −3.05399 + 3.39180i −0.523755 + 0.581689i
\(35\) −2.10819 1.53169i −0.356349 0.258902i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −2.47405 4.28518i −0.406732 0.704480i 0.587790 0.809014i \(-0.299998\pi\)
−0.994521 + 0.104534i \(0.966665\pi\)
\(38\) −0.388199 + 3.69347i −0.0629742 + 0.599160i
\(39\) −0.913952 + 0.664025i −0.146349 + 0.106329i
\(40\) −0.104528 0.994522i −0.0165274 0.157248i
\(41\) −4.05295 4.50126i −0.632964 0.702978i 0.338285 0.941044i \(-0.390153\pi\)
−0.971249 + 0.238066i \(0.923487\pi\)
\(42\) 2.38057 1.05990i 0.367330 0.163546i
\(43\) 8.37667 1.78052i 1.27743 0.271526i 0.481248 0.876584i \(-0.340184\pi\)
0.796181 + 0.605058i \(0.206850\pi\)
\(44\) 4.71580 + 1.00237i 0.710934 + 0.151114i
\(45\) 0.913545 + 0.406737i 0.136183 + 0.0606327i
\(46\) 1.38474 + 4.26179i 0.204169 + 0.628367i
\(47\) 1.56658 + 4.82145i 0.228510 + 0.703280i 0.997916 + 0.0645211i \(0.0205520\pi\)
−0.769407 + 0.638759i \(0.779448\pi\)
\(48\) 0.913545 + 0.406737i 0.131859 + 0.0587074i
\(49\) 0.204908 + 0.0435545i 0.0292725 + 0.00622207i
\(50\) −0.978148 + 0.207912i −0.138331 + 0.0294032i
\(51\) −4.16953 + 1.85640i −0.583851 + 0.259947i
\(52\) 0.755921 + 0.839536i 0.104827 + 0.116423i
\(53\) 0.656704 + 6.24812i 0.0902052 + 0.858246i 0.942280 + 0.334826i \(0.108677\pi\)
−0.852075 + 0.523420i \(0.824656\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 0.503948 4.79474i 0.0679523 0.646523i
\(56\) −1.30293 2.25674i −0.174111 0.301570i
\(57\) −1.85691 + 3.21626i −0.245953 + 0.426004i
\(58\) −0.286207 0.207942i −0.0375809 0.0273041i
\(59\) 0.787413 0.874510i 0.102512 0.113852i −0.689705 0.724090i \(-0.742260\pi\)
0.792218 + 0.610239i \(0.208927\pi\)
\(60\) 0.309017 0.951057i 0.0398939 0.122781i
\(61\) 9.97448 1.27710 0.638551 0.769580i \(-0.279534\pi\)
0.638551 + 0.769580i \(0.279534\pi\)
\(62\) 2.98102 + 4.70250i 0.378590 + 0.597218i
\(63\) 2.60586 0.328308
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 0.755921 0.839536i 0.0937605 0.104132i
\(66\) 3.90040 + 2.83380i 0.480106 + 0.348817i
\(67\) −0.256055 + 0.443500i −0.0312821 + 0.0541821i −0.881243 0.472664i \(-0.843292\pi\)
0.849961 + 0.526846i \(0.176626\pi\)
\(68\) 2.28206 + 3.95264i 0.276740 + 0.479329i
\(69\) −0.468404 + 4.45657i −0.0563892 + 0.536508i
\(70\) −2.10819 + 1.53169i −0.251976 + 0.183072i
\(71\) −1.17136 11.1448i −0.139015 1.32264i −0.812292 0.583251i \(-0.801780\pi\)
0.673277 0.739391i \(-0.264886\pi\)
\(72\) 0.669131 + 0.743145i 0.0788578 + 0.0875805i
\(73\) −0.837072 + 0.372688i −0.0979719 + 0.0436199i −0.455137 0.890421i \(-0.650410\pi\)
0.357166 + 0.934041i \(0.383743\pi\)
\(74\) −4.83998 + 1.02877i −0.562636 + 0.119592i
\(75\) −0.978148 0.207912i −0.112947 0.0240076i
\(76\) 3.39274 + 1.51054i 0.389174 + 0.173271i
\(77\) −3.88226 11.9484i −0.442425 1.36164i
\(78\) 0.349099 + 1.07442i 0.0395276 + 0.121654i
\(79\) 7.45987 + 3.32135i 0.839301 + 0.373681i 0.780933 0.624614i \(-0.214744\pi\)
0.0583674 + 0.998295i \(0.481411\pi\)
\(80\) −0.978148 0.207912i −0.109360 0.0232452i
\(81\) −0.978148 + 0.207912i −0.108683 + 0.0231013i
\(82\) −5.53338 + 2.46362i −0.611059 + 0.272061i
\(83\) 6.59577 + 7.32534i 0.723980 + 0.804061i 0.986998 0.160730i \(-0.0513848\pi\)
−0.263019 + 0.964791i \(0.584718\pi\)
\(84\) −0.272387 2.59159i −0.0297198 0.282765i
\(85\) 3.69245 2.68272i 0.400503 0.290982i
\(86\) 0.895161 8.51689i 0.0965277 0.918400i
\(87\) −0.176886 0.306375i −0.0189642 0.0328469i
\(88\) 2.41058 4.17524i 0.256968 0.445082i
\(89\) 3.79884 + 2.76002i 0.402676 + 0.292561i 0.770630 0.637283i \(-0.219942\pi\)
−0.367954 + 0.929844i \(0.619942\pi\)
\(90\) 0.669131 0.743145i 0.0705326 0.0783343i
\(91\) 0.909703 2.79978i 0.0953628 0.293496i
\(92\) 4.48112 0.467189
\(93\) 0.810617 + 5.50844i 0.0840570 + 0.571199i
\(94\) 5.06957 0.522886
\(95\) 1.14763 3.53205i 0.117745 0.362380i
\(96\) 0.669131 0.743145i 0.0682929 0.0758469i
\(97\) −14.6203 10.6223i −1.48447 1.07853i −0.976082 0.217403i \(-0.930241\pi\)
−0.508388 0.861128i \(-0.669759\pi\)
\(98\) 0.104743 0.181420i 0.0105806 0.0183262i
\(99\) 2.41058 + 4.17524i 0.242272 + 0.419628i
\(100\) −0.104528 + 0.994522i −0.0104528 + 0.0994522i
\(101\) −7.47921 + 5.43397i −0.744209 + 0.540700i −0.894027 0.448014i \(-0.852132\pi\)
0.149817 + 0.988714i \(0.452132\pi\)
\(102\) 0.477080 + 4.53912i 0.0472380 + 0.449440i
\(103\) 5.96889 + 6.62912i 0.588132 + 0.653186i 0.961599 0.274457i \(-0.0884980\pi\)
−0.373468 + 0.927643i \(0.621831\pi\)
\(104\) 1.03204 0.459493i 0.101200 0.0450570i
\(105\) −2.54892 + 0.541789i −0.248749 + 0.0528732i
\(106\) 6.14525 + 1.30621i 0.596879 + 0.126871i
\(107\) −12.9566 5.76863i −1.25256 0.557675i −0.330163 0.943924i \(-0.607104\pi\)
−0.922394 + 0.386249i \(0.873770\pi\)
\(108\) 0.309017 + 0.951057i 0.0297352 + 0.0915155i
\(109\) 5.06859 + 15.5995i 0.485483 + 1.49416i 0.831280 + 0.555854i \(0.187609\pi\)
−0.345797 + 0.938309i \(0.612391\pi\)
\(110\) −4.40434 1.96094i −0.419938 0.186968i
\(111\) −4.83998 1.02877i −0.459390 0.0976464i
\(112\) −2.54892 + 0.541789i −0.240850 + 0.0511943i
\(113\) 0.632823 0.281751i 0.0595310 0.0265049i −0.376755 0.926313i \(-0.622960\pi\)
0.436286 + 0.899808i \(0.356294\pi\)
\(114\) 2.48503 + 2.75990i 0.232744 + 0.258488i
\(115\) −0.468404 4.45657i −0.0436789 0.415577i
\(116\) −0.286207 + 0.207942i −0.0265737 + 0.0193069i
\(117\) −0.118087 + 1.12352i −0.0109171 + 0.103869i
\(118\) −0.588385 1.01911i −0.0541652 0.0938169i
\(119\) 5.94673 10.3000i 0.545136 0.944203i
\(120\) −0.809017 0.587785i −0.0738528 0.0536572i
\(121\) 8.19252 9.09872i 0.744775 0.827156i
\(122\) 3.08228 9.48629i 0.279057 0.858849i
\(123\) −6.05704 −0.546145
\(124\) 5.39353 1.38196i 0.484353 0.124104i
\(125\) 1.00000 0.0894427
\(126\) 0.805256 2.47832i 0.0717379 0.220786i
\(127\) 2.04443 2.27057i 0.181414 0.201480i −0.645578 0.763694i \(-0.723384\pi\)
0.826992 + 0.562214i \(0.190050\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) 4.28190 7.41647i 0.377001 0.652984i
\(130\) −0.564853 0.978355i −0.0495409 0.0858074i
\(131\) 0.469803 4.46988i 0.0410469 0.390535i −0.954640 0.297761i \(-0.903760\pi\)
0.995687 0.0927736i \(-0.0295733\pi\)
\(132\) 3.90040 2.83380i 0.339486 0.246651i
\(133\) −1.01159 9.62467i −0.0877163 0.834565i
\(134\) 0.342668 + 0.380572i 0.0296020 + 0.0328764i
\(135\) 0.913545 0.406737i 0.0786255 0.0350063i
\(136\) 4.46438 0.948934i 0.382818 0.0813704i
\(137\) −11.3480 2.41208i −0.969522 0.206078i −0.304178 0.952615i \(-0.598382\pi\)
−0.665344 + 0.746537i \(0.731715\pi\)
\(138\) 4.09370 + 1.82263i 0.348479 + 0.155153i
\(139\) 1.42643 + 4.39009i 0.120988 + 0.372363i 0.993149 0.116856i \(-0.0372818\pi\)
−0.872161 + 0.489219i \(0.837282\pi\)
\(140\) 0.805256 + 2.47832i 0.0680565 + 0.209456i
\(141\) 4.63128 + 2.06198i 0.390024 + 0.173650i
\(142\) −10.9613 2.32989i −0.919851 0.195520i
\(143\) 5.32747 1.13239i 0.445506 0.0946951i
\(144\) 0.913545 0.406737i 0.0761288 0.0338947i
\(145\) 0.236720 + 0.262904i 0.0196585 + 0.0218330i
\(146\) 0.0957783 + 0.911270i 0.00792667 + 0.0754172i
\(147\) 0.169477 0.123132i 0.0139782 0.0101558i
\(148\) −0.517218 + 4.92100i −0.0425150 + 0.404504i
\(149\) −5.03092 8.71382i −0.412149 0.713864i 0.582975 0.812490i \(-0.301888\pi\)
−0.995125 + 0.0986263i \(0.968555\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 9.19304 + 6.67914i 0.748119 + 0.543540i 0.895243 0.445578i \(-0.147002\pi\)
−0.147124 + 0.989118i \(0.547002\pi\)
\(152\) 2.48503 2.75990i 0.201562 0.223858i
\(153\) −1.41039 + 4.34074i −0.114023 + 0.350928i
\(154\) −12.5633 −1.01238
\(155\) −1.93817 5.21953i −0.155678 0.419243i
\(156\) 1.12971 0.0904489
\(157\) −4.91417 + 15.1243i −0.392193 + 1.20705i 0.538932 + 0.842349i \(0.318828\pi\)
−0.931126 + 0.364698i \(0.881172\pi\)
\(158\) 5.46402 6.06840i 0.434694 0.482776i
\(159\) 5.08268 + 3.69278i 0.403083 + 0.292857i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −5.83858 10.1127i −0.460145 0.796994i
\(162\) −0.104528 + 0.994522i −0.00821253 + 0.0781370i
\(163\) −11.6088 + 8.43427i −0.909270 + 0.660623i −0.940830 0.338879i \(-0.889952\pi\)
0.0315604 + 0.999502i \(0.489952\pi\)
\(164\) 0.633133 + 6.02386i 0.0494394 + 0.470384i
\(165\) −3.22598 3.58282i −0.251142 0.278922i
\(166\) 9.00502 4.00929i 0.698925 0.311181i
\(167\) −15.5653 + 3.30851i −1.20448 + 0.256021i −0.766072 0.642755i \(-0.777792\pi\)
−0.438410 + 0.898775i \(0.644458\pi\)
\(168\) −2.54892 0.541789i −0.196653 0.0417999i
\(169\) −10.7102 4.76848i −0.823861 0.366806i
\(170\) −1.41039 4.34074i −0.108172 0.332919i
\(171\) 1.14763 + 3.53205i 0.0877616 + 0.270102i
\(172\) −7.82343 3.48321i −0.596531 0.265593i
\(173\) −23.1759 4.92618i −1.76203 0.374531i −0.790688 0.612219i \(-0.790277\pi\)
−0.971341 + 0.237689i \(0.923610\pi\)
\(174\) −0.346041 + 0.0735533i −0.0262333 + 0.00557606i
\(175\) 2.38057 1.05990i 0.179954 0.0801209i
\(176\) −3.22598 3.58282i −0.243168 0.270065i
\(177\) −0.123006 1.17032i −0.00924569 0.0879669i
\(178\) 3.79884 2.76002i 0.284735 0.206872i
\(179\) −0.765267 + 7.28103i −0.0571987 + 0.544210i 0.927974 + 0.372645i \(0.121549\pi\)
−0.985173 + 0.171565i \(0.945118\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 5.73103 9.92643i 0.425984 0.737826i −0.570528 0.821278i \(-0.693261\pi\)
0.996512 + 0.0834524i \(0.0265947\pi\)
\(182\) −2.38163 1.73036i −0.176538 0.128263i
\(183\) 6.67423 7.41248i 0.493373 0.547947i
\(184\) 1.38474 4.26179i 0.102084 0.314184i
\(185\) 4.94810 0.363792
\(186\) 5.48933 + 0.931259i 0.402497 + 0.0682832i
\(187\) 22.0043 1.60912
\(188\) 1.56658 4.82145i 0.114255 0.351640i
\(189\) 1.74366 1.93653i 0.126833 0.140862i
\(190\) −3.00454 2.18292i −0.217972 0.158366i
\(191\) 3.00177 5.19922i 0.217201 0.376203i −0.736750 0.676165i \(-0.763641\pi\)
0.953951 + 0.299962i \(0.0969741\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.06454 + 19.6427i −0.148609 + 1.41392i 0.625184 + 0.780477i \(0.285024\pi\)
−0.773793 + 0.633439i \(0.781643\pi\)
\(194\) −14.6203 + 10.6223i −1.04968 + 0.762636i
\(195\) −0.118087 1.12352i −0.00845635 0.0804568i
\(196\) −0.140173 0.155678i −0.0100124 0.0111199i
\(197\) −15.7233 + 7.00045i −1.12024 + 0.498762i −0.881434 0.472307i \(-0.843422\pi\)
−0.238803 + 0.971068i \(0.576755\pi\)
\(198\) 4.71580 1.00237i 0.335137 0.0712356i
\(199\) 23.0549 + 4.90047i 1.63432 + 0.347385i 0.931431 0.363917i \(-0.118561\pi\)
0.702887 + 0.711302i \(0.251894\pi\)
\(200\) 0.913545 + 0.406737i 0.0645974 + 0.0287606i
\(201\) 0.158251 + 0.487045i 0.0111621 + 0.0343535i
\(202\) 2.85681 + 8.79234i 0.201004 + 0.618627i
\(203\) 0.842180 + 0.374963i 0.0591094 + 0.0263172i
\(204\) 4.46438 + 0.948934i 0.312569 + 0.0664387i
\(205\) 5.92468 1.25933i 0.413797 0.0879553i
\(206\) 8.14915 3.62824i 0.567778 0.252791i
\(207\) 2.99845 + 3.33012i 0.208407 + 0.231459i
\(208\) −0.118087 1.12352i −0.00818783 0.0779020i
\(209\) 14.4853 10.5242i 1.00197 0.727975i
\(210\) −0.272387 + 2.59159i −0.0187965 + 0.178836i
\(211\) 3.14135 + 5.44098i 0.216260 + 0.374573i 0.953662 0.300882i \(-0.0972809\pi\)
−0.737402 + 0.675454i \(0.763948\pi\)
\(212\) 3.14127 5.44084i 0.215743 0.373678i
\(213\) −9.06598 6.58682i −0.621191 0.451321i
\(214\) −9.49009 + 10.5398i −0.648729 + 0.720487i
\(215\) −2.64636 + 8.14466i −0.180480 + 0.555461i
\(216\) 1.00000 0.0680414
\(217\) −10.1461 10.3712i −0.688765 0.704043i
\(218\) 16.4023 1.11090
\(219\) −0.283149 + 0.871443i −0.0191334 + 0.0588867i
\(220\) −3.22598 + 3.58282i −0.217496 + 0.241553i
\(221\) 4.17139 + 3.03069i 0.280598 + 0.203866i
\(222\) −2.47405 + 4.28518i −0.166048 + 0.287603i
\(223\) −9.60317 16.6332i −0.643076 1.11384i −0.984742 0.174018i \(-0.944325\pi\)
0.341667 0.939821i \(-0.389009\pi\)
\(224\) −0.272387 + 2.59159i −0.0181996 + 0.173158i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −0.0724080 0.688916i −0.00481651 0.0458260i
\(227\) −0.914857 1.01605i −0.0607212 0.0674377i 0.712019 0.702160i \(-0.247781\pi\)
−0.772740 + 0.634723i \(0.781114\pi\)
\(228\) 3.39274 1.51054i 0.224690 0.100038i
\(229\) 0.296609 0.0630462i 0.0196005 0.00416621i −0.198101 0.980182i \(-0.563477\pi\)
0.217702 + 0.976015i \(0.430144\pi\)
\(230\) −4.38319 0.931676i −0.289019 0.0614329i
\(231\) −11.4771 5.10994i −0.755138 0.336209i
\(232\) 0.109322 + 0.336457i 0.00717731 + 0.0220895i
\(233\) 4.26854 + 13.1372i 0.279642 + 0.860648i 0.987954 + 0.154749i \(0.0494569\pi\)
−0.708312 + 0.705899i \(0.750543\pi\)
\(234\) 1.03204 + 0.459493i 0.0674665 + 0.0300380i
\(235\) −4.95879 1.05402i −0.323476 0.0687569i
\(236\) −1.15105 + 0.244664i −0.0749273 + 0.0159263i
\(237\) 7.45987 3.32135i 0.484571 0.215745i
\(238\) −7.95828 8.83857i −0.515859 0.572919i
\(239\) −1.94168 18.4738i −0.125597 1.19497i −0.857835 0.513925i \(-0.828191\pi\)
0.732239 0.681048i \(-0.238476\pi\)
\(240\) −0.809017 + 0.587785i −0.0522218 + 0.0379414i
\(241\) 1.57963 15.0292i 0.101753 0.968114i −0.817894 0.575369i \(-0.804859\pi\)
0.919647 0.392746i \(-0.128475\pi\)
\(242\) −6.12176 10.6032i −0.393522 0.681600i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −8.06952 5.86285i −0.516598 0.375331i
\(245\) −0.140173 + 0.155678i −0.00895533 + 0.00994590i
\(246\) −1.87173 + 5.76058i −0.119337 + 0.367281i
\(247\) 4.19552 0.266955
\(248\) 0.352366 5.55660i 0.0223753 0.352845i
\(249\) 9.85722 0.624676
\(250\) 0.309017 0.951057i 0.0195440 0.0601501i
\(251\) −8.64519 + 9.60145i −0.545679 + 0.606038i −0.951400 0.307959i \(-0.900354\pi\)
0.405720 + 0.913997i \(0.367021\pi\)
\(252\) −2.10819 1.53169i −0.132803 0.0964872i
\(253\) 10.8021 18.7097i 0.679121 1.17627i
\(254\) −1.52767 2.64601i −0.0958548 0.166025i
\(255\) 0.477080 4.53912i 0.0298759 0.284251i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 0.361744 + 3.44176i 0.0225650 + 0.214691i 0.999994 + 0.00342784i \(0.00109112\pi\)
−0.977429 + 0.211263i \(0.932242\pi\)
\(258\) −5.73030 6.36415i −0.356753 0.396215i
\(259\) 11.7793 5.24449i 0.731932 0.325877i
\(260\) −1.10502 + 0.234879i −0.0685304 + 0.0145666i
\(261\) −0.346041 0.0735533i −0.0214194 0.00455283i
\(262\) −4.10593 1.82808i −0.253665 0.112939i
\(263\) −4.44752 13.6881i −0.274246 0.844042i −0.989418 0.145094i \(-0.953652\pi\)
0.715172 0.698949i \(-0.246348\pi\)
\(264\) −1.48982 4.58519i −0.0916920 0.282199i
\(265\) −5.73938 2.55534i −0.352568 0.156973i
\(266\) −9.46620 2.01210i −0.580410 0.123370i
\(267\) 4.59301 0.976275i 0.281088 0.0597471i
\(268\) 0.467835 0.208294i 0.0285776 0.0127236i
\(269\) 8.33596 + 9.25802i 0.508252 + 0.564472i 0.941591 0.336760i \(-0.109331\pi\)
−0.433338 + 0.901231i \(0.642664\pi\)
\(270\) −0.104528 0.994522i −0.00636140 0.0605247i
\(271\) −16.0438 + 11.6565i −0.974589 + 0.708080i −0.956493 0.291756i \(-0.905761\pi\)
−0.0180963 + 0.999836i \(0.505761\pi\)
\(272\) 0.477080 4.53912i 0.0289273 0.275224i
\(273\) −1.47193 2.54946i −0.0890853 0.154300i
\(274\) −5.80074 + 10.0472i −0.350436 + 0.606972i
\(275\) 3.90040 + 2.83380i 0.235203 + 0.170885i
\(276\) 2.99845 3.33012i 0.180486 0.200450i
\(277\) 2.94446 9.06211i 0.176915 0.544489i −0.822800 0.568330i \(-0.807590\pi\)
0.999716 + 0.0238411i \(0.00758957\pi\)
\(278\) 4.61602 0.276850
\(279\) 4.63598 + 3.08346i 0.277549 + 0.184602i
\(280\) 2.60586 0.155730
\(281\) 3.41397 10.5071i 0.203660 0.626802i −0.796106 0.605158i \(-0.793110\pi\)
0.999766 0.0216438i \(-0.00688997\pi\)
\(282\) 3.39220 3.76742i 0.202003 0.224347i
\(283\) −1.15916 0.842177i −0.0689048 0.0500623i 0.552800 0.833314i \(-0.313559\pi\)
−0.621704 + 0.783252i \(0.713559\pi\)
\(284\) −5.60308 + 9.70483i −0.332482 + 0.575875i
\(285\) −1.85691 3.21626i −0.109994 0.190515i
\(286\) 0.569313 5.41665i 0.0336642 0.320294i
\(287\) 12.7694 9.27748i 0.753752 0.547633i
\(288\) −0.104528 0.994522i −0.00615940 0.0586028i
\(289\) 2.56357 + 2.84713i 0.150798 + 0.167478i
\(290\) 0.323187 0.143892i 0.0189782 0.00844963i
\(291\) −17.6768 + 3.75732i −1.03623 + 0.220258i
\(292\) 0.896266 + 0.190507i 0.0524500 + 0.0111486i
\(293\) 4.70530 + 2.09493i 0.274887 + 0.122387i 0.539550 0.841953i \(-0.318594\pi\)
−0.264664 + 0.964341i \(0.585261\pi\)
\(294\) −0.0647346 0.199232i −0.00377540 0.0116195i
\(295\) 0.363642 + 1.11917i 0.0211720 + 0.0651609i
\(296\) 4.52032 + 2.01258i 0.262738 + 0.116979i
\(297\) 4.71580 + 1.00237i 0.273639 + 0.0581637i
\(298\) −9.84197 + 2.09198i −0.570130 + 0.121185i
\(299\) 4.62469 2.05904i 0.267452 0.119077i
\(300\) 0.669131 + 0.743145i 0.0386323 + 0.0429055i
\(301\) 2.33267 + 22.1938i 0.134453 + 1.27923i
\(302\) 9.19304 6.67914i 0.529000 0.384341i
\(303\) −0.966346 + 9.19417i −0.0555151 + 0.528191i
\(304\) −1.85691 3.21626i −0.106501 0.184465i
\(305\) −4.98724 + 8.63815i −0.285569 + 0.494619i
\(306\) 3.69245 + 2.68272i 0.211083 + 0.153361i
\(307\) −15.3715 + 17.0718i −0.877299 + 0.974340i −0.999836 0.0181245i \(-0.994230\pi\)
0.122536 + 0.992464i \(0.460897\pi\)
\(308\) −3.88226 + 11.9484i −0.221212 + 0.680822i
\(309\) 8.92036 0.507462
\(310\) −5.56300 + 0.230387i −0.315957 + 0.0130851i
\(311\) 4.09350 0.232121 0.116060 0.993242i \(-0.462973\pi\)
0.116060 + 0.993242i \(0.462973\pi\)
\(312\) 0.349099 1.07442i 0.0197638 0.0608268i
\(313\) 7.61118 8.45307i 0.430209 0.477796i −0.488594 0.872511i \(-0.662490\pi\)
0.918804 + 0.394715i \(0.129157\pi\)
\(314\) 12.8655 + 9.34731i 0.726040 + 0.527499i
\(315\) −1.30293 + 2.25674i −0.0734118 + 0.127153i
\(316\) −4.08292 7.07183i −0.229682 0.397821i
\(317\) 3.30337 31.4295i 0.185536 1.76526i −0.365535 0.930798i \(-0.619114\pi\)
0.551071 0.834459i \(-0.314219\pi\)
\(318\) 5.08268 3.69278i 0.285023 0.207081i
\(319\) 0.178283 + 1.69625i 0.00998191 + 0.0949715i
\(320\) 0.669131 + 0.743145i 0.0374055 + 0.0415431i
\(321\) −12.9566 + 5.76863i −0.723164 + 0.321974i
\(322\) −11.4220 + 2.42782i −0.636523 + 0.135297i
\(323\) 16.5799 + 3.52416i 0.922530 + 0.196090i
\(324\) 0.913545 + 0.406737i 0.0507525 + 0.0225965i
\(325\) 0.349099 + 1.07442i 0.0193645 + 0.0595978i
\(326\) 4.43416 + 13.6469i 0.245585 + 0.755834i
\(327\) 14.9843 + 6.67142i 0.828631 + 0.368930i
\(328\) 5.92468 + 1.25933i 0.327135 + 0.0695348i
\(329\) −12.9219 + 2.74664i −0.712408 + 0.151427i
\(330\) −4.40434 + 1.96094i −0.242451 + 0.107946i
\(331\) 9.13229 + 10.1424i 0.501956 + 0.557479i 0.939867 0.341540i \(-0.110948\pi\)
−0.437911 + 0.899018i \(0.644282\pi\)
\(332\) −1.03036 9.80322i −0.0565484 0.538022i
\(333\) −4.00310 + 2.90842i −0.219369 + 0.159381i
\(334\) −1.66337 + 15.8259i −0.0910155 + 0.865955i
\(335\) −0.256055 0.443500i −0.0139898 0.0242310i
\(336\) −1.30293 + 2.25674i −0.0710807 + 0.123115i
\(337\) −22.8841 16.6263i −1.24658 0.905690i −0.248558 0.968617i \(-0.579957\pi\)
−0.998018 + 0.0629268i \(0.979957\pi\)
\(338\) −7.84473 + 8.71245i −0.426697 + 0.473895i
\(339\) 0.214059 0.658807i 0.0116261 0.0357815i
\(340\) −4.56412 −0.247524
\(341\) 7.23149 25.8506i 0.391607 1.39989i
\(342\) 3.71381 0.200820
\(343\) −5.80548 + 17.8674i −0.313466 + 0.964750i
\(344\) −5.73030 + 6.36415i −0.308957 + 0.343132i
\(345\) −3.62530 2.63393i −0.195180 0.141806i
\(346\) −11.8468 + 20.5193i −0.636889 + 1.10312i
\(347\) 6.18632 + 10.7150i 0.332099 + 0.575213i 0.982923 0.184016i \(-0.0589098\pi\)
−0.650824 + 0.759229i \(0.725576\pi\)
\(348\) −0.0369792 + 0.351834i −0.00198229 + 0.0188603i
\(349\) −5.57501 + 4.05048i −0.298423 + 0.216817i −0.726913 0.686729i \(-0.759046\pi\)
0.428490 + 0.903547i \(0.359046\pi\)
\(350\) −0.272387 2.59159i −0.0145597 0.138526i
\(351\) 0.755921 + 0.839536i 0.0403481 + 0.0448111i
\(352\) −4.40434 + 1.96094i −0.234752 + 0.104518i
\(353\) 15.6810 3.33310i 0.834614 0.177403i 0.229266 0.973364i \(-0.426367\pi\)
0.605348 + 0.795961i \(0.293034\pi\)
\(354\) −1.15105 0.244664i −0.0611779 0.0130038i
\(355\) 10.2373 + 4.55796i 0.543342 + 0.241911i
\(356\) −1.45103 4.46580i −0.0769043 0.236687i
\(357\) −3.67528 11.3114i −0.194517 0.598661i
\(358\) 6.68819 + 2.97777i 0.353482 + 0.157380i
\(359\) 20.7981 + 4.42077i 1.09768 + 0.233319i 0.720938 0.692999i \(-0.243711\pi\)
0.376742 + 0.926318i \(0.377044\pi\)
\(360\) −0.978148 + 0.207912i −0.0515529 + 0.0109579i
\(361\) −4.75737 + 2.11812i −0.250388 + 0.111480i
\(362\) −7.66961 8.51797i −0.403106 0.447694i
\(363\) −1.27980 12.1765i −0.0671719 0.639098i
\(364\) −2.38163 + 1.73036i −0.124831 + 0.0906954i
\(365\) 0.0957783 0.911270i 0.00501327 0.0476980i
\(366\) −4.98724 8.63815i −0.260687 0.451523i
\(367\) 12.4450 21.5553i 0.649623 1.12518i −0.333590 0.942718i \(-0.608260\pi\)
0.983213 0.182461i \(-0.0584064\pi\)
\(368\) −3.62530 2.63393i −0.188982 0.137303i
\(369\) −4.05295 + 4.50126i −0.210988 + 0.234326i
\(370\) 1.52905 4.70593i 0.0794914 0.244650i
\(371\) −16.3714 −0.849962
\(372\) 2.58198 4.93289i 0.133869 0.255758i
\(373\) 9.64213 0.499250 0.249625 0.968343i \(-0.419693\pi\)
0.249625 + 0.968343i \(0.419693\pi\)
\(374\) 6.79971 20.9274i 0.351605 1.08213i
\(375\) 0.669131 0.743145i 0.0345538 0.0383758i
\(376\) −4.10137 2.97982i −0.211512 0.153672i
\(377\) −0.199829 + 0.346114i −0.0102917 + 0.0178258i
\(378\) −1.30293 2.25674i −0.0670155 0.116074i
\(379\) −3.44291 + 32.7571i −0.176851 + 1.68262i 0.441924 + 0.897053i \(0.354296\pi\)
−0.618774 + 0.785569i \(0.712370\pi\)
\(380\) −3.00454 + 2.18292i −0.154130 + 0.111982i
\(381\) −0.319371 3.03861i −0.0163619 0.155673i
\(382\) −4.01716 4.46150i −0.205536 0.228270i
\(383\) −20.2885 + 9.03302i −1.03669 + 0.461566i −0.853271 0.521468i \(-0.825385\pi\)
−0.183423 + 0.983034i \(0.558718\pi\)
\(384\) −0.978148 + 0.207912i −0.0499159 + 0.0106099i
\(385\) 12.2887 + 2.61205i 0.626291 + 0.133122i
\(386\) 18.0434 + 8.03343i 0.918384 + 0.408891i
\(387\) −2.64636 8.14466i −0.134522 0.414016i
\(388\) 5.58447 + 17.1872i 0.283509 + 0.872550i
\(389\) 27.2035 + 12.1118i 1.37927 + 0.614093i 0.956390 0.292091i \(-0.0943511\pi\)
0.422884 + 0.906184i \(0.361018\pi\)
\(390\) −1.10502 0.234879i −0.0559549 0.0118936i
\(391\) 20.0054 4.25228i 1.01172 0.215047i
\(392\) −0.191374 + 0.0852054i −0.00966587 + 0.00430352i
\(393\) −3.00741 3.34006i −0.151704 0.168484i
\(394\) 1.79907 + 17.1170i 0.0906357 + 0.862341i
\(395\) −6.60631 + 4.79976i −0.332399 + 0.241502i
\(396\) 0.503948 4.79474i 0.0253243 0.240945i
\(397\) −17.1565 29.7159i −0.861058 1.49140i −0.870909 0.491445i \(-0.836469\pi\)
0.00985040 0.999951i \(-0.496864\pi\)
\(398\) 11.7850 20.4122i 0.590728 1.02317i
\(399\) −7.82941 5.68840i −0.391961 0.284776i
\(400\) 0.669131 0.743145i 0.0334565 0.0371572i
\(401\) −7.50735 + 23.1053i −0.374899 + 1.15382i 0.568647 + 0.822581i \(0.307467\pi\)
−0.943547 + 0.331240i \(0.892533\pi\)
\(402\) 0.512110 0.0255417
\(403\) 4.93133 3.90453i 0.245647 0.194499i
\(404\) 9.24482 0.459947
\(405\) 0.309017 0.951057i 0.0153552 0.0472584i
\(406\) 0.616858 0.685091i 0.0306142 0.0340005i
\(407\) 19.2996 + 14.0220i 0.956644 + 0.695043i
\(408\) 2.28206 3.95264i 0.112979 0.195685i
\(409\) −15.5939 27.0095i −0.771071 1.33553i −0.936977 0.349392i \(-0.886388\pi\)
0.165906 0.986142i \(-0.446945\pi\)
\(410\) 0.633133 6.02386i 0.0312682 0.297497i
\(411\) −9.38580 + 6.81918i −0.462967 + 0.336365i
\(412\) −0.932431 8.87149i −0.0459376 0.437067i
\(413\) 2.05189 + 2.27885i 0.100967 + 0.112135i
\(414\) 4.09370 1.82263i 0.201195 0.0895776i
\(415\) −9.64182 + 2.04943i −0.473298 + 0.100603i
\(416\) −1.10502 0.234879i −0.0541781 0.0115159i
\(417\) 4.21694 + 1.87750i 0.206505 + 0.0919417i
\(418\) −5.53291 17.0285i −0.270623 0.832893i
\(419\) 6.56545 + 20.2064i 0.320743 + 0.987146i 0.973326 + 0.229428i \(0.0736856\pi\)
−0.652583 + 0.757718i \(0.726314\pi\)
\(420\) 2.38057 + 1.05990i 0.116160 + 0.0517178i
\(421\) 15.5881 + 3.31335i 0.759716 + 0.161483i 0.571452 0.820636i \(-0.306381\pi\)
0.188264 + 0.982118i \(0.439714\pi\)
\(422\) 6.14542 1.30625i 0.299154 0.0635872i
\(423\) 4.63128 2.06198i 0.225181 0.100257i
\(424\) −4.20384 4.66884i −0.204156 0.226739i
\(425\) 0.477080 + 4.53912i 0.0231418 + 0.220180i
\(426\) −9.06598 + 6.58682i −0.439248 + 0.319132i
\(427\) −2.71692 + 25.8497i −0.131481 + 1.25096i
\(428\) 7.09136 + 12.2826i 0.342774 + 0.593702i
\(429\) 2.72325 4.71680i 0.131480 0.227729i
\(430\) 6.92826 + 5.03368i 0.334111 + 0.242746i
\(431\) 1.23277 1.36914i 0.0593807 0.0659489i −0.712723 0.701446i \(-0.752538\pi\)
0.772103 + 0.635497i \(0.219205\pi\)
\(432\) 0.309017 0.951057i 0.0148676 0.0457577i
\(433\) 3.54171 0.170204 0.0851018 0.996372i \(-0.472878\pi\)
0.0851018 + 0.996372i \(0.472878\pi\)
\(434\) −12.9989 + 6.44467i −0.623969 + 0.309354i
\(435\) 0.353772 0.0169621
\(436\) 5.06859 15.5995i 0.242742 0.747082i
\(437\) 11.1357 12.3674i 0.532692 0.591615i
\(438\) 0.741294 + 0.538581i 0.0354204 + 0.0257344i
\(439\) −4.89890 + 8.48514i −0.233812 + 0.404974i −0.958927 0.283654i \(-0.908453\pi\)
0.725115 + 0.688628i \(0.241787\pi\)
\(440\) 2.41058 + 4.17524i 0.114920 + 0.199047i
\(441\) 0.0218972 0.208338i 0.00104272 0.00992085i
\(442\) 4.17139 3.03069i 0.198413 0.144155i
\(443\) 2.82817 + 26.9083i 0.134371 + 1.27845i 0.829068 + 0.559148i \(0.188872\pi\)
−0.694697 + 0.719302i \(0.744462\pi\)
\(444\) 3.31093 + 3.67716i 0.157130 + 0.174510i
\(445\) −4.28966 + 1.90988i −0.203350 + 0.0905371i
\(446\) −18.7866 + 3.99322i −0.889573 + 0.189085i
\(447\) −9.84197 2.09198i −0.465509 0.0989471i
\(448\) 2.38057 + 1.05990i 0.112472 + 0.0500755i
\(449\) −0.564036 1.73592i −0.0266185 0.0819233i 0.936865 0.349692i \(-0.113714\pi\)
−0.963483 + 0.267769i \(0.913714\pi\)
\(450\) 0.309017 + 0.951057i 0.0145672 + 0.0448332i
\(451\) 26.6773 + 11.8775i 1.25618 + 0.559289i
\(452\) −0.677574 0.144023i −0.0318704 0.00677426i
\(453\) 11.1149 2.36255i 0.522224 0.111002i
\(454\) −1.24903 + 0.556104i −0.0586198 + 0.0260992i
\(455\) 1.96983 + 2.18771i 0.0923469 + 0.102562i
\(456\) −0.388199 3.69347i −0.0181791 0.172963i
\(457\) −17.4654 + 12.6894i −0.816997 + 0.593583i −0.915851 0.401519i \(-0.868482\pi\)
0.0988539 + 0.995102i \(0.468482\pi\)
\(458\) 0.0316968 0.301575i 0.00148109 0.0140917i
\(459\) 2.28206 + 3.95264i 0.106517 + 0.184494i
\(460\) −2.24056 + 3.88076i −0.104467 + 0.180941i
\(461\) 15.5873 + 11.3249i 0.725975 + 0.527452i 0.888288 0.459288i \(-0.151895\pi\)
−0.162313 + 0.986739i \(0.551895\pi\)
\(462\) −8.40646 + 9.33632i −0.391104 + 0.434365i
\(463\) −10.5095 + 32.3450i −0.488419 + 1.50320i 0.338548 + 0.940949i \(0.390064\pi\)
−0.826967 + 0.562251i \(0.809936\pi\)
\(464\) 0.353772 0.0164234
\(465\) −5.17576 2.05220i −0.240020 0.0951687i
\(466\) 13.8133 0.639889
\(467\) −11.6064 + 35.7207i −0.537079 + 1.65296i 0.202036 + 0.979378i \(0.435244\pi\)
−0.739115 + 0.673580i \(0.764756\pi\)
\(468\) 0.755921 0.839536i 0.0349425 0.0388076i
\(469\) −1.07962 0.784392i −0.0498523 0.0362198i
\(470\) −2.53478 + 4.39038i −0.116921 + 0.202513i
\(471\) 7.95129 + 13.7720i 0.366376 + 0.634582i
\(472\) −0.123006 + 1.17032i −0.00566181 + 0.0538685i
\(473\) −33.4022 + 24.2681i −1.53584 + 1.11585i
\(474\) −0.853563 8.12111i −0.0392054 0.373015i
\(475\) 2.48503 + 2.75990i 0.114021 + 0.126633i
\(476\) −10.8652 + 4.83751i −0.498007 + 0.221727i
\(477\) 6.14525 1.30621i 0.281372 0.0598074i
\(478\) −18.1697 3.86208i −0.831062 0.176648i
\(479\) −18.9195 8.42349i −0.864452 0.384879i −0.0738943 0.997266i \(-0.523543\pi\)
−0.790558 + 0.612387i \(0.790209\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) 1.72738 + 5.31632i 0.0787616 + 0.242403i
\(482\) −13.8055 6.14659i −0.628822 0.279969i
\(483\) −11.4220 2.42782i −0.519719 0.110470i
\(484\) −11.9760 + 2.54557i −0.544363 + 0.115708i
\(485\) 16.5093 7.35044i 0.749651 0.333766i
\(486\) 0.669131 + 0.743145i 0.0303524 + 0.0337097i
\(487\) 1.88064 + 17.8931i 0.0852199 + 0.810813i 0.950751 + 0.309957i \(0.100315\pi\)
−0.865531 + 0.500856i \(0.833019\pi\)
\(488\) −8.06952 + 5.86285i −0.365290 + 0.265399i
\(489\) −1.49990 + 14.2706i −0.0678280 + 0.645340i
\(490\) 0.104743 + 0.181420i 0.00473179 + 0.00819571i
\(491\) −18.2018 + 31.5264i −0.821435 + 1.42277i 0.0831788 + 0.996535i \(0.473493\pi\)
−0.904614 + 0.426232i \(0.859841\pi\)
\(492\) 4.90025 + 3.56024i 0.220920 + 0.160508i
\(493\) −1.08042 + 1.19992i −0.0486595 + 0.0540419i
\(494\) 1.29649 3.99018i 0.0583317 0.179527i
\(495\) −4.82115 −0.216695
\(496\) −5.17576 2.05220i −0.232398 0.0921467i
\(497\) 29.2017 1.30988
\(498\) 3.04605 9.37477i 0.136497 0.420094i
\(499\) 23.7342 26.3595i 1.06249 1.18001i 0.0794080 0.996842i \(-0.474697\pi\)
0.983081 0.183171i \(-0.0586363\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) −7.95654 + 13.7811i −0.355472 + 0.615695i
\(502\) 6.46001 + 11.1891i 0.288324 + 0.499393i
\(503\) 1.52987 14.5558i 0.0682137 0.649010i −0.905984 0.423313i \(-0.860867\pi\)
0.974197 0.225698i \(-0.0724662\pi\)
\(504\) −2.10819 + 1.53169i −0.0939061 + 0.0682268i
\(505\) −0.966346 9.19417i −0.0430018 0.409135i
\(506\) −14.4560 16.0550i −0.642648 0.713732i
\(507\) −10.7102 + 4.76848i −0.475656 + 0.211776i
\(508\) −2.98858 + 0.635243i −0.132597 + 0.0281843i
\(509\) 14.1411 + 3.00579i 0.626794 + 0.133229i 0.510348 0.859968i \(-0.329516\pi\)
0.116446 + 0.993197i \(0.462850\pi\)
\(510\) −4.16953 1.85640i −0.184630 0.0822026i
\(511\) −0.737847 2.27086i −0.0326404 0.100457i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) 3.39274 + 1.51054i 0.149793 + 0.0666922i
\(514\) 3.38510 + 0.719524i 0.149310 + 0.0317369i
\(515\) −8.72543 + 1.85465i −0.384488 + 0.0817255i
\(516\) −7.82343 + 3.48321i −0.344407 + 0.153340i
\(517\) −16.3543 18.1633i −0.719263 0.798822i
\(518\) −1.34780 12.8234i −0.0592188 0.563430i
\(519\) −19.1686 + 13.9268i −0.841406 + 0.611317i
\(520\) −0.118087 + 1.12352i −0.00517844 + 0.0492695i
\(521\) 15.1212 + 26.1907i 0.662472 + 1.14744i 0.979964 + 0.199174i \(0.0638260\pi\)
−0.317492 + 0.948261i \(0.602841\pi\)
\(522\) −0.176886 + 0.306375i −0.00774209 + 0.0134097i
\(523\) 1.96004 + 1.42405i 0.0857067 + 0.0622696i 0.629813 0.776746i \(-0.283131\pi\)
−0.544107 + 0.839016i \(0.683131\pi\)
\(524\) −3.00741 + 3.34006i −0.131379 + 0.145911i
\(525\) 0.805256 2.47832i 0.0351442 0.108163i
\(526\) −14.3925 −0.627542
\(527\) 22.7674 11.2877i 0.991763 0.491701i
\(528\) −4.82115 −0.209814
\(529\) −0.902205 + 2.77670i −0.0392263 + 0.120726i
\(530\) −4.20384 + 4.66884i −0.182603 + 0.202801i
\(531\) −0.952027 0.691688i −0.0413144 0.0300167i
\(532\) −4.83884 + 8.38112i −0.209790 + 0.363368i
\(533\) 3.42134 + 5.92593i 0.148195 + 0.256681i
\(534\) 0.490826 4.66990i 0.0212401 0.202086i
\(535\) 11.4741 8.33639i 0.496067 0.360414i
\(536\) −0.0535300 0.509304i −0.00231215 0.0219986i
\(537\) 4.89879 + 5.44066i 0.211399 + 0.234782i
\(538\) 11.3809 5.06708i 0.490664 0.218457i
\(539\) −0.987891 + 0.209983i −0.0425515 + 0.00904460i
\(540\) −0.978148 0.207912i −0.0420928 0.00894709i
\(541\) −17.3739 7.73535i −0.746962 0.332569i −0.00228803 0.999997i \(-0.500728\pi\)
−0.744674 + 0.667429i \(0.767395\pi\)
\(542\) 6.12817 + 18.8606i 0.263228 + 0.810131i
\(543\) −3.54197 10.9011i −0.152000 0.467809i
\(544\) −4.16953 1.85640i −0.178767 0.0795923i
\(545\) −16.0439 3.41023i −0.687244 0.146078i
\(546\) −2.87953 + 0.612063i −0.123232 + 0.0261939i
\(547\) 32.3052 14.3832i 1.38127 0.614981i 0.424394 0.905478i \(-0.360487\pi\)
0.956876 + 0.290496i \(0.0938204\pi\)
\(548\) 7.76291 + 8.62158i 0.331615 + 0.368296i
\(549\) −1.04262 9.91984i −0.0444978 0.423368i
\(550\) 3.90040 2.83380i 0.166313 0.120834i
\(551\) −0.137334 + 1.30665i −0.00585062 + 0.0556650i
\(552\) −2.24056 3.88076i −0.0953645 0.165176i
\(553\) −10.6395 + 18.4282i −0.452439 + 0.783647i
\(554\) −7.70869 5.60069i −0.327511 0.237951i
\(555\) 3.31093 3.67716i 0.140541 0.156087i
\(556\) 1.42643 4.39009i 0.0604940 0.186181i
\(557\) 25.3166 1.07270 0.536349 0.843996i \(-0.319803\pi\)
0.536349 + 0.843996i \(0.319803\pi\)
\(558\) 4.36514 3.45623i 0.184791 0.146314i
\(559\) −9.67459 −0.409192
\(560\) 0.805256 2.47832i 0.0340283 0.104728i
\(561\) 14.7238 16.3524i 0.621638 0.690399i
\(562\) −8.93788 6.49375i −0.377022 0.273922i
\(563\) −7.24758 + 12.5532i −0.305449 + 0.529053i −0.977361 0.211577i \(-0.932140\pi\)
0.671912 + 0.740631i \(0.265473\pi\)
\(564\) −2.53478 4.39038i −0.106734 0.184868i
\(565\) −0.0724080 + 0.688916i −0.00304623 + 0.0289829i
\(566\) −1.15916 + 0.842177i −0.0487230 + 0.0353994i
\(567\) −0.272387 2.59159i −0.0114392 0.108836i
\(568\) 7.49839 + 8.32780i 0.314625 + 0.349427i
\(569\) 9.89017 4.40339i 0.414617 0.184600i −0.188817 0.982012i \(-0.560465\pi\)
0.603434 + 0.797413i \(0.293799\pi\)
\(570\) −3.63266 + 0.772145i −0.152155 + 0.0323416i
\(571\) 4.58685 + 0.974965i 0.191954 + 0.0408010i 0.302885 0.953027i \(-0.402050\pi\)
−0.110932 + 0.993828i \(0.535383\pi\)
\(572\) −4.97562 2.21529i −0.208041 0.0926258i
\(573\) −1.85520 5.70971i −0.0775020 0.238527i
\(574\) −4.87746 15.0113i −0.203581 0.626559i
\(575\) 4.09370 + 1.82263i 0.170719 + 0.0760091i
\(576\) −0.978148 0.207912i −0.0407562 0.00866299i
\(577\) −23.8495 + 5.06937i −0.992868 + 0.211041i −0.675579 0.737288i \(-0.736106\pi\)
−0.317290 + 0.948329i \(0.602773\pi\)
\(578\) 3.49997 1.55829i 0.145580 0.0648162i
\(579\) 13.2160 + 14.6778i 0.549237 + 0.609989i
\(580\) −0.0369792 0.351834i −0.00153548 0.0146091i
\(581\) −20.7809 + 15.0982i −0.862135 + 0.626378i
\(582\) −1.88901 + 17.9727i −0.0783020 + 0.744994i
\(583\) −15.1445 26.2311i −0.627223 1.08638i
\(584\) 0.458145 0.793530i 0.0189582 0.0328365i
\(585\) −0.913952 0.664025i −0.0377873 0.0274541i
\(586\) 3.44642 3.82764i 0.142370 0.158118i
\(587\) −8.32859 + 25.6328i −0.343758 + 1.05798i 0.618488 + 0.785794i \(0.287746\pi\)
−0.962246 + 0.272183i \(0.912254\pi\)
\(588\) −0.209485 −0.00863903
\(589\) 9.58898 18.3198i 0.395107 0.754855i
\(590\) 1.17677 0.0484468
\(591\) −5.31857 + 16.3689i −0.218777 + 0.673326i
\(592\) 3.31093 3.67716i 0.136078 0.151130i
\(593\) 17.0393 + 12.3798i 0.699720 + 0.508376i 0.879841 0.475268i \(-0.157649\pi\)
−0.180121 + 0.983644i \(0.557649\pi\)
\(594\) 2.41058 4.17524i 0.0989072 0.171312i
\(595\) 5.94673 + 10.3000i 0.243792 + 0.422261i
\(596\) −1.05175 + 10.0067i −0.0430813 + 0.409892i
\(597\) 19.0685 13.8541i 0.780421 0.567009i
\(598\) −0.529159 5.03462i −0.0216389 0.205881i
\(599\) −14.6245 16.2422i −0.597543 0.663638i 0.366180 0.930544i \(-0.380665\pi\)
−0.963723 + 0.266906i \(0.913999\pi\)
\(600\) 0.913545 0.406737i 0.0372953 0.0166050i
\(601\) 21.2269 4.51192i 0.865864 0.184045i 0.246494 0.969144i \(-0.420721\pi\)
0.619370 + 0.785099i \(0.287388\pi\)
\(602\) 21.8284 + 4.63978i 0.889660 + 0.189103i
\(603\) 0.467835 + 0.208294i 0.0190517 + 0.00848238i
\(604\) −3.51143 10.8071i −0.142878 0.439733i
\(605\) 3.78346 + 11.6443i 0.153819 + 0.473408i
\(606\) 8.44556 + 3.76021i 0.343077 + 0.152748i
\(607\) −29.5974 6.29112i −1.20132 0.255349i −0.436568 0.899671i \(-0.643806\pi\)
−0.764754 + 0.644322i \(0.777139\pi\)
\(608\) −3.63266 + 0.772145i −0.147324 + 0.0313146i
\(609\) 0.842180 0.374963i 0.0341268 0.0151942i
\(610\) 6.67423 + 7.41248i 0.270232 + 0.300123i
\(611\) −0.598648 5.69575i −0.0242187 0.230426i
\(612\) 3.69245 2.68272i 0.149258 0.108443i
\(613\) 0.589629 5.60994i 0.0238149 0.226584i −0.976141 0.217140i \(-0.930327\pi\)
0.999955 0.00944374i \(-0.00300608\pi\)
\(614\) 11.4862 + 19.8947i 0.463545 + 0.802883i
\(615\) 3.02852 5.24555i 0.122122 0.211521i
\(616\) 10.1639 + 7.38450i 0.409515 + 0.297530i
\(617\) −3.93686 + 4.37233i −0.158492 + 0.176023i −0.817161 0.576410i \(-0.804453\pi\)
0.658669 + 0.752433i \(0.271120\pi\)
\(618\) 2.75654 8.48377i 0.110884 0.341267i
\(619\) 6.21391 0.249758 0.124879 0.992172i \(-0.460146\pi\)
0.124879 + 0.992172i \(0.460146\pi\)
\(620\) −1.49995 + 5.36192i −0.0602394 + 0.215340i
\(621\) 4.48112 0.179821
\(622\) 1.26496 3.89315i 0.0507203 0.156101i
\(623\) −8.18758 + 9.09323i −0.328028 + 0.364312i
\(624\) −0.913952 0.664025i −0.0365874 0.0265823i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −5.68737 9.85081i −0.227313 0.393717i
\(627\) 1.87157 17.8068i 0.0747432 0.711134i
\(628\) 12.8655 9.34731i 0.513388 0.372998i
\(629\) 2.36064 + 22.4600i 0.0941251 + 0.895540i
\(630\) 1.74366 + 1.93653i 0.0694691 + 0.0771533i
\(631\) 36.0897 16.0682i 1.43671 0.639663i 0.467072 0.884220i \(-0.345309\pi\)
0.969635 + 0.244557i \(0.0786424\pi\)
\(632\) −7.98740 + 1.69777i −0.317722 + 0.0675338i
\(633\) 6.14542 + 1.30625i 0.244258 + 0.0519187i
\(634\) −28.8704 12.8539i −1.14659 0.510495i
\(635\) 0.944155 + 2.90581i 0.0374676 + 0.115314i
\(636\) −1.94141 5.97505i −0.0769820 0.236926i
\(637\) −0.216197 0.0962571i −0.00856604 0.00381385i
\(638\) 1.66832 + 0.354612i 0.0660493 + 0.0140392i
\(639\) −10.9613 + 2.32989i −0.433622 + 0.0921691i
\(640\) 0.913545 0.406737i 0.0361111 0.0160777i
\(641\) −28.8219 32.0099i −1.13839 1.26432i −0.959890 0.280377i \(-0.909541\pi\)
−0.178505 0.983939i \(-0.557126\pi\)
\(642\) 1.48250 + 14.1050i 0.0585095 + 0.556681i
\(643\) −0.615260 + 0.447012i −0.0242635 + 0.0176284i −0.599851 0.800112i \(-0.704773\pi\)
0.575587 + 0.817740i \(0.304773\pi\)
\(644\) −1.22060 + 11.6132i −0.0480982 + 0.457624i
\(645\) 4.28190 + 7.41647i 0.168600 + 0.292023i
\(646\) 8.47515 14.6794i 0.333450 0.577553i
\(647\) 37.3799 + 27.1581i 1.46956 + 1.06770i 0.980742 + 0.195307i \(0.0625703\pi\)
0.488814 + 0.872388i \(0.337430\pi\)
\(648\) 0.669131 0.743145i 0.0262859 0.0291935i
\(649\) −1.75317 + 5.39571i −0.0688181 + 0.211800i
\(650\) 1.12971 0.0443107
\(651\) −14.4964 + 0.600357i −0.568159 + 0.0235299i
\(652\) 14.3492 0.561960
\(653\) 13.7660 42.3673i 0.538705 1.65796i −0.196801 0.980443i \(-0.563055\pi\)
0.735505 0.677519i \(-0.236945\pi\)
\(654\) 10.9753 12.1893i 0.429168 0.476639i
\(655\) 3.63612 + 2.64180i 0.142075 + 0.103224i
\(656\) 3.02852 5.24555i 0.118244 0.204804i
\(657\) 0.458145 + 0.793530i 0.0178739 + 0.0309585i
\(658\) −1.38088 + 13.1382i −0.0538324 + 0.512181i
\(659\) 8.10498 5.88862i 0.315725 0.229388i −0.418624 0.908160i \(-0.637487\pi\)
0.734349 + 0.678772i \(0.237487\pi\)
\(660\) 0.503948 + 4.79474i 0.0196161 + 0.186635i
\(661\) −16.6536 18.4957i −0.647750 0.719400i 0.326417 0.945226i \(-0.394159\pi\)
−0.974168 + 0.225826i \(0.927492\pi\)
\(662\) 12.4681 5.55114i 0.484585 0.215751i
\(663\) 5.04344 1.07202i 0.195871 0.0416337i
\(664\) −9.64182 2.04943i −0.374175 0.0795334i
\(665\) 8.84100 + 3.93627i 0.342839 + 0.152642i
\(666\) 1.52905 + 4.70593i 0.0592494 + 0.182351i
\(667\) 0.489882 + 1.50770i 0.0189683 + 0.0583785i
\(668\) 14.5373 + 6.47243i 0.562466 + 0.250426i
\(669\) −18.7866 3.99322i −0.726333 0.154387i
\(670\) −0.500919 + 0.106474i −0.0193522 + 0.00411343i
\(671\) −43.9310 + 19.5594i −1.69594 + 0.755081i
\(672\) 1.74366 + 1.93653i 0.0672632 + 0.0747034i
\(673\) 0.669204 + 6.36705i 0.0257959 + 0.245432i 0.999820 + 0.0189862i \(0.00604386\pi\)
−0.974024 + 0.226446i \(0.927289\pi\)
\(674\) −22.8841 + 16.6263i −0.881462 + 0.640420i
\(675\) −0.104528 + 0.994522i −0.00402330 + 0.0382792i
\(676\) 5.86188 + 10.1531i 0.225457 + 0.390503i
\(677\) −22.8438 + 39.5666i −0.877957 + 1.52067i −0.0243781 + 0.999703i \(0.507761\pi\)
−0.853579 + 0.520963i \(0.825573\pi\)
\(678\) −0.560415 0.407165i −0.0215226 0.0156371i
\(679\) 31.5110 34.9965i 1.20928 1.34304i
\(680\) −1.41039 + 4.34074i −0.0540860 + 0.166460i
\(681\) −1.36723 −0.0523925
\(682\) −22.3508 14.8658i −0.855855 0.569242i
\(683\) 5.13667 0.196549 0.0982747 0.995159i \(-0.468668\pi\)
0.0982747 + 0.995159i \(0.468668\pi\)
\(684\) 1.14763 3.53205i 0.0438808 0.135051i
\(685\) 7.76291 8.62158i 0.296605 0.329414i
\(686\) 15.1989 + 11.0427i 0.580298 + 0.421611i
\(687\) 0.151618 0.262610i 0.00578458 0.0100192i
\(688\) 4.28190 + 7.41647i 0.163246 + 0.282750i
\(689\) 0.741883 7.05855i 0.0282635 0.268909i
\(690\) −3.62530 + 2.63393i −0.138013 + 0.100272i
\(691\) −2.87174 27.3228i −0.109246 1.03941i −0.902551 0.430582i \(-0.858308\pi\)
0.793305 0.608824i \(-0.208358\pi\)
\(692\) 15.8541 + 17.6078i 0.602684 + 0.669348i
\(693\) −11.4771 + 5.10994i −0.435979 + 0.194111i
\(694\) 12.1023 2.57242i 0.459396 0.0976476i
\(695\) −4.51515 0.959724i −0.171269 0.0364044i
\(696\) 0.323187 + 0.143892i 0.0122504 + 0.00545421i
\(697\) 8.54279 + 26.2920i 0.323581 + 0.995880i
\(698\) 2.12946 + 6.55382i 0.0806014 + 0.248066i
\(699\) 12.6191 + 5.61837i 0.477297 + 0.212506i
\(700\) −2.54892 0.541789i −0.0963400 0.0204777i
\(701\) −18.8441 + 4.00544i −0.711732 + 0.151283i −0.549530 0.835474i \(-0.685193\pi\)
−0.162203 + 0.986757i \(0.551860\pi\)
\(702\) 1.03204 0.459493i 0.0389518 0.0173425i
\(703\) 12.2962 + 13.6563i 0.463759 + 0.515056i
\(704\) 0.503948 + 4.79474i 0.0189932 + 0.180709i
\(705\) −4.10137 + 2.97982i −0.154466 + 0.112226i
\(706\) 1.67573 15.9435i 0.0630668 0.600041i
\(707\) −12.0454 20.8632i −0.453012 0.784640i
\(708\) −0.588385 + 1.01911i −0.0221129 + 0.0383006i
\(709\) −1.28489 0.933528i −0.0482551 0.0350594i 0.563396 0.826187i \(-0.309494\pi\)
−0.611651 + 0.791127i \(0.709494\pi\)
\(710\) 7.49839 8.32780i 0.281410 0.312537i
\(711\) 2.52338 7.76618i 0.0946343 0.291254i
\(712\) −4.69562 −0.175976
\(713\) 1.57899 24.8998i 0.0591338 0.932504i
\(714\) −11.8935 −0.445102
\(715\) −1.68306 + 5.17992i −0.0629428 + 0.193718i
\(716\) 4.89879 5.44066i 0.183077 0.203327i
\(717\) −15.0280 10.9185i −0.561230 0.407757i
\(718\) 10.6314 18.4141i 0.396759 0.687206i
\(719\) −18.6110 32.2352i −0.694073 1.20217i −0.970492 0.241132i \(-0.922481\pi\)
0.276420 0.961037i \(-0.410852\pi\)
\(720\) −0.104528 + 0.994522i −0.00389555 + 0.0370636i
\(721\) −18.8058 + 13.6632i −0.700364 + 0.508844i
\(722\) 0.544341 + 5.17906i 0.0202583 + 0.192745i
\(723\) −10.1119 11.2304i −0.376065 0.417662i
\(724\) −10.4711 + 4.66204i −0.389156 + 0.173263i
\(725\) −0.346041 + 0.0735533i −0.0128516 + 0.00273170i
\(726\) −11.9760 2.54557i −0.444470 0.0944751i
\(727\) −20.1171 8.95671i −0.746102 0.332186i −0.00177243 0.999998i \(-0.500564\pi\)
−0.744330 + 0.667812i \(0.767231\pi\)
\(728\) 0.909703 + 2.79978i 0.0337158 + 0.103767i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −0.837072 0.372688i −0.0309814 0.0137938i
\(731\) −38.2321 8.12649i −1.41407 0.300569i
\(732\) −9.75651 + 2.07381i −0.360611 + 0.0766503i
\(733\) −32.9468 + 14.6688i −1.21692 + 0.541806i −0.911850 0.410525i \(-0.865346\pi\)
−0.305067 + 0.952331i \(0.598679\pi\)
\(734\) −16.6546 18.4968i −0.614734 0.682731i
\(735\) 0.0218972 + 0.208338i 0.000807690 + 0.00768466i
\(736\) −3.62530 + 2.63393i −0.133630 + 0.0970881i
\(737\) 0.258077 2.45543i 0.00950637 0.0904471i
\(738\) 3.02852 + 5.24555i 0.111481 + 0.193091i
\(739\) 6.83797 11.8437i 0.251539 0.435678i −0.712411 0.701763i \(-0.752397\pi\)
0.963950 + 0.266085i \(0.0857301\pi\)
\(740\) −4.00310 2.90842i −0.147157 0.106916i
\(741\) 2.80735 3.11788i 0.103131 0.114538i
\(742\) −5.05905 + 15.5702i −0.185724 + 0.571598i
\(743\) 12.6434 0.463842 0.231921 0.972735i \(-0.425499\pi\)
0.231921 + 0.972735i \(0.425499\pi\)
\(744\) −3.89358 3.97995i −0.142746 0.145912i
\(745\) 10.0618 0.368638
\(746\) 2.97958 9.17021i 0.109090 0.335745i
\(747\) 6.59577 7.32534i 0.241327 0.268020i
\(748\) −17.8019 12.9338i −0.650901 0.472907i
\(749\) 18.4791 32.0067i 0.675212 1.16950i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 1.06158 10.1002i 0.0387374 0.368562i −0.957931 0.286999i \(-0.907342\pi\)
0.996668 0.0815627i \(-0.0259911\pi\)
\(752\) −4.10137 + 2.97982i −0.149561 + 0.108663i
\(753\) 1.35051 + 12.8492i 0.0492153 + 0.468253i
\(754\) 0.267424 + 0.297004i 0.00973900 + 0.0108163i
\(755\) −10.3808 + 4.62184i −0.377797 + 0.168206i
\(756\) −2.54892 + 0.541789i −0.0927032 + 0.0197047i
\(757\) 9.75364 + 2.07320i 0.354502 + 0.0753518i 0.381721 0.924278i \(-0.375332\pi\)
−0.0272185 + 0.999630i \(0.508665\pi\)
\(758\) 30.0900 + 13.3969i 1.09292 + 0.486598i
\(759\) −6.67605 20.5468i −0.242325 0.745801i
\(760\) 1.14763 + 3.53205i 0.0416290 + 0.128121i
\(761\) 18.9846 + 8.45250i 0.688192 + 0.306403i 0.720877 0.693063i \(-0.243739\pi\)
−0.0326851 + 0.999466i \(0.510406\pi\)
\(762\) −2.98858 0.635243i −0.108265 0.0230124i
\(763\) −41.8081 + 8.88659i −1.51356 + 0.321716i
\(764\) −5.48451 + 2.44186i −0.198423 + 0.0883435i
\(765\) −3.05399 3.39180i −0.110417 0.122631i
\(766\) 2.32142 + 22.0869i 0.0838765 + 0.798031i
\(767\) −1.07551 + 0.781405i −0.0388345 + 0.0282149i
\(768\) −0.104528 + 0.994522i −0.00377185 + 0.0358867i
\(769\) −18.4829 32.0134i −0.666511 1.15443i −0.978873 0.204468i \(-0.934454\pi\)
0.312362 0.949963i \(-0.398880\pi\)
\(770\) 6.28163 10.8801i 0.226374 0.392092i
\(771\) 2.79978 + 2.03416i 0.100832 + 0.0732585i
\(772\) 13.2160 14.6778i 0.475653 0.528266i
\(773\) 1.55010 4.77072i 0.0557533 0.171591i −0.919302 0.393553i \(-0.871246\pi\)
0.975055 + 0.221962i \(0.0712459\pi\)
\(774\) −8.56381 −0.307820
\(775\) 5.48933 + 0.931259i 0.197183 + 0.0334518i
\(776\) 18.0717 0.648737
\(777\) 3.98449 12.2630i 0.142943 0.439933i
\(778\) 19.9254 22.1294i 0.714359 0.793376i
\(779\) 18.1986 + 13.2221i 0.652032 + 0.473729i
\(780\) −0.564853 + 0.978355i −0.0202250 + 0.0350307i
\(781\) 27.0133 + 46.7885i 0.966613 + 1.67422i
\(782\) 2.13785 20.3403i 0.0764495 0.727368i
\(783\) −0.286207 + 0.207942i −0.0102282 + 0.00743124i
\(784\) 0.0218972 + 0.208338i 0.000782042 + 0.00744064i
\(785\) −10.6409 11.8179i −0.379790 0.421800i
\(786\) −4.10593 + 1.82808i −0.146454 + 0.0652053i
\(787\) −24.0513 + 5.11226i −0.857336 + 0.182232i −0.615550 0.788097i \(-0.711066\pi\)
−0.241785 + 0.970330i \(0.577733\pi\)
\(788\) 16.8352 + 3.57842i 0.599728 + 0.127476i
\(789\) −13.1482 5.85395i −0.468088 0.208406i
\(790\) 2.52338 + 7.76618i 0.0897780 + 0.276308i
\(791\) 0.557809 + 1.71676i 0.0198334 + 0.0610410i
\(792\) −4.40434 1.96094i −0.156502 0.0696790i
\(793\) −11.0220 2.34280i −0.391403 0.0831952i
\(794\) −33.5631 + 7.13406i −1.19111 + 0.253178i
\(795\) −5.73938 + 2.55534i −0.203555 + 0.0906285i
\(796\) −15.7714 17.5159i −0.559002 0.620834i
\(797\) 4.56382 + 43.4218i 0.161659 + 1.53808i 0.711426 + 0.702761i \(0.248050\pi\)
−0.549767 + 0.835318i \(0.685284\pi\)
\(798\) −7.82941 + 5.68840i −0.277158 + 0.201367i
\(799\) 2.41859 23.0114i 0.0855636 0.814084i
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) 2.34781 4.06653i 0.0829558 0.143684i
\(802\) 19.6545 + 14.2798i 0.694025 + 0.504238i
\(803\) 2.95593 3.28290i 0.104313 0.115851i
\(804\) 0.158251 0.487045i 0.00558107 0.0171768i
\(805\) 11.6772 0.411566
\(806\) −2.18957 5.89654i −0.0771242 0.207697i
\(807\) 12.4579 0.438539
\(808\) 2.85681 8.79234i 0.100502 0.309314i
\(809\) 24.0800 26.7436i 0.846609 0.940254i −0.152234 0.988344i \(-0.548647\pi\)
0.998843 + 0.0480904i \(0.0153135\pi\)
\(810\) −0.809017 0.587785i −0.0284260 0.0206527i
\(811\) −9.46077 + 16.3865i −0.332212 + 0.575409i −0.982945 0.183898i \(-0.941128\pi\)
0.650733 + 0.759307i \(0.274462\pi\)
\(812\) −0.460940 0.798372i −0.0161758 0.0280174i
\(813\) −2.07292 + 19.7225i −0.0727006 + 0.691700i
\(814\) 19.2996 14.0220i 0.676449 0.491469i
\(815\) −1.49990 14.2706i −0.0525393 0.499878i
\(816\) −3.05399 3.39180i −0.106911 0.118737i
\(817\) −29.0547 + 12.9360i −1.01650 + 0.452574i
\(818\) −30.5064 + 6.48432i −1.06663 + 0.226719i
\(819\) −2.87953 0.612063i −0.100619 0.0213872i
\(820\) −5.53338 2.46362i −0.193234 0.0860333i
\(821\) −12.6447 38.9165i −0.441304 1.35819i −0.886487 0.462754i \(-0.846861\pi\)
0.445183 0.895440i \(-0.353139\pi\)
\(822\) 3.58506 + 11.0337i 0.125043 + 0.384843i
\(823\) 12.7367 + 5.67075i 0.443974 + 0.197670i 0.616533 0.787329i \(-0.288537\pi\)
−0.172559 + 0.984999i \(0.555203\pi\)
\(824\) −8.72543 1.85465i −0.303965 0.0646097i
\(825\) 4.71580 1.00237i 0.164183 0.0348982i
\(826\) 2.80139 1.24726i 0.0974727 0.0433976i
\(827\) −37.6979 41.8677i −1.31088 1.45588i −0.804990 0.593288i \(-0.797830\pi\)
−0.505894 0.862596i \(-0.668837\pi\)
\(828\) −0.468404 4.45657i −0.0162782 0.154876i
\(829\) −34.0634 + 24.7485i −1.18307 + 0.859552i −0.992515 0.122125i \(-0.961029\pi\)
−0.190557 + 0.981676i \(0.561029\pi\)
\(830\) −1.03036 + 9.80322i −0.0357643 + 0.340275i
\(831\) −4.76423 8.25189i −0.165269 0.286255i
\(832\) −0.564853 + 0.978355i −0.0195828 + 0.0339184i
\(833\) −0.773515 0.561991i −0.0268007 0.0194718i
\(834\) 3.08872 3.43037i 0.106954 0.118784i
\(835\) 4.91741 15.1342i 0.170174 0.523742i
\(836\) −17.9049 −0.619253
\(837\) 5.39353 1.38196i 0.186428 0.0477677i
\(838\) 21.2462 0.733939
\(839\) 0.482967 1.48642i 0.0166739 0.0513169i −0.942373 0.334563i \(-0.891411\pi\)
0.959047 + 0.283246i \(0.0914113\pi\)
\(840\) 1.74366 1.93653i 0.0601620 0.0668167i
\(841\) 23.3602 + 16.9722i 0.805526 + 0.585249i
\(842\) 7.96816 13.8013i 0.274601 0.475623i
\(843\) −5.52391 9.56770i −0.190254 0.329529i
\(844\) 0.656722 6.24829i 0.0226053 0.215075i
\(845\) 9.48472 6.89105i 0.326284 0.237059i
\(846\) −0.529914 5.04180i −0.0182188 0.173341i
\(847\) 21.3486 + 23.7100i 0.733546 + 0.814685i
\(848\) −5.73938 + 2.55534i −0.197091 + 0.0877507i
\(849\) −1.40149 + 0.297895i −0.0480989 + 0.0102237i
\(850\) 4.46438 + 0.948934i 0.153127 + 0.0325482i
\(851\) 20.2561 + 9.01859i 0.694369 + 0.309153i
\(852\) 3.46290 + 10.6577i 0.118637 + 0.365127i
\(853\) −9.26921 28.5277i −0.317372 0.976770i −0.974767 0.223224i \(-0.928342\pi\)
0.657396 0.753546i \(-0.271658\pi\)
\(854\) 23.7450 + 10.5719i 0.812536 + 0.361765i
\(855\) −3.63266 0.772145i −0.124234 0.0264068i
\(856\) 13.8728 2.94875i 0.474162 0.100786i
\(857\) −9.89198 + 4.40419i −0.337904 + 0.150444i −0.568672 0.822564i \(-0.692543\pi\)
0.230768 + 0.973009i \(0.425876\pi\)
\(858\) −3.64441 4.04753i −0.124418 0.138180i
\(859\) −0.569722 5.42055i −0.0194387 0.184947i 0.980494 0.196549i \(-0.0629735\pi\)
−0.999933 + 0.0116023i \(0.996307\pi\)
\(860\) 6.92826 5.03368i 0.236252 0.171647i
\(861\) 1.64986 15.6973i 0.0562269 0.534964i
\(862\) −0.921176 1.59552i −0.0313754 0.0543438i
\(863\) 4.86548 8.42726i 0.165623 0.286867i −0.771253 0.636528i \(-0.780370\pi\)
0.936876 + 0.349661i \(0.113703\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) 15.8541 17.6078i 0.539057 0.598683i
\(866\) 1.09445 3.36837i 0.0371909 0.114462i
\(867\) 3.83120 0.130114
\(868\) 2.11235 + 14.3542i 0.0716980 + 0.487214i
\(869\) −39.3688 −1.33549
\(870\) 0.109322 0.336457i 0.00370635 0.0114070i
\(871\) 0.387115 0.429934i 0.0131169 0.0145678i
\(872\) −13.2697 9.64103i −0.449370 0.326487i
\(873\) −9.03587 + 15.6506i −0.305818 + 0.529692i
\(874\) −8.32102 14.4124i −0.281463 0.487507i
\(875\) −0.272387 + 2.59159i −0.00920835 + 0.0876116i
\(876\) 0.741294 0.538581i 0.0250460 0.0181970i
\(877\) 0.927287 + 8.82254i 0.0313122 + 0.297916i 0.998959 + 0.0456087i \(0.0145227\pi\)
−0.967647 + 0.252307i \(0.918811\pi\)
\(878\) 6.55601 + 7.28118i 0.221254 + 0.245728i
\(879\) 4.70530 2.09493i 0.158706 0.0706604i
\(880\) 4.71580 1.00237i 0.158970 0.0337900i
\(881\) 10.6939 + 2.27306i 0.360287 + 0.0765813i 0.384499 0.923126i \(-0.374374\pi\)
−0.0242120 + 0.999707i \(0.507708\pi\)
\(882\) −0.191374 0.0852054i −0.00644391 0.00286901i
\(883\) −13.8043 42.4854i −0.464553 1.42975i −0.859544 0.511062i \(-0.829252\pi\)
0.394991 0.918685i \(-0.370748\pi\)
\(884\) −1.59333 4.90376i −0.0535894 0.164931i
\(885\) 1.07503 + 0.478635i 0.0361368 + 0.0160892i
\(886\) 26.4652 + 5.62536i 0.889117 + 0.188988i
\(887\) 35.6228 7.57186i 1.19610 0.254238i 0.433525 0.901142i \(-0.357270\pi\)
0.762572 + 0.646904i \(0.223936\pi\)
\(888\) 4.52032 2.01258i 0.151692 0.0675376i
\(889\) 5.32750 + 5.91678i 0.178678 + 0.198443i
\(890\) 0.490826 + 4.66990i 0.0164525 + 0.156535i
\(891\) 3.90040 2.83380i 0.130668 0.0949360i
\(892\) −2.00761 + 19.1011i −0.0672197 + 0.639553i
\(893\) −9.41372 16.3050i −0.315018 0.545627i
\(894\) −5.03092 + 8.71382i −0.168259 + 0.291434i
\(895\) −5.92292 4.30325i −0.197981 0.143842i
\(896\) 1.74366 1.93653i 0.0582517 0.0646950i
\(897\) 1.56435 4.81458i 0.0522322 0.160754i
\(898\) −1.82526 −0.0609096
\(899\) 1.05460 + 1.66361i 0.0351729 + 0.0554846i
\(900\) 1.00000 0.0333333
\(901\) 8.86083 27.2708i 0.295197 0.908524i
\(902\) 19.5399 21.7012i 0.650607 0.722572i
\(903\) 18.0541 + 13.1171i 0.600803 + 0.436509i
\(904\) −0.346355 + 0.599905i −0.0115196 + 0.0199526i
\(905\) 5.73103 + 9.92643i 0.190506 + 0.329966i
\(906\) 1.18778 11.3010i 0.0394614 0.375450i
\(907\) 37.1958 27.0244i 1.23507 0.897329i 0.237808 0.971312i \(-0.423571\pi\)
0.997259 + 0.0739834i \(0.0235712\pi\)
\(908\) 0.142915 + 1.35974i 0.00474279 + 0.0451246i
\(909\) 6.18599 + 6.87024i 0.205176 + 0.227871i
\(910\) 2.68935 1.19738i 0.0891511 0.0396926i
\(911\) 4.45927 0.947846i 0.147742 0.0314035i −0.133447 0.991056i \(-0.542605\pi\)
0.281189 + 0.959652i \(0.409271\pi\)
\(912\) −3.63266 0.772145i −0.120289 0.0255683i
\(913\) −43.4146 19.3294i −1.43681 0.639710i
\(914\) 6.67119 + 20.5318i 0.220663 + 0.679132i
\(915\) 3.08228 + 9.48629i 0.101897 + 0.313607i
\(916\) −0.277020 0.123337i −0.00915298 0.00407517i
\(917\) 11.4561 + 2.43507i 0.378314 + 0.0804131i
\(918\) 4.46438 0.948934i 0.147347 0.0313195i
\(919\) −22.5371 + 10.0342i −0.743430 + 0.330997i −0.743259 0.669003i \(-0.766721\pi\)
−0.000171105 1.00000i \(0.500054\pi\)
\(920\) 2.99845 + 3.33012i 0.0988560 + 0.109791i
\(921\) 2.40127 + 22.8465i 0.0791245 + 0.752819i
\(922\) 15.5873 11.3249i 0.513342 0.372965i
\(923\) −1.32330 + 12.5903i −0.0435569 + 0.414416i
\(924\) 6.28163 + 10.8801i 0.206650 + 0.357929i
\(925\) −2.47405 + 4.28518i −0.0813463 + 0.140896i
\(926\) 27.5143 + 19.9903i 0.904176 + 0.656922i
\(927\) 5.96889 6.62912i 0.196044 0.217729i
\(928\) 0.109322 0.336457i 0.00358865 0.0110447i
\(929\) 13.1860 0.432620 0.216310 0.976325i \(-0.430598\pi\)
0.216310 + 0.976325i \(0.430598\pi\)
\(930\) −3.55116 + 4.28827i −0.116447 + 0.140618i
\(931\) −0.777990 −0.0254976
\(932\) 4.26854 13.1372i 0.139821 0.430324i
\(933\) 2.73908 3.04206i 0.0896736 0.0995926i
\(934\) 30.3859 + 22.0766i 0.994256 + 0.722369i
\(935\) −11.0022 + 19.0563i −0.359809 + 0.623208i
\(936\) −0.564853 0.978355i −0.0184628 0.0319785i
\(937\) 1.61039 15.3219i 0.0526092 0.500543i −0.936212 0.351436i \(-0.885693\pi\)
0.988821 0.149107i \(-0.0476399\pi\)
\(938\) −1.07962 + 0.784392i −0.0352509 + 0.0256113i
\(939\) −1.18898 11.3124i −0.0388010 0.369167i
\(940\) 3.39220 + 3.76742i 0.110641 + 0.122880i
\(941\) 34.9900 15.5785i 1.14064 0.507846i 0.252581 0.967576i \(-0.418720\pi\)
0.888059 + 0.459730i \(0.152054\pi\)
\(942\) 15.5551 3.30633i 0.506812 0.107726i
\(943\) 26.5492 + 5.64320i 0.864560 + 0.183768i
\(944\) 1.07503 + 0.478635i 0.0349893 + 0.0155783i
\(945\) 0.805256 + 2.47832i 0.0261950 + 0.0806198i
\(946\) 12.7585 + 39.2667i 0.414815 + 1.27667i
\(947\) 38.1510 + 16.9859i 1.23974 + 0.551969i 0.918647 0.395079i \(-0.129283\pi\)
0.321094 + 0.947047i \(0.395949\pi\)
\(948\) −7.98740 1.69777i −0.259419 0.0551411i
\(949\) 1.01252 0.215217i 0.0328677 0.00698625i
\(950\) 3.39274 1.51054i 0.110075 0.0490085i
\(951\) −21.1463 23.4853i −0.685715 0.761564i
\(952\) 1.24321 + 11.8283i 0.0402925 + 0.383358i
\(953\) 18.8255 13.6775i 0.609818 0.443059i −0.239532 0.970888i \(-0.576994\pi\)
0.849350 + 0.527830i \(0.176994\pi\)
\(954\) 0.656704 6.24812i 0.0212616 0.202290i
\(955\) 3.00177 + 5.19922i 0.0971351 + 0.168243i
\(956\) −9.28780 + 16.0869i −0.300389 + 0.520289i
\(957\) 1.37985 + 1.00252i 0.0446042 + 0.0324069i
\(958\) −13.8576 + 15.3905i −0.447720 + 0.497244i
\(959\) 9.34216 28.7522i 0.301674 0.928457i
\(960\) 1.00000 0.0322749
\(961\) −5.77853 30.4567i −0.186404 0.982473i
\(962\) 5.58991 0.180226
\(963\) −4.38270 + 13.4886i −0.141231 + 0.434663i
\(964\) −10.1119 + 11.2304i −0.325682 + 0.361706i
\(965\) −15.9789 11.6093i −0.514377 0.373717i
\(966\) −5.83858 + 10.1127i −0.187853 + 0.325372i
\(967\) −8.48056 14.6888i −0.272716 0.472359i 0.696840 0.717227i \(-0.254589\pi\)
−0.969556 + 0.244868i \(0.921255\pi\)
\(968\) −1.27980 + 12.1765i −0.0411342 + 0.391366i
\(969\) 13.7131 9.96313i 0.440527 0.320062i
\(970\) −1.88901 17.9727i −0.0606525 0.577070i
\(971\) −28.0482 31.1507i −0.900110 0.999674i −0.999989 0.00467401i \(-0.998512\pi\)
0.0998789 0.995000i \(-0.468154\pi\)
\(972\) 0.913545 0.406737i 0.0293020 0.0130461i
\(973\) −11.7658 + 2.50091i −0.377196 + 0.0801754i
\(974\) 17.5985 + 3.74067i 0.563892 + 0.119859i
\(975\) 1.03204 + 0.459493i 0.0330517 + 0.0147156i
\(976\) 3.08228 + 9.48629i 0.0986615 + 0.303649i
\(977\) 12.4103 + 38.1951i 0.397042 + 1.22197i 0.927360 + 0.374170i \(0.122072\pi\)
−0.530319 + 0.847798i \(0.677928\pi\)
\(978\) 13.1087 + 5.83636i 0.419169 + 0.186626i
\(979\) −22.1436 4.70677i −0.707713 0.150429i
\(980\) 0.204908 0.0435545i 0.00654553 0.00139130i
\(981\) 14.9843 6.67142i 0.478410 0.213002i
\(982\) 24.3587 + 27.0531i 0.777319 + 0.863300i
\(983\) 0.977753 + 9.30270i 0.0311855 + 0.296710i 0.998987 + 0.0449960i \(0.0143275\pi\)
−0.967802 + 0.251714i \(0.919006\pi\)
\(984\) 4.90025 3.56024i 0.156214 0.113496i
\(985\) 1.79907 17.1170i 0.0573230 0.545392i
\(986\) 0.807329 + 1.39833i 0.0257106 + 0.0445320i
\(987\) −6.60530 + 11.4407i −0.210249 + 0.364162i
\(988\) −3.39425 2.46607i −0.107985 0.0784560i
\(989\) −25.6782 + 28.5185i −0.816518 + 0.906835i
\(990\) −1.48982 + 4.58519i −0.0473495 + 0.145727i
\(991\) −5.81947 −0.184862 −0.0924308 0.995719i \(-0.529464\pi\)
−0.0924308 + 0.995719i \(0.529464\pi\)
\(992\) −3.55116 + 4.28827i −0.112749 + 0.136153i
\(993\) 13.6480 0.433106
\(994\) 9.02383 27.7725i 0.286218 0.880890i
\(995\) −15.7714 + 17.5159i −0.499986 + 0.555291i
\(996\) −7.97466 5.79393i −0.252687 0.183588i
\(997\) 12.3357 21.3661i 0.390676 0.676670i −0.601863 0.798599i \(-0.705575\pi\)
0.992539 + 0.121929i \(0.0389080\pi\)
\(998\) −17.7351 30.7181i −0.561395 0.972365i
\(999\) −0.517218 + 4.92100i −0.0163640 + 0.155694i
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 930.2.bg.g.541.1 yes 24
31.20 even 15 inner 930.2.bg.g.361.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.g.361.1 24 31.20 even 15 inner
930.2.bg.g.541.1 yes 24 1.1 even 1 trivial