Properties

Label 770.2.n.j.71.3
Level $770$
Weight $2$
Character 770.71
Analytic conductor $6.148$
Analytic rank $0$
Dimension $12$
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] = [770,2,Mod(71,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.n (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: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} - 350 x^{3} + 510 x^{2} - 175 x + 25 \) 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 71.3
Root \(0.885530 + 2.72538i\) of defining polynomial
Character \(\chi\) \(=\) 770.71
Dual form 770.2.n.j.141.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(2.31835 + 1.68438i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.885530 - 2.72538i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.61056 + 4.95678i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(2.31835 + 1.68438i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.885530 - 2.72538i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.61056 + 4.95678i) q^{9} -1.00000 q^{10} +(3.27905 + 0.497839i) q^{11} -2.86564 q^{12} +(-1.74183 - 5.36082i) q^{13} +(0.809017 + 0.587785i) q^{14} +(2.31835 - 1.68438i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.719966 + 2.21583i) q^{17} +(4.21649 - 3.06346i) q^{18} +(6.32242 + 4.59351i) q^{19} +(0.309017 + 0.951057i) q^{20} -2.86564 q^{21} +(-0.539809 - 3.27240i) q^{22} +7.98434 q^{23} +(0.885530 + 2.72538i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.56018 + 3.31317i) q^{26} +(-1.95867 + 6.02818i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-2.42257 + 1.76010i) q^{29} +(-2.31835 - 1.68438i) q^{30} +(1.57145 + 4.83644i) q^{31} -1.00000 q^{32} +(6.76342 + 6.67732i) q^{33} +2.32986 q^{34} +(0.309017 + 0.951057i) q^{35} +(-4.21649 - 3.06346i) q^{36} +(1.12195 - 0.815144i) q^{37} +(2.41495 - 7.43245i) q^{38} +(4.99146 - 15.3621i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-5.58347 - 4.05663i) q^{41} +(0.885530 + 2.72538i) q^{42} -11.5492 q^{43} +(-2.94543 + 1.52462i) q^{44} +5.21187 q^{45} +(-2.46730 - 7.59356i) q^{46} +(4.16255 + 3.02427i) q^{47} +(2.31835 - 1.68438i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-5.40142 + 3.92436i) q^{51} +(4.56018 + 3.31317i) q^{52} +(0.180063 + 0.554176i) q^{53} +6.33840 q^{54} +(1.48675 - 2.96472i) q^{55} -1.00000 q^{56} +(6.92037 + 21.2987i) q^{57} +(2.42257 + 1.76010i) q^{58} +(-11.1881 + 8.12860i) q^{59} +(-0.885530 + 2.72538i) q^{60} +(2.41788 - 7.44148i) q^{61} +(4.11412 - 2.98908i) q^{62} +(-4.21649 - 3.06346i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.63670 q^{65} +(4.26050 - 8.49580i) q^{66} -0.0485769 q^{67} +(-0.719966 - 2.21583i) q^{68} +(18.5105 + 13.4486i) q^{69} +(0.809017 - 0.587785i) q^{70} +(1.37624 - 4.23563i) q^{71} +(-1.61056 + 4.95678i) q^{72} +(0.272488 - 0.197974i) q^{73} +(-1.12195 - 0.815144i) q^{74} +(-0.885530 - 2.72538i) q^{75} -7.81494 q^{76} +(-2.94543 + 1.52462i) q^{77} -16.1527 q^{78} +(0.325367 + 1.00138i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-2.04515 + 1.48589i) q^{81} +(-2.13269 + 6.56376i) q^{82} +(3.34711 - 10.3014i) q^{83} +(2.31835 - 1.68438i) q^{84} +(1.88489 + 1.36946i) q^{85} +(3.56891 + 10.9840i) q^{86} -8.58103 q^{87} +(2.36018 + 2.33014i) q^{88} -18.5268 q^{89} +(-1.61056 - 4.95678i) q^{90} +(4.56018 + 3.31317i) q^{91} +(-6.45947 + 4.69308i) q^{92} +(-4.50321 + 13.8595i) q^{93} +(1.58995 - 4.89337i) q^{94} +(6.32242 - 4.59351i) q^{95} +(-2.31835 - 1.68438i) q^{96} +(-1.64762 - 5.07084i) q^{97} -1.00000 q^{98} +(2.81341 + 17.0553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) 2.31835 + 1.68438i 1.33850 + 0.972476i 0.999498 + 0.0316901i \(0.0100890\pi\)
0.339001 + 0.940786i \(0.389911\pi\)
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) 0.885530 2.72538i 0.361516 1.11263i
\(7\) −0.809017 + 0.587785i −0.305780 + 0.222162i
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 1.61056 + 4.95678i 0.536852 + 1.65226i
\(10\) −1.00000 −0.316228
\(11\) 3.27905 + 0.497839i 0.988670 + 0.150104i
\(12\) −2.86564 −0.827238
\(13\) −1.74183 5.36082i −0.483098 1.48682i −0.834717 0.550680i \(-0.814369\pi\)
0.351619 0.936143i \(-0.385631\pi\)
\(14\) 0.809017 + 0.587785i 0.216219 + 0.157092i
\(15\) 2.31835 1.68438i 0.598595 0.434905i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) −0.719966 + 2.21583i −0.174617 + 0.537417i −0.999616 0.0277181i \(-0.991176\pi\)
0.824998 + 0.565135i \(0.191176\pi\)
\(18\) 4.21649 3.06346i 0.993836 0.722064i
\(19\) 6.32242 + 4.59351i 1.45046 + 1.05382i 0.985723 + 0.168376i \(0.0538522\pi\)
0.464740 + 0.885447i \(0.346148\pi\)
\(20\) 0.309017 + 0.951057i 0.0690983 + 0.212663i
\(21\) −2.86564 −0.625333
\(22\) −0.539809 3.27240i −0.115088 0.697678i
\(23\) 7.98434 1.66485 0.832425 0.554138i \(-0.186952\pi\)
0.832425 + 0.554138i \(0.186952\pi\)
\(24\) 0.885530 + 2.72538i 0.180758 + 0.556316i
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) −4.56018 + 3.31317i −0.894325 + 0.649765i
\(27\) −1.95867 + 6.02818i −0.376947 + 1.16012i
\(28\) 0.309017 0.951057i 0.0583987 0.179733i
\(29\) −2.42257 + 1.76010i −0.449860 + 0.326842i −0.789540 0.613699i \(-0.789681\pi\)
0.339681 + 0.940541i \(0.389681\pi\)
\(30\) −2.31835 1.68438i −0.423270 0.307524i
\(31\) 1.57145 + 4.83644i 0.282241 + 0.868650i 0.987212 + 0.159413i \(0.0509602\pi\)
−0.704971 + 0.709237i \(0.749040\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.76342 + 6.67732i 1.17736 + 1.16237i
\(34\) 2.32986 0.399567
\(35\) 0.309017 + 0.951057i 0.0522334 + 0.160758i
\(36\) −4.21649 3.06346i −0.702748 0.510576i
\(37\) 1.12195 0.815144i 0.184447 0.134009i −0.491730 0.870748i \(-0.663635\pi\)
0.676177 + 0.736739i \(0.263635\pi\)
\(38\) 2.41495 7.43245i 0.391757 1.20570i
\(39\) 4.99146 15.3621i 0.799274 2.45991i
\(40\) 0.809017 0.587785i 0.127917 0.0929370i
\(41\) −5.58347 4.05663i −0.871991 0.633538i 0.0591296 0.998250i \(-0.481167\pi\)
−0.931120 + 0.364712i \(0.881167\pi\)
\(42\) 0.885530 + 2.72538i 0.136640 + 0.420535i
\(43\) −11.5492 −1.76124 −0.880622 0.473820i \(-0.842875\pi\)
−0.880622 + 0.473820i \(0.842875\pi\)
\(44\) −2.94543 + 1.52462i −0.444040 + 0.229845i
\(45\) 5.21187 0.776939
\(46\) −2.46730 7.59356i −0.363783 1.11961i
\(47\) 4.16255 + 3.02427i 0.607170 + 0.441135i 0.848417 0.529329i \(-0.177556\pi\)
−0.241246 + 0.970464i \(0.577556\pi\)
\(48\) 2.31835 1.68438i 0.334625 0.243119i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −0.309017 + 0.951057i −0.0437016 + 0.134500i
\(51\) −5.40142 + 3.92436i −0.756350 + 0.549521i
\(52\) 4.56018 + 3.31317i 0.632384 + 0.459454i
\(53\) 0.180063 + 0.554176i 0.0247335 + 0.0761219i 0.962661 0.270709i \(-0.0872580\pi\)
−0.937928 + 0.346830i \(0.887258\pi\)
\(54\) 6.33840 0.862547
\(55\) 1.48675 2.96472i 0.200474 0.399763i
\(56\) −1.00000 −0.133631
\(57\) 6.92037 + 21.2987i 0.916625 + 2.82108i
\(58\) 2.42257 + 1.76010i 0.318099 + 0.231112i
\(59\) −11.1881 + 8.12860i −1.45656 + 1.05825i −0.472319 + 0.881428i \(0.656583\pi\)
−0.984242 + 0.176826i \(0.943417\pi\)
\(60\) −0.885530 + 2.72538i −0.114321 + 0.351845i
\(61\) 2.41788 7.44148i 0.309578 0.952783i −0.668351 0.743846i \(-0.733000\pi\)
0.977929 0.208937i \(-0.0670005\pi\)
\(62\) 4.11412 2.98908i 0.522494 0.379614i
\(63\) −4.21649 3.06346i −0.531228 0.385959i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −5.63670 −0.699146
\(66\) 4.26050 8.49580i 0.524431 1.04576i
\(67\) −0.0485769 −0.00593462 −0.00296731 0.999996i \(-0.500945\pi\)
−0.00296731 + 0.999996i \(0.500945\pi\)
\(68\) −0.719966 2.21583i −0.0873087 0.268708i
\(69\) 18.5105 + 13.4486i 2.22840 + 1.61903i
\(70\) 0.809017 0.587785i 0.0966960 0.0702538i
\(71\) 1.37624 4.23563i 0.163330 0.502677i −0.835580 0.549369i \(-0.814868\pi\)
0.998909 + 0.0466921i \(0.0148680\pi\)
\(72\) −1.61056 + 4.95678i −0.189806 + 0.584162i
\(73\) 0.272488 0.197974i 0.0318923 0.0231711i −0.571725 0.820445i \(-0.693726\pi\)
0.603617 + 0.797274i \(0.293726\pi\)
\(74\) −1.12195 0.815144i −0.130424 0.0947585i
\(75\) −0.885530 2.72538i −0.102252 0.314700i
\(76\) −7.81494 −0.896435
\(77\) −2.94543 + 1.52462i −0.335663 + 0.173746i
\(78\) −16.1527 −1.82893
\(79\) 0.325367 + 1.00138i 0.0366067 + 0.112664i 0.967690 0.252143i \(-0.0811352\pi\)
−0.931083 + 0.364806i \(0.881135\pi\)
\(80\) −0.809017 0.587785i −0.0904508 0.0657164i
\(81\) −2.04515 + 1.48589i −0.227239 + 0.165099i
\(82\) −2.13269 + 6.56376i −0.235517 + 0.724846i
\(83\) 3.34711 10.3014i 0.367393 1.13072i −0.581075 0.813850i \(-0.697368\pi\)
0.948469 0.316871i \(-0.102632\pi\)
\(84\) 2.31835 1.68438i 0.252952 0.183781i
\(85\) 1.88489 + 1.36946i 0.204446 + 0.148538i
\(86\) 3.56891 + 10.9840i 0.384846 + 1.18443i
\(87\) −8.58103 −0.919983
\(88\) 2.36018 + 2.33014i 0.251596 + 0.248393i
\(89\) −18.5268 −1.96384 −0.981921 0.189291i \(-0.939381\pi\)
−0.981921 + 0.189291i \(0.939381\pi\)
\(90\) −1.61056 4.95678i −0.169767 0.522490i
\(91\) 4.56018 + 3.31317i 0.478037 + 0.347314i
\(92\) −6.45947 + 4.69308i −0.673446 + 0.489287i
\(93\) −4.50321 + 13.8595i −0.466961 + 1.43716i
\(94\) 1.58995 4.89337i 0.163991 0.504713i
\(95\) 6.32242 4.59351i 0.648667 0.471284i
\(96\) −2.31835 1.68438i −0.236615 0.171911i
\(97\) −1.64762 5.07084i −0.167290 0.514866i 0.831908 0.554914i \(-0.187249\pi\)
−0.999198 + 0.0400482i \(0.987249\pi\)
\(98\) −1.00000 −0.101015
\(99\) 2.81341 + 17.0553i 0.282758 + 1.71412i
\(100\) 1.00000 0.100000
\(101\) −5.64578 17.3759i −0.561776 1.72897i −0.677340 0.735670i \(-0.736867\pi\)
0.115564 0.993300i \(-0.463133\pi\)
\(102\) 5.40142 + 3.92436i 0.534820 + 0.388570i
\(103\) 9.08908 6.60361i 0.895574 0.650673i −0.0417513 0.999128i \(-0.513294\pi\)
0.937325 + 0.348455i \(0.113294\pi\)
\(104\) 1.74183 5.36082i 0.170801 0.525671i
\(105\) −0.885530 + 2.72538i −0.0864189 + 0.265970i
\(106\) 0.471410 0.342499i 0.0457874 0.0332665i
\(107\) −3.95736 2.87519i −0.382573 0.277955i 0.379833 0.925055i \(-0.375982\pi\)
−0.762405 + 0.647100i \(0.775982\pi\)
\(108\) −1.95867 6.02818i −0.188473 0.580062i
\(109\) 6.26442 0.600023 0.300011 0.953936i \(-0.403009\pi\)
0.300011 + 0.953936i \(0.403009\pi\)
\(110\) −3.27905 0.497839i −0.312645 0.0474671i
\(111\) 3.97408 0.377203
\(112\) 0.309017 + 0.951057i 0.0291994 + 0.0898664i
\(113\) −8.22373 5.97489i −0.773624 0.562071i 0.129435 0.991588i \(-0.458684\pi\)
−0.903059 + 0.429517i \(0.858684\pi\)
\(114\) 18.1178 13.1633i 1.69688 1.23286i
\(115\) 2.46730 7.59356i 0.230077 0.708103i
\(116\) 0.925339 2.84790i 0.0859155 0.264421i
\(117\) 23.7671 17.2678i 2.19727 1.59641i
\(118\) 11.1881 + 8.12860i 1.02994 + 0.748298i
\(119\) −0.719966 2.21583i −0.0659991 0.203124i
\(120\) 2.86564 0.261596
\(121\) 10.5043 + 3.26487i 0.954938 + 0.296807i
\(122\) −7.82443 −0.708391
\(123\) −6.11152 18.8093i −0.551058 1.69598i
\(124\) −4.11412 2.98908i −0.369459 0.268428i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) −1.61056 + 4.95678i −0.143480 + 0.441585i
\(127\) 2.03558 6.26487i 0.180628 0.555917i −0.819217 0.573483i \(-0.805592\pi\)
0.999846 + 0.0175661i \(0.00559175\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) −26.7752 19.4533i −2.35742 1.71277i
\(130\) 1.74183 + 5.36082i 0.152769 + 0.470175i
\(131\) 1.20821 0.105562 0.0527808 0.998606i \(-0.483192\pi\)
0.0527808 + 0.998606i \(0.483192\pi\)
\(132\) −9.39656 1.42662i −0.817865 0.124172i
\(133\) −7.81494 −0.677641
\(134\) 0.0150111 + 0.0461994i 0.00129676 + 0.00399102i
\(135\) 5.12787 + 3.72562i 0.441337 + 0.320650i
\(136\) −1.88489 + 1.36946i −0.161628 + 0.117430i
\(137\) 4.35184 13.3936i 0.371803 1.14429i −0.573807 0.818991i \(-0.694534\pi\)
0.945610 0.325302i \(-0.105466\pi\)
\(138\) 7.07037 21.7604i 0.601870 1.85237i
\(139\) −2.21905 + 1.61224i −0.188218 + 0.136748i −0.677904 0.735151i \(-0.737111\pi\)
0.489686 + 0.871899i \(0.337111\pi\)
\(140\) −0.809017 0.587785i −0.0683744 0.0496769i
\(141\) 4.55623 + 14.0226i 0.383703 + 1.18092i
\(142\) −4.45361 −0.373739
\(143\) −3.04274 18.4455i −0.254446 1.54249i
\(144\) 5.21187 0.434322
\(145\) 0.925339 + 2.84790i 0.0768452 + 0.236505i
\(146\) −0.272488 0.197974i −0.0225513 0.0163844i
\(147\) 2.31835 1.68438i 0.191214 0.138925i
\(148\) −0.428546 + 1.31893i −0.0352263 + 0.108415i
\(149\) −5.30404 + 16.3242i −0.434524 + 1.33733i 0.459049 + 0.888411i \(0.348190\pi\)
−0.893573 + 0.448917i \(0.851810\pi\)
\(150\) −2.31835 + 1.68438i −0.189292 + 0.137529i
\(151\) −4.80802 3.49323i −0.391271 0.284275i 0.374705 0.927144i \(-0.377744\pi\)
−0.765976 + 0.642869i \(0.777744\pi\)
\(152\) 2.41495 + 7.43245i 0.195878 + 0.602851i
\(153\) −12.1429 −0.981696
\(154\) 2.36018 + 2.33014i 0.190189 + 0.187768i
\(155\) 5.08533 0.408464
\(156\) 4.99146 + 15.3621i 0.399637 + 1.22996i
\(157\) 13.5872 + 9.87170i 1.08438 + 0.787847i 0.978441 0.206526i \(-0.0662157\pi\)
0.105937 + 0.994373i \(0.466216\pi\)
\(158\) 0.851822 0.618885i 0.0677673 0.0492358i
\(159\) −0.515994 + 1.58807i −0.0409210 + 0.125942i
\(160\) −0.309017 + 0.951057i −0.0244299 + 0.0751876i
\(161\) −6.45947 + 4.69308i −0.509077 + 0.369866i
\(162\) 2.04515 + 1.48589i 0.160682 + 0.116743i
\(163\) 0.751037 + 2.31146i 0.0588258 + 0.181047i 0.976151 0.217090i \(-0.0696567\pi\)
−0.917326 + 0.398138i \(0.869657\pi\)
\(164\) 6.90154 0.538920
\(165\) 8.44052 4.36899i 0.657094 0.340126i
\(166\) −10.8315 −0.840686
\(167\) −3.40864 10.4907i −0.263768 0.811795i −0.991975 0.126437i \(-0.959646\pi\)
0.728206 0.685358i \(-0.240354\pi\)
\(168\) −2.31835 1.68438i −0.178864 0.129953i
\(169\) −15.1871 + 11.0341i −1.16824 + 0.848777i
\(170\) 0.719966 2.21583i 0.0552189 0.169946i
\(171\) −12.5864 + 38.7369i −0.962506 + 2.96229i
\(172\) 9.34354 6.78848i 0.712438 0.517617i
\(173\) −11.8882 8.63730i −0.903845 0.656682i 0.0356057 0.999366i \(-0.488664\pi\)
−0.939451 + 0.342684i \(0.888664\pi\)
\(174\) 2.65168 + 8.16104i 0.201024 + 0.618687i
\(175\) 1.00000 0.0755929
\(176\) 1.48675 2.96472i 0.112068 0.223474i
\(177\) −39.6294 −2.97873
\(178\) 5.72511 + 17.6201i 0.429115 + 1.32068i
\(179\) −3.65184 2.65322i −0.272951 0.198311i 0.442886 0.896578i \(-0.353955\pi\)
−0.715837 + 0.698267i \(0.753955\pi\)
\(180\) −4.21649 + 3.06346i −0.314278 + 0.228337i
\(181\) −3.14487 + 9.67891i −0.233756 + 0.719427i 0.763528 + 0.645775i \(0.223466\pi\)
−0.997284 + 0.0736525i \(0.976534\pi\)
\(182\) 1.74183 5.36082i 0.129113 0.397370i
\(183\) 18.1398 13.1793i 1.34093 0.974242i
\(184\) 6.45947 + 4.69308i 0.476198 + 0.345978i
\(185\) −0.428546 1.31893i −0.0315074 0.0969697i
\(186\) 14.5727 1.06852
\(187\) −3.46393 + 6.90738i −0.253307 + 0.505117i
\(188\) −5.14520 −0.375252
\(189\) −1.95867 6.02818i −0.142473 0.438485i
\(190\) −6.32242 4.59351i −0.458677 0.333248i
\(191\) −9.70127 + 7.04838i −0.701959 + 0.510003i −0.880570 0.473917i \(-0.842840\pi\)
0.178611 + 0.983920i \(0.442840\pi\)
\(192\) −0.885530 + 2.72538i −0.0639076 + 0.196687i
\(193\) −5.52363 + 17.0000i −0.397600 + 1.22369i 0.529319 + 0.848423i \(0.322448\pi\)
−0.926918 + 0.375263i \(0.877552\pi\)
\(194\) −4.31351 + 3.13395i −0.309692 + 0.225005i
\(195\) −13.0678 9.49433i −0.935806 0.679903i
\(196\) 0.309017 + 0.951057i 0.0220726 + 0.0679326i
\(197\) −11.7871 −0.839795 −0.419897 0.907572i \(-0.637934\pi\)
−0.419897 + 0.907572i \(0.637934\pi\)
\(198\) 15.3512 7.94609i 1.09096 0.564704i
\(199\) −13.9342 −0.987767 −0.493884 0.869528i \(-0.664423\pi\)
−0.493884 + 0.869528i \(0.664423\pi\)
\(200\) −0.309017 0.951057i −0.0218508 0.0672499i
\(201\) −0.112618 0.0818219i −0.00794348 0.00577127i
\(202\) −14.7809 + 10.7389i −1.03998 + 0.755588i
\(203\) 0.925339 2.84790i 0.0649460 0.199883i
\(204\) 2.06316 6.34975i 0.144450 0.444572i
\(205\) −5.58347 + 4.05663i −0.389966 + 0.283327i
\(206\) −9.08908 6.60361i −0.633266 0.460095i
\(207\) 12.8592 + 39.5766i 0.893778 + 2.75076i
\(208\) −5.63670 −0.390835
\(209\) 18.4447 + 18.2099i 1.27585 + 1.25960i
\(210\) 2.86564 0.197748
\(211\) 8.17339 + 25.1551i 0.562680 + 1.73175i 0.674747 + 0.738049i \(0.264253\pi\)
−0.112067 + 0.993701i \(0.535747\pi\)
\(212\) −0.471410 0.342499i −0.0323766 0.0235230i
\(213\) 10.3250 7.50156i 0.707458 0.513999i
\(214\) −1.51158 + 4.65216i −0.103329 + 0.318015i
\(215\) −3.56891 + 10.9840i −0.243398 + 0.749102i
\(216\) −5.12787 + 3.72562i −0.348908 + 0.253496i
\(217\) −4.11412 2.98908i −0.279285 0.202912i
\(218\) −1.93581 5.95782i −0.131110 0.403515i
\(219\) 0.965185 0.0652211
\(220\) 0.539809 + 3.27240i 0.0363939 + 0.220625i
\(221\) 13.1327 0.883401
\(222\) −1.22806 3.77957i −0.0824218 0.253668i
\(223\) −19.8932 14.4532i −1.33215 0.967860i −0.999694 0.0247396i \(-0.992124\pi\)
−0.332451 0.943120i \(-0.607876\pi\)
\(224\) 0.809017 0.587785i 0.0540547 0.0392731i
\(225\) 1.61056 4.95678i 0.107370 0.330452i
\(226\) −3.14119 + 9.66758i −0.208949 + 0.643078i
\(227\) 4.52437 3.28714i 0.300293 0.218175i −0.427427 0.904050i \(-0.640580\pi\)
0.727720 + 0.685874i \(0.240580\pi\)
\(228\) −18.1178 13.1633i −1.19988 0.871762i
\(229\) −2.50409 7.70679i −0.165475 0.509279i 0.833596 0.552374i \(-0.186278\pi\)
−0.999071 + 0.0430954i \(0.986278\pi\)
\(230\) −7.98434 −0.526472
\(231\) −9.39656 1.42662i −0.618248 0.0938650i
\(232\) −2.99446 −0.196596
\(233\) 3.70224 + 11.3943i 0.242542 + 0.746467i 0.996031 + 0.0890066i \(0.0283692\pi\)
−0.753489 + 0.657460i \(0.771631\pi\)
\(234\) −23.7671 17.2678i −1.55370 1.12883i
\(235\) 4.16255 3.02427i 0.271535 0.197282i
\(236\) 4.27346 13.1523i 0.278178 0.856145i
\(237\) −0.932383 + 2.86958i −0.0605648 + 0.186399i
\(238\) −1.88489 + 1.36946i −0.122180 + 0.0887687i
\(239\) 5.23120 + 3.80069i 0.338378 + 0.245846i 0.743977 0.668205i \(-0.232937\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(240\) −0.885530 2.72538i −0.0571607 0.175923i
\(241\) 20.3441 1.31048 0.655238 0.755423i \(-0.272568\pi\)
0.655238 + 0.755423i \(0.272568\pi\)
\(242\) −0.140931 10.9991i −0.00905938 0.707049i
\(243\) 11.7710 0.755112
\(244\) 2.41788 + 7.44148i 0.154789 + 0.476392i
\(245\) −0.809017 0.587785i −0.0516862 0.0375522i
\(246\) −16.0002 + 11.6248i −1.02013 + 0.741171i
\(247\) 13.6123 41.8945i 0.866132 2.66568i
\(248\) −1.57145 + 4.83644i −0.0997874 + 0.307114i
\(249\) 25.1112 18.2443i 1.59135 1.15619i
\(250\) 0.809017 + 0.587785i 0.0511667 + 0.0371748i
\(251\) 3.88875 + 11.9683i 0.245456 + 0.755434i 0.995561 + 0.0941164i \(0.0300026\pi\)
−0.750106 + 0.661318i \(0.769997\pi\)
\(252\) 5.21187 0.328317
\(253\) 26.1810 + 3.97491i 1.64599 + 0.249901i
\(254\) −6.58727 −0.413322
\(255\) 2.06316 + 6.34975i 0.129200 + 0.397637i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −2.79916 + 2.03371i −0.174607 + 0.126859i −0.671656 0.740863i \(-0.734417\pi\)
0.497050 + 0.867722i \(0.334417\pi\)
\(258\) −10.2272 + 31.4761i −0.636718 + 1.95962i
\(259\) −0.428546 + 1.31893i −0.0266286 + 0.0819543i
\(260\) 4.56018 3.31317i 0.282811 0.205474i
\(261\) −12.6261 9.17340i −0.781536 0.567819i
\(262\) −0.373357 1.14907i −0.0230661 0.0709900i
\(263\) −8.01789 −0.494404 −0.247202 0.968964i \(-0.579511\pi\)
−0.247202 + 0.968964i \(0.579511\pi\)
\(264\) 1.54690 + 9.37751i 0.0952048 + 0.577146i
\(265\) 0.582695 0.0357946
\(266\) 2.41495 + 7.43245i 0.148070 + 0.455713i
\(267\) −42.9517 31.2062i −2.62860 1.90979i
\(268\) 0.0392996 0.0285528i 0.00240060 0.00174414i
\(269\) −5.73690 + 17.6563i −0.349785 + 1.07653i 0.609187 + 0.793026i \(0.291496\pi\)
−0.958972 + 0.283500i \(0.908504\pi\)
\(270\) 1.95867 6.02818i 0.119201 0.366863i
\(271\) −20.3914 + 14.8152i −1.23869 + 0.899960i −0.997510 0.0705210i \(-0.977534\pi\)
−0.241178 + 0.970481i \(0.577534\pi\)
\(272\) 1.88489 + 1.36946i 0.114289 + 0.0830355i
\(273\) 4.99146 + 15.3621i 0.302097 + 0.929759i
\(274\) −14.0829 −0.850777
\(275\) −2.36018 2.33014i −0.142324 0.140512i
\(276\) −22.8802 −1.37723
\(277\) −3.77868 11.6296i −0.227039 0.698754i −0.998078 0.0619665i \(-0.980263\pi\)
0.771039 0.636788i \(-0.219737\pi\)
\(278\) 2.21905 + 1.61224i 0.133090 + 0.0966956i
\(279\) −21.4422 + 15.5787i −1.28371 + 0.932672i
\(280\) −0.309017 + 0.951057i −0.0184673 + 0.0568365i
\(281\) 8.21782 25.2919i 0.490234 1.50879i −0.334020 0.942566i \(-0.608405\pi\)
0.824254 0.566220i \(-0.191595\pi\)
\(282\) 11.9284 8.66646i 0.710323 0.516080i
\(283\) 11.1013 + 8.06560i 0.659906 + 0.479450i 0.866631 0.498949i \(-0.166281\pi\)
−0.206725 + 0.978399i \(0.566281\pi\)
\(284\) 1.37624 + 4.23563i 0.0816649 + 0.251339i
\(285\) 22.3948 1.32655
\(286\) −16.6025 + 8.59380i −0.981725 + 0.508162i
\(287\) 6.90154 0.407385
\(288\) −1.61056 4.95678i −0.0949029 0.292081i
\(289\) 9.36175 + 6.80171i 0.550691 + 0.400101i
\(290\) 2.42257 1.76010i 0.142258 0.103357i
\(291\) 4.72147 14.5312i 0.276777 0.851833i
\(292\) −0.104081 + 0.320329i −0.00609089 + 0.0187458i
\(293\) −0.578013 + 0.419951i −0.0337679 + 0.0245338i −0.604541 0.796574i \(-0.706644\pi\)
0.570773 + 0.821108i \(0.306644\pi\)
\(294\) −2.31835 1.68438i −0.135209 0.0982349i
\(295\) 4.27346 + 13.1523i 0.248810 + 0.765759i
\(296\) 1.38681 0.0806064
\(297\) −9.42365 + 18.7916i −0.546815 + 1.09040i
\(298\) 17.1642 0.994298
\(299\) −13.9074 42.8026i −0.804286 2.47534i
\(300\) 2.31835 + 1.68438i 0.133850 + 0.0972476i
\(301\) 9.34354 6.78848i 0.538553 0.391281i
\(302\) −1.83650 + 5.65216i −0.105679 + 0.325245i
\(303\) 16.1788 49.7931i 0.929445 2.86054i
\(304\) 6.32242 4.59351i 0.362616 0.263456i
\(305\) −6.33010 4.59909i −0.362460 0.263343i
\(306\) 3.75236 + 11.5486i 0.214508 + 0.660189i
\(307\) −19.3442 −1.10403 −0.552015 0.833834i \(-0.686141\pi\)
−0.552015 + 0.833834i \(0.686141\pi\)
\(308\) 1.48675 2.96472i 0.0847157 0.168931i
\(309\) 32.1946 1.83149
\(310\) −1.57145 4.83644i −0.0892526 0.274691i
\(311\) −1.47831 1.07405i −0.0838271 0.0609039i 0.545082 0.838382i \(-0.316498\pi\)
−0.628909 + 0.777479i \(0.716498\pi\)
\(312\) 13.0678 9.49433i 0.739820 0.537510i
\(313\) −3.03797 + 9.34991i −0.171716 + 0.528488i −0.999468 0.0326057i \(-0.989619\pi\)
0.827752 + 0.561094i \(0.189619\pi\)
\(314\) 5.18986 15.9727i 0.292881 0.901394i
\(315\) −4.21649 + 3.06346i −0.237572 + 0.172606i
\(316\) −0.851822 0.618885i −0.0479187 0.0348150i
\(317\) −4.28127 13.1764i −0.240460 0.740060i −0.996350 0.0853616i \(-0.972795\pi\)
0.755890 0.654699i \(-0.227205\pi\)
\(318\) 1.66979 0.0936372
\(319\) −8.81996 + 4.56540i −0.493823 + 0.255613i
\(320\) 1.00000 0.0559017
\(321\) −4.33163 13.3314i −0.241768 0.744086i
\(322\) 6.45947 + 4.69308i 0.359972 + 0.261535i
\(323\) −14.7303 + 10.7022i −0.819618 + 0.595487i
\(324\) 0.781179 2.40422i 0.0433988 0.133568i
\(325\) −1.74183 + 5.36082i −0.0966196 + 0.297365i
\(326\) 1.96624 1.42856i 0.108900 0.0791205i
\(327\) 14.5231 + 10.5517i 0.803130 + 0.583508i
\(328\) −2.13269 6.56376i −0.117758 0.362423i
\(329\) −5.14520 −0.283664
\(330\) −6.76342 6.67732i −0.372314 0.367574i
\(331\) 8.02084 0.440865 0.220433 0.975402i \(-0.429253\pi\)
0.220433 + 0.975402i \(0.429253\pi\)
\(332\) 3.34711 + 10.3014i 0.183697 + 0.565360i
\(333\) 5.84745 + 4.24842i 0.320438 + 0.232812i
\(334\) −8.92393 + 6.48361i −0.488296 + 0.354768i
\(335\) −0.0150111 + 0.0461994i −0.000820144 + 0.00252414i
\(336\) −0.885530 + 2.72538i −0.0483096 + 0.148682i
\(337\) 9.38943 6.82182i 0.511475 0.371608i −0.301908 0.953337i \(-0.597624\pi\)
0.813383 + 0.581729i \(0.197624\pi\)
\(338\) 15.1871 + 11.0341i 0.826071 + 0.600176i
\(339\) −9.00149 27.7038i −0.488894 1.50466i
\(340\) −2.32986 −0.126354
\(341\) 2.74511 + 16.6412i 0.148656 + 0.901174i
\(342\) 40.7304 2.20245
\(343\) 0.309017 + 0.951057i 0.0166853 + 0.0513522i
\(344\) −9.34354 6.78848i −0.503770 0.366010i
\(345\) 18.5105 13.4486i 0.996571 0.724051i
\(346\) −4.54090 + 13.9754i −0.244120 + 0.751325i
\(347\) −8.16734 + 25.1365i −0.438446 + 1.34940i 0.451069 + 0.892489i \(0.351043\pi\)
−0.889514 + 0.456907i \(0.848957\pi\)
\(348\) 6.94220 5.04380i 0.372141 0.270376i
\(349\) −22.1490 16.0922i −1.18561 0.861396i −0.192816 0.981235i \(-0.561762\pi\)
−0.992793 + 0.119839i \(0.961762\pi\)
\(350\) −0.309017 0.951057i −0.0165177 0.0508361i
\(351\) 35.7276 1.90700
\(352\) −3.27905 0.497839i −0.174774 0.0265349i
\(353\) 21.3772 1.13779 0.568897 0.822409i \(-0.307370\pi\)
0.568897 + 0.822409i \(0.307370\pi\)
\(354\) 12.2462 + 37.6898i 0.650877 + 2.00319i
\(355\) −3.60305 2.61777i −0.191230 0.138937i
\(356\) 14.9885 10.8898i 0.794391 0.577159i
\(357\) 2.06316 6.34975i 0.109194 0.336064i
\(358\) −1.39488 + 4.29300i −0.0737217 + 0.226892i
\(359\) 8.81053 6.40123i 0.465002 0.337844i −0.330488 0.943810i \(-0.607213\pi\)
0.795490 + 0.605966i \(0.207213\pi\)
\(360\) 4.21649 + 3.06346i 0.222228 + 0.161458i
\(361\) 13.0014 + 40.0141i 0.684283 + 2.10601i
\(362\) 10.1770 0.534891
\(363\) 18.8534 + 25.2624i 0.989545 + 1.32593i
\(364\) −5.63670 −0.295443
\(365\) −0.104081 0.320329i −0.00544785 0.0167668i
\(366\) −18.1398 13.1793i −0.948180 0.688893i
\(367\) −9.15059 + 6.64829i −0.477657 + 0.347038i −0.800418 0.599442i \(-0.795389\pi\)
0.322761 + 0.946481i \(0.395389\pi\)
\(368\) 2.46730 7.59356i 0.128617 0.395842i
\(369\) 11.1153 34.2094i 0.578640 1.78087i
\(370\) −1.12195 + 0.815144i −0.0583273 + 0.0423773i
\(371\) −0.471410 0.342499i −0.0244744 0.0177817i
\(372\) −4.50321 13.8595i −0.233481 0.718580i
\(373\) 11.6658 0.604034 0.302017 0.953303i \(-0.402340\pi\)
0.302017 + 0.953303i \(0.402340\pi\)
\(374\) 7.63972 + 1.15989i 0.395040 + 0.0599767i
\(375\) −2.86564 −0.147981
\(376\) 1.58995 + 4.89337i 0.0819956 + 0.252356i
\(377\) 13.6553 + 9.92114i 0.703283 + 0.510965i
\(378\) −5.12787 + 3.72562i −0.263749 + 0.191625i
\(379\) 0.190691 0.586886i 0.00979512 0.0301463i −0.946040 0.324051i \(-0.894955\pi\)
0.955835 + 0.293905i \(0.0949549\pi\)
\(380\) −2.41495 + 7.43245i −0.123884 + 0.381277i
\(381\) 15.2716 11.0955i 0.782387 0.568438i
\(382\) 9.70127 + 7.04838i 0.496360 + 0.360627i
\(383\) −8.17261 25.1527i −0.417601 1.28524i −0.909904 0.414819i \(-0.863845\pi\)
0.492303 0.870424i \(-0.336155\pi\)
\(384\) 2.86564 0.146236
\(385\) 0.539809 + 3.27240i 0.0275112 + 0.166777i
\(386\) 17.8748 0.909806
\(387\) −18.6007 57.2471i −0.945527 2.91003i
\(388\) 4.31351 + 3.13395i 0.218986 + 0.159102i
\(389\) −1.29803 + 0.943076i −0.0658129 + 0.0478158i −0.620205 0.784440i \(-0.712951\pi\)
0.554392 + 0.832255i \(0.312951\pi\)
\(390\) −4.99146 + 15.3621i −0.252753 + 0.777892i
\(391\) −5.74845 + 17.6919i −0.290712 + 0.894719i
\(392\) 0.809017 0.587785i 0.0408615 0.0296876i
\(393\) 2.80105 + 2.03508i 0.141294 + 0.102656i
\(394\) 3.64241 + 11.2102i 0.183502 + 0.564761i
\(395\) 1.05291 0.0529776
\(396\) −12.3010 12.1444i −0.618146 0.610277i
\(397\) 5.28819 0.265407 0.132703 0.991156i \(-0.457634\pi\)
0.132703 + 0.991156i \(0.457634\pi\)
\(398\) 4.30590 + 13.2522i 0.215835 + 0.664272i
\(399\) −18.1178 13.1633i −0.907022 0.658990i
\(400\) −0.809017 + 0.587785i −0.0404508 + 0.0293893i
\(401\) −4.20445 + 12.9400i −0.209960 + 0.646192i 0.789513 + 0.613734i \(0.210333\pi\)
−0.999473 + 0.0324575i \(0.989667\pi\)
\(402\) −0.0430163 + 0.132391i −0.00214546 + 0.00660304i
\(403\) 23.1900 16.8485i 1.15518 0.839286i
\(404\) 14.7809 + 10.7389i 0.735375 + 0.534281i
\(405\) 0.781179 + 2.40422i 0.0388171 + 0.119467i
\(406\) −2.99446 −0.148613
\(407\) 4.08473 2.11435i 0.202473 0.104804i
\(408\) −6.67652 −0.330537
\(409\) −1.05137 3.23578i −0.0519868 0.159999i 0.921693 0.387921i \(-0.126807\pi\)
−0.973679 + 0.227922i \(0.926807\pi\)
\(410\) 5.58347 + 4.05663i 0.275748 + 0.200342i
\(411\) 32.6490 23.7209i 1.61046 1.17006i
\(412\) −3.47172 + 10.6849i −0.171039 + 0.526405i
\(413\) 4.27346 13.1523i 0.210283 0.647185i
\(414\) 33.6659 24.4597i 1.65459 1.20213i
\(415\) −8.76286 6.36659i −0.430152 0.312524i
\(416\) 1.74183 + 5.36082i 0.0854005 + 0.262836i
\(417\) −7.86016 −0.384914
\(418\) 11.6189 23.1691i 0.568299 1.13324i
\(419\) −39.5263 −1.93099 −0.965493 0.260428i \(-0.916136\pi\)
−0.965493 + 0.260428i \(0.916136\pi\)
\(420\) −0.885530 2.72538i −0.0432094 0.132985i
\(421\) 12.6706 + 9.20571i 0.617526 + 0.448659i 0.852057 0.523450i \(-0.175355\pi\)
−0.234530 + 0.972109i \(0.575355\pi\)
\(422\) 21.3982 15.5467i 1.04165 0.756802i
\(423\) −8.28662 + 25.5036i −0.402909 + 1.24003i
\(424\) −0.180063 + 0.554176i −0.00874461 + 0.0269131i
\(425\) 1.88489 1.36946i 0.0914308 0.0664284i
\(426\) −10.3250 7.50156i −0.500249 0.363452i
\(427\) 2.41788 + 7.44148i 0.117010 + 0.360118i
\(428\) 4.89157 0.236443
\(429\) 24.0151 47.8883i 1.15946 2.31207i
\(430\) 11.5492 0.556954
\(431\) 1.74023 + 5.35587i 0.0838239 + 0.257983i 0.984180 0.177170i \(-0.0566942\pi\)
−0.900356 + 0.435153i \(0.856694\pi\)
\(432\) 5.12787 + 3.72562i 0.246715 + 0.179249i
\(433\) 27.9291 20.2917i 1.34219 0.975156i 0.342827 0.939399i \(-0.388616\pi\)
0.999360 0.0357576i \(-0.0113844\pi\)
\(434\) −1.57145 + 4.83644i −0.0754322 + 0.232156i
\(435\) −2.65168 + 8.16104i −0.127138 + 0.391292i
\(436\) −5.06802 + 3.68214i −0.242714 + 0.176342i
\(437\) 50.4804 + 36.6761i 2.41480 + 1.75446i
\(438\) −0.298258 0.917945i −0.0142513 0.0438611i
\(439\) 30.0533 1.43437 0.717184 0.696884i \(-0.245431\pi\)
0.717184 + 0.696884i \(0.245431\pi\)
\(440\) 2.94543 1.52462i 0.140418 0.0726832i
\(441\) 5.21187 0.248184
\(442\) −4.05823 12.4899i −0.193030 0.594086i
\(443\) 25.9412 + 18.8474i 1.23251 + 0.895468i 0.997075 0.0764234i \(-0.0243501\pi\)
0.235430 + 0.971891i \(0.424350\pi\)
\(444\) −3.21510 + 2.33590i −0.152582 + 0.110857i
\(445\) −5.72511 + 17.6201i −0.271396 + 0.835272i
\(446\) −7.59851 + 23.3858i −0.359800 + 1.10735i
\(447\) −39.7927 + 28.9111i −1.88213 + 1.36745i
\(448\) −0.809017 0.587785i −0.0382225 0.0277702i
\(449\) −2.86677 8.82300i −0.135291 0.416383i 0.860344 0.509714i \(-0.170249\pi\)
−0.995635 + 0.0933305i \(0.970249\pi\)
\(450\) −5.21187 −0.245690
\(451\) −16.2889 16.0815i −0.767015 0.757250i
\(452\) 10.1651 0.478126
\(453\) −5.26274 16.1970i −0.247265 0.761003i
\(454\) −4.52437 3.28714i −0.212339 0.154273i
\(455\) 4.56018 3.31317i 0.213785 0.155324i
\(456\) −6.92037 + 21.2987i −0.324076 + 0.997403i
\(457\) −6.20449 + 19.0955i −0.290234 + 0.893248i 0.694547 + 0.719448i \(0.255605\pi\)
−0.984781 + 0.173801i \(0.944395\pi\)
\(458\) −6.55579 + 4.76306i −0.306332 + 0.222563i
\(459\) −11.9472 8.68016i −0.557648 0.405155i
\(460\) 2.46730 + 7.59356i 0.115038 + 0.354052i
\(461\) 14.6490 0.682272 0.341136 0.940014i \(-0.389188\pi\)
0.341136 + 0.940014i \(0.389188\pi\)
\(462\) 1.54690 + 9.37751i 0.0719681 + 0.436281i
\(463\) 11.0973 0.515737 0.257869 0.966180i \(-0.416980\pi\)
0.257869 + 0.966180i \(0.416980\pi\)
\(464\) 0.925339 + 2.84790i 0.0429578 + 0.132210i
\(465\) 11.7896 + 8.56562i 0.546728 + 0.397221i
\(466\) 9.69259 7.04208i 0.449001 0.326218i
\(467\) 7.63033 23.4838i 0.353090 1.08670i −0.604019 0.796970i \(-0.706435\pi\)
0.957109 0.289729i \(-0.0935650\pi\)
\(468\) −9.07821 + 27.9399i −0.419640 + 1.29152i
\(469\) 0.0392996 0.0285528i 0.00181469 0.00131845i
\(470\) −4.16255 3.02427i −0.192004 0.139499i
\(471\) 14.8722 + 45.7720i 0.685277 + 2.10906i
\(472\) −13.8292 −0.636540
\(473\) −37.8705 5.74966i −1.74129 0.264370i
\(474\) 3.01726 0.138587
\(475\) −2.41495 7.43245i −0.110805 0.341024i
\(476\) 1.88489 + 1.36946i 0.0863940 + 0.0627689i
\(477\) −2.45693 + 1.78506i −0.112495 + 0.0817323i
\(478\) 1.99814 6.14964i 0.0913928 0.281278i
\(479\) −9.64485 + 29.6838i −0.440684 + 1.35629i 0.446464 + 0.894802i \(0.352683\pi\)
−0.887148 + 0.461485i \(0.847317\pi\)
\(480\) −2.31835 + 1.68438i −0.105818 + 0.0768810i
\(481\) −6.32408 4.59472i −0.288353 0.209501i
\(482\) −6.28666 19.3483i −0.286349 0.881293i
\(483\) −22.8802 −1.04109
\(484\) −10.4172 + 3.53294i −0.473510 + 0.160588i
\(485\) −5.33180 −0.242104
\(486\) −3.63745 11.1949i −0.164998 0.507811i
\(487\) −2.44952 1.77968i −0.110998 0.0806449i 0.530901 0.847434i \(-0.321853\pi\)
−0.641900 + 0.766789i \(0.721853\pi\)
\(488\) 6.33010 4.59909i 0.286550 0.208191i
\(489\) −2.15220 + 6.62379i −0.0973258 + 0.299538i
\(490\) −0.309017 + 0.951057i −0.0139600 + 0.0429644i
\(491\) 11.9791 8.70331i 0.540608 0.392775i −0.283703 0.958912i \(-0.591563\pi\)
0.824311 + 0.566138i \(0.191563\pi\)
\(492\) 16.0002 + 11.6248i 0.721344 + 0.524087i
\(493\) −2.15591 6.63520i −0.0970972 0.298834i
\(494\) −44.0504 −1.98192
\(495\) 17.0900 + 2.59467i 0.768137 + 0.116622i
\(496\) 5.08533 0.228338
\(497\) 1.37624 + 4.23563i 0.0617328 + 0.189994i
\(498\) −25.1112 18.2443i −1.12526 0.817548i
\(499\) 5.65863 4.11124i 0.253315 0.184044i −0.453880 0.891063i \(-0.649960\pi\)
0.707195 + 0.707019i \(0.249960\pi\)
\(500\) 0.309017 0.951057i 0.0138197 0.0425325i
\(501\) 9.76791 30.0625i 0.436398 1.34310i
\(502\) 10.1809 7.39684i 0.454395 0.330137i
\(503\) 1.56788 + 1.13913i 0.0699081 + 0.0507912i 0.622190 0.782866i \(-0.286243\pi\)
−0.552282 + 0.833657i \(0.686243\pi\)
\(504\) −1.61056 4.95678i −0.0717398 0.220792i
\(505\) −18.2701 −0.813011
\(506\) −4.31002 26.1280i −0.191604 1.16153i
\(507\) −53.7947 −2.38910
\(508\) 2.03558 + 6.26487i 0.0903142 + 0.277959i
\(509\) −10.4783 7.61290i −0.464441 0.337436i 0.330830 0.943690i \(-0.392671\pi\)
−0.795271 + 0.606254i \(0.792671\pi\)
\(510\) 5.40142 3.92436i 0.239179 0.173774i
\(511\) −0.104081 + 0.320329i −0.00460428 + 0.0141705i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) −40.0740 + 29.1155i −1.76931 + 1.28548i
\(514\) 2.79916 + 2.03371i 0.123465 + 0.0897029i
\(515\) −3.47172 10.6849i −0.152982 0.470831i
\(516\) 33.0959 1.45697
\(517\) 12.1436 + 11.9890i 0.534075 + 0.527276i
\(518\) 1.38681 0.0609327
\(519\) −13.0126 40.0485i −0.571188 1.75794i
\(520\) −4.56018 3.31317i −0.199977 0.145292i
\(521\) 4.77691 3.47063i 0.209280 0.152051i −0.478208 0.878247i \(-0.658713\pi\)
0.687488 + 0.726196i \(0.258713\pi\)
\(522\) −4.82274 + 14.8429i −0.211086 + 0.649655i
\(523\) −5.62239 + 17.3039i −0.245850 + 0.756649i 0.749645 + 0.661840i \(0.230224\pi\)
−0.995495 + 0.0948089i \(0.969776\pi\)
\(524\) −0.977461 + 0.710167i −0.0427006 + 0.0310238i
\(525\) 2.31835 + 1.68438i 0.101181 + 0.0735123i
\(526\) 2.47766 + 7.62546i 0.108031 + 0.332486i
\(527\) −11.8481 −0.516111
\(528\) 8.44052 4.36899i 0.367327 0.190136i
\(529\) 40.7497 1.77173
\(530\) −0.180063 0.554176i −0.00782142 0.0240718i
\(531\) −58.3106 42.3652i −2.53047 1.83849i
\(532\) 6.32242 4.59351i 0.274112 0.199154i
\(533\) −12.0213 + 36.9979i −0.520702 + 1.60256i
\(534\) −16.4061 + 50.4927i −0.709961 + 2.18503i
\(535\) −3.95736 + 2.87519i −0.171092 + 0.124305i
\(536\) −0.0392996 0.0285528i −0.00169748 0.00123329i
\(537\) −3.99722 12.3022i −0.172493 0.530878i
\(538\) 18.5650 0.800393
\(539\) 1.48675 2.96472i 0.0640390 0.127700i
\(540\) −6.33840 −0.272761
\(541\) −4.68238 14.4109i −0.201311 0.619573i −0.999845 0.0176221i \(-0.994390\pi\)
0.798533 0.601951i \(-0.205610\pi\)
\(542\) 20.3914 + 14.8152i 0.875885 + 0.636368i
\(543\) −23.5938 + 17.1419i −1.01251 + 0.735630i
\(544\) 0.719966 2.21583i 0.0308683 0.0950028i
\(545\) 1.93581 5.95782i 0.0829211 0.255205i
\(546\) 13.0678 9.49433i 0.559251 0.406320i
\(547\) 8.36275 + 6.07590i 0.357566 + 0.259787i 0.752036 0.659122i \(-0.229072\pi\)
−0.394470 + 0.918909i \(0.629072\pi\)
\(548\) 4.35184 + 13.3936i 0.185902 + 0.572146i
\(549\) 40.7799 1.74044
\(550\) −1.48675 + 2.96472i −0.0633954 + 0.126416i
\(551\) −23.4015 −0.996938
\(552\) 7.07037 + 21.7604i 0.300935 + 0.926183i
\(553\) −0.851822 0.618885i −0.0362232 0.0263177i
\(554\) −9.89272 + 7.18748i −0.420301 + 0.305367i
\(555\) 1.22806 3.77957i 0.0521281 0.160434i
\(556\) 0.847603 2.60865i 0.0359464 0.110632i
\(557\) 5.18625 3.76803i 0.219749 0.159657i −0.472465 0.881350i \(-0.656636\pi\)
0.692214 + 0.721693i \(0.256636\pi\)
\(558\) 21.4422 + 15.5787i 0.907722 + 0.659499i
\(559\) 20.1169 + 61.9134i 0.850853 + 2.61866i
\(560\) 1.00000 0.0422577
\(561\) −19.6652 + 10.1791i −0.830266 + 0.429763i
\(562\) −26.5934 −1.12178
\(563\) −11.2328 34.5710i −0.473405 1.45699i −0.848096 0.529842i \(-0.822251\pi\)
0.374691 0.927150i \(-0.377749\pi\)
\(564\) −11.9284 8.66646i −0.502274 0.364924i
\(565\) −8.22373 + 5.97489i −0.345975 + 0.251366i
\(566\) 4.24034 13.0504i 0.178235 0.548550i
\(567\) 0.781179 2.40422i 0.0328064 0.100968i
\(568\) 3.60305 2.61777i 0.151180 0.109839i
\(569\) 36.5596 + 26.5621i 1.53266 + 1.11354i 0.954739 + 0.297445i \(0.0961344\pi\)
0.577917 + 0.816095i \(0.303866\pi\)
\(570\) −6.92037 21.2987i −0.289862 0.892104i
\(571\) 24.7479 1.03567 0.517834 0.855481i \(-0.326738\pi\)
0.517834 + 0.855481i \(0.326738\pi\)
\(572\) 13.3036 + 13.1343i 0.556253 + 0.549171i
\(573\) −34.3630 −1.43554
\(574\) −2.13269 6.56376i −0.0890169 0.273966i
\(575\) −6.45947 4.69308i −0.269378 0.195715i
\(576\) −4.21649 + 3.06346i −0.175687 + 0.127644i
\(577\) −0.811773 + 2.49838i −0.0337946 + 0.104009i −0.966531 0.256550i \(-0.917414\pi\)
0.932736 + 0.360559i \(0.117414\pi\)
\(578\) 3.57587 11.0054i 0.148737 0.457764i
\(579\) −41.4401 + 30.1080i −1.72219 + 1.25125i
\(580\) −2.42257 1.76010i −0.100592 0.0730841i
\(581\) 3.34711 + 10.3014i 0.138862 + 0.427372i
\(582\) −15.2790 −0.633334
\(583\) 0.314544 + 1.90681i 0.0130271 + 0.0789720i
\(584\) 0.336814 0.0139374
\(585\) −9.07821 27.9399i −0.375338 1.15517i
\(586\) 0.578013 + 0.419951i 0.0238775 + 0.0173480i
\(587\) −10.4339 + 7.58071i −0.430655 + 0.312889i −0.781911 0.623390i \(-0.785755\pi\)
0.351256 + 0.936280i \(0.385755\pi\)
\(588\) −0.885530 + 2.72538i −0.0365186 + 0.112393i
\(589\) −12.2808 + 37.7965i −0.506022 + 1.55738i
\(590\) 11.1881 8.12860i 0.460605 0.334649i
\(591\) −27.3266 19.8539i −1.12406 0.816680i
\(592\) −0.428546 1.31893i −0.0176131 0.0542077i
\(593\) −33.4157 −1.37222 −0.686110 0.727498i \(-0.740683\pi\)
−0.686110 + 0.727498i \(0.740683\pi\)
\(594\) 20.7839 + 3.15550i 0.852775 + 0.129472i
\(595\) −2.32986 −0.0955149
\(596\) −5.30404 16.3242i −0.217262 0.668664i
\(597\) −32.3043 23.4704i −1.32213 0.960580i
\(598\) −36.4100 + 26.4534i −1.48892 + 1.08176i
\(599\) 10.6556 32.7946i 0.435377 1.33995i −0.457323 0.889301i \(-0.651192\pi\)
0.892700 0.450652i \(-0.148808\pi\)
\(600\) 0.885530 2.72538i 0.0361516 0.111263i
\(601\) 26.4921 19.2476i 1.08063 0.785127i 0.102841 0.994698i \(-0.467207\pi\)
0.977794 + 0.209571i \(0.0672066\pi\)
\(602\) −9.34354 6.78848i −0.380814 0.276678i
\(603\) −0.0782358 0.240785i −0.00318601 0.00980553i
\(604\) 5.94304 0.241819
\(605\) 6.35109 8.98129i 0.258209 0.365142i
\(606\) −52.3556 −2.12680
\(607\) −1.79094 5.51193i −0.0726918 0.223722i 0.908109 0.418733i \(-0.137526\pi\)
−0.980801 + 0.195011i \(0.937526\pi\)
\(608\) −6.32242 4.59351i −0.256408 0.186291i
\(609\) 6.94220 5.04380i 0.281312 0.204385i
\(610\) −2.41788 + 7.44148i −0.0978972 + 0.301297i
\(611\) 8.96208 27.5824i 0.362567 1.11587i
\(612\) 9.82382 7.13742i 0.397104 0.288513i
\(613\) 31.8434 + 23.1356i 1.28614 + 0.934437i 0.999720 0.0236667i \(-0.00753406\pi\)
0.286422 + 0.958104i \(0.407534\pi\)
\(614\) 5.97768 + 18.3974i 0.241239 + 0.742459i
\(615\) −19.7773 −0.797498
\(616\) −3.27905 0.497839i −0.132117 0.0200585i
\(617\) −16.3175 −0.656918 −0.328459 0.944518i \(-0.606529\pi\)
−0.328459 + 0.944518i \(0.606529\pi\)
\(618\) −9.94869 30.6189i −0.400195 1.23167i
\(619\) 36.1810 + 26.2870i 1.45424 + 1.05656i 0.984819 + 0.173587i \(0.0555358\pi\)
0.469417 + 0.882977i \(0.344464\pi\)
\(620\) −4.11412 + 2.98908i −0.165227 + 0.120044i
\(621\) −15.6387 + 48.1310i −0.627560 + 1.93143i
\(622\) −0.564663 + 1.73785i −0.0226409 + 0.0696816i
\(623\) 14.9885 10.8898i 0.600503 0.436291i
\(624\) −13.0678 9.49433i −0.523131 0.380077i
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) 9.83108 0.392929
\(627\) 12.0889 + 73.2847i 0.482784 + 2.92671i
\(628\) −16.7947 −0.670183
\(629\) 0.998452 + 3.07292i 0.0398109 + 0.122525i
\(630\) 4.21649 + 3.06346i 0.167989 + 0.122051i
\(631\) 24.3599 17.6985i 0.969752 0.704566i 0.0143573 0.999897i \(-0.495430\pi\)
0.955395 + 0.295331i \(0.0954298\pi\)
\(632\) −0.325367 + 1.00138i −0.0129424 + 0.0398326i
\(633\) −23.4220 + 72.0854i −0.930940 + 2.86514i
\(634\) −11.2085 + 8.14346i −0.445147 + 0.323418i
\(635\) −5.32922 3.87190i −0.211483 0.153652i
\(636\) −0.515994 1.58807i −0.0204605 0.0629709i
\(637\) −5.63670 −0.223334
\(638\) 7.06747 + 6.97750i 0.279804 + 0.276242i
\(639\) 23.2116 0.918237
\(640\) −0.309017 0.951057i −0.0122150 0.0375938i
\(641\) 0.758680 + 0.551214i 0.0299661 + 0.0217716i 0.602667 0.797992i \(-0.294105\pi\)
−0.572701 + 0.819764i \(0.694105\pi\)
\(642\) −11.3404 + 8.23925i −0.447568 + 0.325177i
\(643\) 13.9028 42.7885i 0.548273 1.68741i −0.164804 0.986326i \(-0.552699\pi\)
0.713077 0.701085i \(-0.247301\pi\)
\(644\) 2.46730 7.59356i 0.0972251 0.299228i
\(645\) −26.7752 + 19.4533i −1.05427 + 0.765973i
\(646\) 14.7303 + 10.7022i 0.579558 + 0.421073i
\(647\) −10.1716 31.3050i −0.399888 1.23073i −0.925089 0.379750i \(-0.876010\pi\)
0.525202 0.850978i \(-0.323990\pi\)
\(648\) −2.52795 −0.0993072
\(649\) −40.7329 + 21.0842i −1.59891 + 0.827628i
\(650\) 5.63670 0.221089
\(651\) −4.50321 13.8595i −0.176495 0.543195i
\(652\) −1.96624 1.42856i −0.0770040 0.0559466i
\(653\) 2.68675 1.95203i 0.105140 0.0763890i −0.533973 0.845502i \(-0.679302\pi\)
0.639113 + 0.769113i \(0.279302\pi\)
\(654\) 5.54733 17.0729i 0.216918 0.667605i
\(655\) 0.373357 1.14907i 0.0145883 0.0448980i
\(656\) −5.58347 + 4.05663i −0.217998 + 0.158385i
\(657\) 1.42017 + 1.03181i 0.0554061 + 0.0402549i
\(658\) 1.58995 + 4.89337i 0.0619828 + 0.190764i
\(659\) −20.5642 −0.801069 −0.400535 0.916282i \(-0.631176\pi\)
−0.400535 + 0.916282i \(0.631176\pi\)
\(660\) −4.26050 + 8.49580i −0.165840 + 0.330699i
\(661\) −43.9387 −1.70902 −0.854508 0.519438i \(-0.826141\pi\)
−0.854508 + 0.519438i \(0.826141\pi\)
\(662\) −2.47858 7.62827i −0.0963326 0.296481i
\(663\) 30.4462 + 22.1204i 1.18243 + 0.859086i
\(664\) 8.76286 6.36659i 0.340065 0.247072i
\(665\) −2.41495 + 7.43245i −0.0936477 + 0.288218i
\(666\) 2.23353 6.87409i 0.0865474 0.266365i
\(667\) −19.3426 + 14.0532i −0.748949 + 0.544143i
\(668\) 8.92393 + 6.48361i 0.345277 + 0.250859i
\(669\) −21.7746 67.0152i −0.841854 2.59096i
\(670\) 0.0485769 0.00187669
\(671\) 11.6330 23.1972i 0.449087 0.895520i
\(672\) 2.86564 0.110544
\(673\) −0.192636 0.592874i −0.00742559 0.0228536i 0.947275 0.320421i \(-0.103825\pi\)
−0.954701 + 0.297568i \(0.903825\pi\)
\(674\) −9.38943 6.82182i −0.361667 0.262767i
\(675\) 5.12787 3.72562i 0.197372 0.143399i
\(676\) 5.80097 17.8536i 0.223114 0.686675i
\(677\) −9.47479 + 29.1604i −0.364146 + 1.12073i 0.586369 + 0.810044i \(0.300557\pi\)
−0.950514 + 0.310681i \(0.899443\pi\)
\(678\) −23.5662 + 17.1219i −0.905055 + 0.657561i
\(679\) 4.31351 + 3.13395i 0.165537 + 0.120270i
\(680\) 0.719966 + 2.21583i 0.0276094 + 0.0849731i
\(681\) 16.0258 0.614112
\(682\) 14.9785 7.75318i 0.573555 0.296884i
\(683\) −4.08570 −0.156335 −0.0781676 0.996940i \(-0.524907\pi\)
−0.0781676 + 0.996940i \(0.524907\pi\)
\(684\) −12.5864 38.7369i −0.481253 1.48114i
\(685\) −11.3933 8.27770i −0.435315 0.316275i
\(686\) 0.809017 0.587785i 0.0308884 0.0224417i
\(687\) 7.17580 22.0848i 0.273774 0.842589i
\(688\) −3.56891 + 10.9840i −0.136064 + 0.418761i
\(689\) 2.65719 1.93056i 0.101231 0.0735486i
\(690\) −18.5105 13.4486i −0.704682 0.511981i
\(691\) −3.01411 9.27646i −0.114662 0.352893i 0.877214 0.480099i \(-0.159399\pi\)
−0.991876 + 0.127206i \(0.959399\pi\)
\(692\) 14.6947 0.558607
\(693\) −12.3010 12.1444i −0.467275 0.461326i
\(694\) 26.4301 1.00327
\(695\) 0.847603 + 2.60865i 0.0321514 + 0.0989519i
\(696\) −6.94220 5.04380i −0.263143 0.191185i
\(697\) 13.0087 9.45136i 0.492739 0.357996i
\(698\) −8.46017 + 26.0377i −0.320222 + 0.985542i
\(699\) −10.6093 + 32.6520i −0.401279 + 1.23501i
\(700\) −0.809017 + 0.587785i −0.0305780 + 0.0222162i
\(701\) 6.75471 + 4.90758i 0.255122 + 0.185357i 0.707994 0.706219i \(-0.249600\pi\)
−0.452872 + 0.891576i \(0.649600\pi\)
\(702\) −11.0404 33.9790i −0.416695 1.28245i
\(703\) 10.8378 0.408755
\(704\) 0.539809 + 3.27240i 0.0203448 + 0.123333i
\(705\) 14.7443 0.555301
\(706\) −6.60592 20.3309i −0.248617 0.765164i
\(707\) 14.7809 + 10.7389i 0.555891 + 0.403879i
\(708\) 32.0609 23.2936i 1.20492 0.875427i
\(709\) 12.8706 39.6117i 0.483366 1.48765i −0.350967 0.936388i \(-0.614147\pi\)
0.834333 0.551261i \(-0.185853\pi\)
\(710\) −1.37624 + 4.23563i −0.0516494 + 0.158961i
\(711\) −4.43958 + 3.22555i −0.166497 + 0.120967i
\(712\) −14.9885 10.8898i −0.561719 0.408113i
\(713\) 12.5470 + 38.6158i 0.469890 + 1.44617i
\(714\) −6.67652 −0.249863
\(715\) −18.4830 2.80617i −0.691225 0.104945i
\(716\) 4.51392 0.168693
\(717\) 5.72594 + 17.6226i 0.213839 + 0.658129i
\(718\) −8.81053 6.40123i −0.328806 0.238892i
\(719\) −21.9996 + 15.9836i −0.820446 + 0.596089i −0.916840 0.399254i \(-0.869269\pi\)
0.0963940 + 0.995343i \(0.469269\pi\)
\(720\) 1.61056 4.95678i 0.0600218 0.184728i
\(721\) −3.47172 + 10.6849i −0.129294 + 0.397925i
\(722\) 34.0380 24.7301i 1.26676 0.920358i
\(723\) 47.1646 + 34.2671i 1.75407 + 1.27441i
\(724\) −3.14487 9.67891i −0.116878 0.359714i
\(725\) 2.99446 0.111211
\(726\) 18.1999 25.7371i 0.675462 0.955194i
\(727\) 26.4443 0.980766 0.490383 0.871507i \(-0.336857\pi\)
0.490383 + 0.871507i \(0.336857\pi\)
\(728\) 1.74183 + 5.36082i 0.0645567 + 0.198685i
\(729\) 33.4248 + 24.2845i 1.23796 + 0.899427i
\(730\) −0.272488 + 0.197974i −0.0100852 + 0.00732735i
\(731\) 8.31506 25.5911i 0.307544 0.946522i
\(732\) −6.92877 + 21.3246i −0.256095 + 0.788178i
\(733\) −20.3844 + 14.8101i −0.752914 + 0.547024i −0.896729 0.442581i \(-0.854063\pi\)
0.143815 + 0.989605i \(0.454063\pi\)
\(734\) 9.15059 + 6.64829i 0.337754 + 0.245393i
\(735\) −0.885530 2.72538i −0.0326633 0.100527i
\(736\) −7.98434 −0.294307
\(737\) −0.159286 0.0241835i −0.00586738 0.000890810i
\(738\) −35.9699 −1.32407
\(739\) 1.82531 + 5.61772i 0.0671450 + 0.206651i 0.979000 0.203862i \(-0.0653495\pi\)
−0.911855 + 0.410513i \(0.865349\pi\)
\(740\) 1.12195 + 0.815144i 0.0412437 + 0.0299653i
\(741\) 102.124 74.1976i 3.75163 2.72572i
\(742\) −0.180063 + 0.554176i −0.00661030 + 0.0203444i
\(743\) 6.05499 18.6353i 0.222136 0.683664i −0.776434 0.630199i \(-0.782973\pi\)
0.998570 0.0534654i \(-0.0170267\pi\)
\(744\) −11.7896 + 8.56562i −0.432226 + 0.314031i
\(745\) 13.8862 + 10.0889i 0.508750 + 0.369628i
\(746\) −3.60494 11.0949i −0.131986 0.406212i
\(747\) 56.4523 2.06548
\(748\) −1.25768 7.62423i −0.0459853 0.278769i
\(749\) 4.89157 0.178734
\(750\) 0.885530 + 2.72538i 0.0323350 + 0.0995168i
\(751\) −0.376424 0.273488i −0.0137359 0.00997972i 0.580896 0.813978i \(-0.302702\pi\)
−0.594632 + 0.803998i \(0.702702\pi\)
\(752\) 4.16255 3.02427i 0.151793 0.110284i
\(753\) −11.1437 + 34.2969i −0.406100 + 1.24985i
\(754\) 5.21585 16.0527i 0.189950 0.584606i
\(755\) −4.80802 + 3.49323i −0.174982 + 0.127132i
\(756\) 5.12787 + 3.72562i 0.186499 + 0.135499i
\(757\) −2.11887 6.52121i −0.0770116 0.237017i 0.905138 0.425117i \(-0.139767\pi\)
−0.982150 + 0.188100i \(0.939767\pi\)
\(758\) −0.617088 −0.0224136
\(759\) 54.0015 + 53.3140i 1.96013 + 1.93518i
\(760\) 7.81494 0.283478
\(761\) 12.8279 + 39.4802i 0.465011 + 1.43116i 0.858969 + 0.512027i \(0.171105\pi\)
−0.393959 + 0.919128i \(0.628895\pi\)
\(762\) −15.2716 11.0955i −0.553231 0.401946i
\(763\) −5.06802 + 3.68214i −0.183475 + 0.133302i
\(764\) 3.70555 11.4045i 0.134062 0.412601i
\(765\) −3.75236 + 11.5486i −0.135667 + 0.417540i
\(766\) −21.3962 + 15.5452i −0.773075 + 0.561672i
\(767\) 63.0637 + 45.8184i 2.27710 + 1.65441i
\(768\) −0.885530 2.72538i −0.0319538 0.0983437i
\(769\) −17.8632 −0.644164 −0.322082 0.946712i \(-0.604383\pi\)
−0.322082 + 0.946712i \(0.604383\pi\)
\(770\) 2.94543 1.52462i 0.106146 0.0549433i
\(771\) −9.91495 −0.357078
\(772\) −5.52363 17.0000i −0.198800 0.611843i
\(773\) −8.02110 5.82767i −0.288499 0.209607i 0.434117 0.900857i \(-0.357060\pi\)
−0.722616 + 0.691250i \(0.757060\pi\)
\(774\) −48.6973 + 35.3806i −1.75039 + 1.27173i
\(775\) 1.57145 4.83644i 0.0564483 0.173730i
\(776\) 1.64762 5.07084i 0.0591460 0.182033i
\(777\) −3.21510 + 2.33590i −0.115341 + 0.0838001i
\(778\) 1.29803 + 0.943076i 0.0465367 + 0.0338109i
\(779\) −16.6669 51.2954i −0.597153 1.83785i
\(780\) 16.1527 0.578360
\(781\) 6.62142 13.2037i 0.236933 0.472466i
\(782\) 18.6024 0.665220
\(783\) −5.86517 18.0511i −0.209604 0.645095i
\(784\) −0.809017 0.587785i −0.0288935 0.0209923i
\(785\) 13.5872 9.87170i 0.484949 0.352336i
\(786\) 1.06990 3.29283i 0.0381622 0.117451i
\(787\) −0.251113 + 0.772846i −0.00895120 + 0.0275490i −0.955432 0.295210i \(-0.904610\pi\)
0.946481 + 0.322759i \(0.104610\pi\)
\(788\) 9.53595 6.92827i 0.339704 0.246810i
\(789\) −18.5883 13.5052i −0.661759 0.480796i
\(790\) −0.325367 1.00138i −0.0115760 0.0356274i
\(791\) 10.1651 0.361429
\(792\) −7.74876 + 15.4517i −0.275340 + 0.549053i
\(793\) −44.1039 −1.56618
\(794\) −1.63414 5.02937i −0.0579935 0.178486i
\(795\) 1.35089 + 0.981478i 0.0479111 + 0.0348094i
\(796\) 11.2730 8.19030i 0.399560 0.290297i
\(797\) 9.99149 30.7507i 0.353917 1.08924i −0.602718 0.797954i \(-0.705916\pi\)
0.956635 0.291290i \(-0.0940844\pi\)
\(798\) −6.92037 + 21.2987i −0.244978 + 0.753966i
\(799\) −9.69815 + 7.04612i −0.343096 + 0.249274i
\(800\) 0.809017 + 0.587785i 0.0286031 + 0.0207813i
\(801\) −29.8385 91.8335i −1.05429 3.24478i
\(802\) 13.6059 0.480441
\(803\) 0.992060 0.513511i 0.0350090 0.0181214i
\(804\) 0.139204 0.00490934
\(805\) 2.46730 + 7.59356i 0.0869608 + 0.267638i
\(806\) −23.1900 16.8485i −0.816834 0.593465i
\(807\) −43.0401 + 31.2705i −1.51508 + 1.10077i
\(808\) 5.64578 17.3759i 0.198618 0.611283i
\(809\) −7.58639 + 23.3485i −0.266723 + 0.820890i 0.724568 + 0.689203i \(0.242039\pi\)
−0.991291 + 0.131687i \(0.957961\pi\)
\(810\) 2.04515 1.48589i 0.0718593 0.0522089i
\(811\) −33.4443 24.2987i −1.17439 0.853243i −0.182861 0.983139i \(-0.558536\pi\)
−0.991528 + 0.129896i \(0.958536\pi\)
\(812\) 0.925339 + 2.84790i 0.0324730 + 0.0999417i
\(813\) −72.2287 −2.53317
\(814\) −3.27311 3.23144i −0.114723 0.113262i
\(815\) 2.43041 0.0851335
\(816\) 2.06316 + 6.34975i 0.0722250 + 0.222286i
\(817\) −73.0192 53.0516i −2.55462 1.85604i
\(818\) −2.75252 + 1.99982i −0.0962395 + 0.0699221i
\(819\) −9.07821 + 27.9399i −0.317218 + 0.976297i
\(820\) 2.13269 6.56376i 0.0744769 0.229216i
\(821\) −12.9602 + 9.41613i −0.452314 + 0.328625i −0.790509 0.612451i \(-0.790184\pi\)
0.338195 + 0.941076i \(0.390184\pi\)
\(822\) −32.6490 23.7209i −1.13876 0.827360i
\(823\) 5.98204 + 18.4108i 0.208521 + 0.641761i 0.999550 + 0.0299831i \(0.00954534\pi\)
−0.791030 + 0.611778i \(0.790455\pi\)
\(824\) 11.2347 0.391380
\(825\) −1.54690 9.37751i −0.0538560 0.326483i
\(826\) −13.8292 −0.481179
\(827\) 13.3420 + 41.0625i 0.463947 + 1.42788i 0.860302 + 0.509785i \(0.170275\pi\)
−0.396354 + 0.918098i \(0.629725\pi\)
\(828\) −33.6659 24.4597i −1.16997 0.850033i
\(829\) 31.2150 22.6791i 1.08414 0.787676i 0.105742 0.994394i \(-0.466278\pi\)
0.978401 + 0.206717i \(0.0662781\pi\)
\(830\) −3.34711 + 10.3014i −0.116180 + 0.357565i
\(831\) 10.8283 33.3262i 0.375630 1.15607i
\(832\) 4.56018 3.31317i 0.158096 0.114863i
\(833\) 1.88489 + 1.36946i 0.0653077 + 0.0474488i
\(834\) 2.42892 + 7.47545i 0.0841067 + 0.258854i
\(835\) −11.0306 −0.381729
\(836\) −25.6256 3.89058i −0.886279 0.134559i
\(837\) −32.2329 −1.11413
\(838\) 12.2143 + 37.5918i 0.421936 + 1.29859i
\(839\) −7.53991 5.47806i −0.260306 0.189124i 0.449976 0.893041i \(-0.351433\pi\)
−0.710282 + 0.703917i \(0.751433\pi\)
\(840\) −2.31835 + 1.68438i −0.0799906 + 0.0581166i
\(841\) −6.19060 + 19.0527i −0.213469 + 0.656990i
\(842\) 4.83973 14.8952i 0.166788 0.513321i
\(843\) 61.6528 44.7934i 2.12344 1.54277i
\(844\) −21.3982 15.5467i −0.736557 0.535140i
\(845\) 5.80097 + 17.8536i 0.199559 + 0.614181i
\(846\) 26.8161 0.921956
\(847\) −10.4172 + 3.53294i −0.357940 + 0.121393i
\(848\) 0.582695 0.0200098
\(849\) 12.1513 + 37.3977i 0.417030 + 1.28349i
\(850\) −1.88489 1.36946i −0.0646514 0.0469720i
\(851\) 8.95802 6.50838i 0.307077 0.223105i
\(852\) −3.94381 + 12.1378i −0.135113 + 0.415834i
\(853\) 2.98414 9.18424i 0.102175 0.314462i −0.886882 0.461996i \(-0.847133\pi\)
0.989057 + 0.147534i \(0.0471334\pi\)
\(854\) 6.33010 4.59909i 0.216611 0.157377i
\(855\) 32.9516 + 23.9407i 1.12692 + 0.818756i
\(856\) −1.51158 4.65216i −0.0516647 0.159007i
\(857\) 7.88344 0.269293 0.134647 0.990894i \(-0.457010\pi\)
0.134647 + 0.990894i \(0.457010\pi\)
\(858\) −52.9655 8.04145i −1.80821 0.274530i
\(859\) 9.00176 0.307136 0.153568 0.988138i \(-0.450924\pi\)
0.153568 + 0.988138i \(0.450924\pi\)
\(860\) −3.56891 10.9840i −0.121699 0.374551i
\(861\) 16.0002 + 11.6248i 0.545285 + 0.396172i
\(862\) 4.55598 3.31011i 0.155177 0.112743i
\(863\) −4.50825 + 13.8750i −0.153463 + 0.472310i −0.998002 0.0631841i \(-0.979874\pi\)
0.844539 + 0.535494i \(0.179874\pi\)
\(864\) 1.95867 6.02818i 0.0666354 0.205083i
\(865\) −11.8882 + 8.63730i −0.404212 + 0.293677i
\(866\) −27.9291 20.2917i −0.949070 0.689540i
\(867\) 10.2471 + 31.5375i 0.348011 + 1.07107i
\(868\) 5.08533 0.172607
\(869\) 0.568370 + 3.44554i 0.0192806 + 0.116882i
\(870\) 8.58103 0.290924
\(871\) 0.0846130 + 0.260412i 0.00286700 + 0.00882372i
\(872\) 5.06802 + 3.68214i 0.171625 + 0.124693i
\(873\) 22.4815 16.3337i 0.760882 0.552813i
\(874\) 19.2818 59.3432i 0.652216 2.00731i
\(875\) 0.309017 0.951057i 0.0104467 0.0321516i
\(876\) −0.780851 + 0.567321i −0.0263825 + 0.0191680i
\(877\) −13.8190 10.0401i −0.466634 0.339029i 0.329494 0.944158i \(-0.393122\pi\)
−0.796128 + 0.605128i \(0.793122\pi\)
\(878\) −9.28699 28.5824i −0.313421 0.964610i
\(879\) −2.04739 −0.0690568
\(880\) −2.36018 2.33014i −0.0795618 0.0785489i
\(881\) −30.9541 −1.04287 −0.521435 0.853291i \(-0.674603\pi\)
−0.521435 + 0.853291i \(0.674603\pi\)
\(882\) −1.61056 4.95678i −0.0542302 0.166903i
\(883\) 10.9999 + 7.99186i 0.370175 + 0.268948i 0.757283 0.653086i \(-0.226526\pi\)
−0.387109 + 0.922034i \(0.626526\pi\)
\(884\) −10.6246 + 7.71921i −0.357343 + 0.259625i
\(885\) −12.2462 + 37.6898i −0.411650 + 1.26693i
\(886\) 9.90867 30.4958i 0.332888 1.02453i
\(887\) −13.9071 + 10.1041i −0.466955 + 0.339263i −0.796253 0.604963i \(-0.793188\pi\)
0.329298 + 0.944226i \(0.393188\pi\)
\(888\) 3.21510 + 2.33590i 0.107892 + 0.0783878i
\(889\) 2.03558 + 6.26487i 0.0682711 + 0.210117i
\(890\) 18.5268 0.621021
\(891\) −7.44589 + 3.85415i −0.249447 + 0.129119i
\(892\) 24.5893 0.823311
\(893\) 12.4254 + 38.2414i 0.415800 + 1.27970i
\(894\) 39.7927 + 28.9111i 1.33087 + 0.966931i
\(895\) −3.65184 + 2.65322i −0.122068 + 0.0886873i
\(896\) −0.309017 + 0.951057i −0.0103235 + 0.0317726i
\(897\) 39.8535 122.657i 1.33067 4.09538i
\(898\) −7.50530 + 5.45292i −0.250455 + 0.181966i
\(899\) −12.3196 8.95069i −0.410880 0.298522i
\(900\) 1.61056 + 4.95678i 0.0536852 + 0.165226i
\(901\) −1.35760 −0.0452281
\(902\) −10.2609 + 20.4611i −0.341651 + 0.681281i
\(903\) 33.0959 1.10136
\(904\) −3.14119 9.66758i −0.104474 0.321539i
\(905\) 8.23337 + 5.98189i 0.273686 + 0.198845i
\(906\) −13.7780 + 10.0103i −0.457744 + 0.332571i
\(907\) −7.29036 + 22.4374i −0.242073 + 0.745023i 0.754032 + 0.656838i \(0.228107\pi\)
−0.996104 + 0.0881845i \(0.971893\pi\)
\(908\) −1.72815 + 5.31871i −0.0573508 + 0.176508i
\(909\) 77.0358 55.9698i 2.55512 1.85640i
\(910\) −4.56018 3.31317i −0.151169 0.109830i
\(911\) 15.4724 + 47.6191i 0.512623 + 1.57769i 0.787566 + 0.616230i \(0.211341\pi\)
−0.274944 + 0.961460i \(0.588659\pi\)
\(912\) 22.3948 0.741565
\(913\) 16.1038 32.1123i 0.532957 1.06276i
\(914\) 20.0782 0.664127
\(915\) −6.92877 21.3246i −0.229058 0.704968i
\(916\) 6.55579 + 4.76306i 0.216609 + 0.157376i
\(917\) −0.977461 + 0.710167i −0.0322786 + 0.0234518i
\(918\) −4.56343 + 14.0448i −0.150616 + 0.463547i
\(919\) −4.06752 + 12.5185i −0.134175 + 0.412949i −0.995461 0.0951725i \(-0.969660\pi\)
0.861286 + 0.508121i \(0.169660\pi\)
\(920\) 6.45947 4.69308i 0.212962 0.154726i
\(921\) −44.8465 32.5829i −1.47774 1.07364i
\(922\) −4.52679 13.9320i −0.149082 0.458827i
\(923\) −25.1036 −0.826296
\(924\) 8.44052 4.36899i 0.277673 0.143729i
\(925\) −1.38681 −0.0455979
\(926\) −3.42927 10.5542i −0.112693 0.346833i
\(927\) 47.3711 + 34.4171i 1.55587 + 1.13041i
\(928\) 2.42257 1.76010i 0.0795247 0.0577781i
\(929\) −3.05081 + 9.38942i −0.100094 + 0.308057i −0.988548 0.150909i \(-0.951780\pi\)
0.888454 + 0.458966i \(0.151780\pi\)
\(930\) 4.50321 13.8595i 0.147666 0.454470i
\(931\) 6.32242 4.59351i 0.207209 0.150546i
\(932\) −9.69259 7.04208i −0.317491 0.230671i
\(933\) −1.61812 4.98005i −0.0529748 0.163040i
\(934\) −24.6923 −0.807956
\(935\) 5.49889 + 5.42889i 0.179833 + 0.177544i
\(936\) 29.3777 0.960240
\(937\) 1.48941 + 4.58393i 0.0486569 + 0.149751i 0.972433 0.233183i \(-0.0749140\pi\)
−0.923776 + 0.382933i \(0.874914\pi\)
\(938\) −0.0392996 0.0285528i −0.00128318 0.000932282i
\(939\) −22.7919 + 16.5593i −0.743784 + 0.540391i
\(940\) −1.58995 + 4.89337i −0.0518586 + 0.159604i
\(941\) −17.7346 + 54.5815i −0.578132 + 1.77931i 0.0471262 + 0.998889i \(0.484994\pi\)
−0.625258 + 0.780418i \(0.715006\pi\)
\(942\) 38.9360 28.2887i 1.26860 0.921695i
\(943\) −44.5803 32.3895i −1.45173 1.05475i
\(944\) 4.27346 + 13.1523i 0.139089 + 0.428072i
\(945\) −6.33840 −0.206188
\(946\) 6.23439 + 37.7938i 0.202697 + 1.22878i
\(947\) −4.22221 −0.137203 −0.0686017 0.997644i \(-0.521854\pi\)
−0.0686017 + 0.997644i \(0.521854\pi\)
\(948\) −0.932383 2.86958i −0.0302824 0.0931997i
\(949\) −1.53593 1.11592i −0.0498584 0.0362243i
\(950\) −6.32242 + 4.59351i −0.205126 + 0.149033i
\(951\) 12.2686 37.7588i 0.397835 1.22441i
\(952\) 0.719966 2.21583i 0.0233342 0.0718154i
\(953\) 4.13003 3.00064i 0.133785 0.0972004i −0.518880 0.854847i \(-0.673651\pi\)
0.652665 + 0.757647i \(0.273651\pi\)
\(954\) 2.45693 + 1.78506i 0.0795459 + 0.0577935i
\(955\) 3.70555 + 11.4045i 0.119909 + 0.369042i
\(956\) −6.46612 −0.209129
\(957\) −28.1376 4.27197i −0.909560 0.138093i
\(958\) 31.2114 1.00839
\(959\) 4.35184 + 13.3936i 0.140528 + 0.432502i
\(960\) 2.31835 + 1.68438i 0.0748243 + 0.0543631i
\(961\) 4.15787 3.02087i 0.134125 0.0974474i
\(962\) −2.41559 + 7.43441i −0.0778816 + 0.239695i
\(963\) 7.87814 24.2464i 0.253870 0.781330i
\(964\) −16.4587 + 11.9579i −0.530099 + 0.385139i
\(965\) 14.4611 + 10.5066i 0.465518 + 0.338218i
\(966\) 7.07037 + 21.7604i 0.227486 + 0.700128i
\(967\) 61.6521 1.98260 0.991298 0.131633i \(-0.0420221\pi\)
0.991298 + 0.131633i \(0.0420221\pi\)
\(968\) 6.57912 + 8.81562i 0.211461 + 0.283345i
\(969\) −52.1766 −1.67616
\(970\) 1.64762 + 5.07084i 0.0529018 + 0.162815i
\(971\) 21.0918 + 15.3241i 0.676869 + 0.491774i 0.872317 0.488940i \(-0.162616\pi\)
−0.195449 + 0.980714i \(0.562616\pi\)
\(972\) −9.52296 + 6.91884i −0.305449 + 0.221922i
\(973\) 0.847603 2.60865i 0.0271729 0.0836296i
\(974\) −0.935632 + 2.87958i −0.0299796 + 0.0922677i
\(975\) −13.0678 + 9.49433i −0.418505 + 0.304062i
\(976\) −6.33010 4.59909i −0.202621 0.147213i
\(977\) 5.88482 + 18.1116i 0.188272 + 0.579442i 0.999989 0.00460870i \(-0.00146700\pi\)
−0.811717 + 0.584050i \(0.801467\pi\)
\(978\) 6.96466 0.222705
\(979\) −60.7504 9.22338i −1.94159 0.294781i
\(980\) 1.00000 0.0319438
\(981\) 10.0892 + 31.0514i 0.322123 + 0.991394i
\(982\) −11.9791 8.70331i −0.382268 0.277734i
\(983\) 15.6421 11.3646i 0.498905 0.362476i −0.309693 0.950836i \(-0.600226\pi\)
0.808599 + 0.588361i \(0.200226\pi\)
\(984\) 6.11152 18.8093i 0.194828 0.599620i
\(985\) −3.64241 + 11.2102i −0.116057 + 0.357186i
\(986\) −5.64424 + 4.10078i −0.179749 + 0.130595i
\(987\) −11.9284 8.66646i −0.379684 0.275856i
\(988\) 13.6123 + 41.8945i 0.433066 + 1.33284i
\(989\) −92.2131 −2.93221
\(990\) −2.81341 17.0553i −0.0894161 0.542053i
\(991\) −28.4567 −0.903958 −0.451979 0.892029i \(-0.649282\pi\)
−0.451979 + 0.892029i \(0.649282\pi\)
\(992\) −1.57145 4.83644i −0.0498937 0.153557i
\(993\) 18.5951 + 13.5101i 0.590098 + 0.428731i
\(994\) 3.60305 2.61777i 0.114282 0.0830305i
\(995\) −4.30590 + 13.2522i −0.136506 + 0.420122i
\(996\) −9.59161 + 29.5199i −0.303922 + 0.935375i
\(997\) −11.4188 + 8.29624i −0.361637 + 0.262744i −0.753734 0.657179i \(-0.771750\pi\)
0.392098 + 0.919924i \(0.371750\pi\)
\(998\) −5.65863 4.11124i −0.179121 0.130139i
\(999\) 2.71630 + 8.35991i 0.0859399 + 0.264496i
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 770.2.n.j.71.3 12
11.3 even 5 8470.2.a.cw.1.1 6
11.8 odd 10 8470.2.a.dc.1.1 6
11.9 even 5 inner 770.2.n.j.141.3 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.n.j.71.3 12 1.1 even 1 trivial
770.2.n.j.141.3 yes 12 11.9 even 5 inner
8470.2.a.cw.1.1 6 11.3 even 5
8470.2.a.dc.1.1 6 11.8 odd 10