Properties

Label 370.2.l.c.11.1
Level $370$
Weight $2$
Character 370.11
Analytic conductor $2.954$
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] = [370,2,Mod(11,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.l (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.116304318664704.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.1
Root \(-1.41362 + 0.0408194i\) of defining polynomial
Character \(\chi\) \(=\) 370.11
Dual form 370.2.l.c.101.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.671462 + 1.16301i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-0.461662 + 0.799622i) q^{7} +1.00000i q^{8} +(0.598279 + 1.03625i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.671462 + 1.16301i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.34292i q^{6} +(-0.461662 + 0.799622i) q^{7} +1.00000i q^{8} +(0.598279 + 1.03625i) q^{9} +1.00000 q^{10} -2.56596 q^{11} +(0.671462 + 1.16301i) q^{12} +(-1.66565 - 0.961662i) q^{13} -0.923324i q^{14} +(1.16301 - 0.671462i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.77990 + 1.02763i) q^{17} +(-1.03625 - 0.598279i) q^{18} +(-6.29199 - 3.63268i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.619977 - 1.07383i) q^{21} +(2.22219 - 1.28298i) q^{22} +8.22046i q^{23} +(-1.16301 - 0.671462i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.92332 q^{26} -5.63565 q^{27} +(0.461662 + 0.799622i) q^{28} -5.75683i q^{29} +(-0.671462 + 1.16301i) q^{30} -10.5357i q^{31} +(0.866025 + 0.500000i) q^{32} +(1.72295 - 2.98423i) q^{33} +(1.02763 - 1.77990i) q^{34} +(0.799622 - 0.461662i) q^{35} +1.19656 q^{36} +(-3.95342 - 4.62282i) q^{37} +7.26537 q^{38} +(2.23684 - 1.29144i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.50097 + 2.59975i) q^{41} +(1.07383 + 0.619977i) q^{42} +6.95091i q^{43} +(-1.28298 + 2.22219i) q^{44} -1.19656i q^{45} +(-4.11023 - 7.11913i) q^{46} -10.5209 q^{47} +1.34292 q^{48} +(3.07374 + 5.32387i) q^{49} +(-0.866025 - 0.500000i) q^{50} -2.76005i q^{51} +(-1.66565 + 0.961662i) q^{52} +(2.61745 + 4.53356i) q^{53} +(4.88062 - 2.81783i) q^{54} +(2.22219 + 1.28298i) q^{55} +(-0.799622 - 0.461662i) q^{56} +(8.44966 - 4.87842i) q^{57} +(2.87842 + 4.98556i) q^{58} +(-3.68685 + 2.12860i) q^{59} -1.34292i q^{60} +(3.49339 + 2.01691i) q^{61} +(5.26786 + 9.12420i) q^{62} -1.10481 q^{63} -1.00000 q^{64} +(0.961662 + 1.66565i) q^{65} +3.44589i q^{66} +(1.66204 - 2.87874i) q^{67} +2.05525i q^{68} +(-9.56044 - 5.51972i) q^{69} +(-0.461662 + 0.799622i) q^{70} +(-7.86679 + 13.6257i) q^{71} +(-1.03625 + 0.598279i) q^{72} +7.08485 q^{73} +(5.73517 + 2.02678i) q^{74} -1.34292 q^{75} +(-6.29199 + 3.63268i) q^{76} +(1.18461 - 2.05180i) q^{77} +(-1.29144 + 2.23684i) q^{78} +(12.0757 + 6.97191i) q^{79} +1.00000i q^{80} +(1.98929 - 3.44555i) q^{81} -3.00193i q^{82} +(2.86398 + 4.96056i) q^{83} -1.23995 q^{84} +2.05525 q^{85} +(-3.47546 - 6.01967i) q^{86} +(6.69523 + 3.86549i) q^{87} -2.56596i q^{88} +(-3.60036 + 2.07867i) q^{89} +(0.598279 + 1.03625i) q^{90} +(1.53793 - 0.887926i) q^{91} +(7.11913 + 4.11023i) q^{92} +(12.2531 + 7.07433i) q^{93} +(9.11134 - 5.26043i) q^{94} +(3.63268 + 6.29199i) q^{95} +(-1.16301 + 0.671462i) q^{96} -9.92333i q^{97} +(-5.32387 - 3.07374i) q^{98} +(-1.53516 - 2.65898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{3} + 6 q^{4} + 2 q^{7} - 2 q^{9} + 12 q^{10} - 16 q^{11} - 4 q^{12} + 6 q^{13} - 6 q^{16} - 6 q^{17} + 18 q^{19} - 14 q^{21} + 6 q^{22} + 6 q^{25} + 8 q^{26} - 32 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{33} - 10 q^{34} - 6 q^{35} - 4 q^{36} - 26 q^{37} + 8 q^{38} + 18 q^{39} + 6 q^{40} + 4 q^{41} + 18 q^{42} - 8 q^{44} - 4 q^{46} - 20 q^{47} - 8 q^{48} + 2 q^{49} + 6 q^{52} - 2 q^{53} + 6 q^{55} + 6 q^{56} + 36 q^{57} + 8 q^{58} + 12 q^{59} + 24 q^{61} + 10 q^{62} - 16 q^{63} - 12 q^{64} + 4 q^{65} + 28 q^{67} - 6 q^{69} + 2 q^{70} - 40 q^{71} - 12 q^{73} + 14 q^{74} + 8 q^{75} + 18 q^{76} - 24 q^{77} - 10 q^{78} + 24 q^{79} - 6 q^{81} - 16 q^{83} - 28 q^{84} - 20 q^{85} - 16 q^{86} - 24 q^{87} + 6 q^{89} - 2 q^{90} - 18 q^{91} + 6 q^{92} + 78 q^{93} + 4 q^{95} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.671462 + 1.16301i −0.387669 + 0.671462i −0.992135 0.125169i \(-0.960053\pi\)
0.604467 + 0.796630i \(0.293386\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.866025 0.500000i −0.387298 0.223607i
\(6\) 1.34292i 0.548246i
\(7\) −0.461662 + 0.799622i −0.174492 + 0.302229i −0.939985 0.341215i \(-0.889162\pi\)
0.765493 + 0.643444i \(0.222495\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.598279 + 1.03625i 0.199426 + 0.345416i
\(10\) 1.00000 0.316228
\(11\) −2.56596 −0.773667 −0.386834 0.922149i \(-0.626431\pi\)
−0.386834 + 0.922149i \(0.626431\pi\)
\(12\) 0.671462 + 1.16301i 0.193834 + 0.335731i
\(13\) −1.66565 0.961662i −0.461968 0.266717i 0.250904 0.968012i \(-0.419272\pi\)
−0.712871 + 0.701295i \(0.752606\pi\)
\(14\) 0.923324i 0.246769i
\(15\) 1.16301 0.671462i 0.300287 0.173371i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.77990 + 1.02763i −0.431689 + 0.249236i −0.700066 0.714078i \(-0.746846\pi\)
0.268377 + 0.963314i \(0.413513\pi\)
\(18\) −1.03625 0.598279i −0.244246 0.141016i
\(19\) −6.29199 3.63268i −1.44348 0.833395i −0.445402 0.895330i \(-0.646939\pi\)
−0.998080 + 0.0619354i \(0.980273\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) −0.619977 1.07383i −0.135290 0.234329i
\(22\) 2.22219 1.28298i 0.473773 0.273533i
\(23\) 8.22046i 1.71408i 0.515246 + 0.857042i \(0.327701\pi\)
−0.515246 + 0.857042i \(0.672299\pi\)
\(24\) −1.16301 0.671462i −0.237398 0.137062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.92332 0.377195
\(27\) −5.63565 −1.08458
\(28\) 0.461662 + 0.799622i 0.0872459 + 0.151114i
\(29\) 5.75683i 1.06902i −0.845163 0.534508i \(-0.820497\pi\)
0.845163 0.534508i \(-0.179503\pi\)
\(30\) −0.671462 + 1.16301i −0.122592 + 0.212335i
\(31\) 10.5357i 1.89227i −0.323770 0.946136i \(-0.604950\pi\)
0.323770 0.946136i \(-0.395050\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 1.72295 2.98423i 0.299926 0.519488i
\(34\) 1.02763 1.77990i 0.176236 0.305251i
\(35\) 0.799622 0.461662i 0.135161 0.0780351i
\(36\) 1.19656 0.199426
\(37\) −3.95342 4.62282i −0.649938 0.759988i
\(38\) 7.26537 1.17860
\(39\) 2.23684 1.29144i 0.358181 0.206796i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −1.50097 + 2.59975i −0.234411 + 0.406013i −0.959101 0.283062i \(-0.908650\pi\)
0.724690 + 0.689075i \(0.241983\pi\)
\(42\) 1.07383 + 0.619977i 0.165696 + 0.0956645i
\(43\) 6.95091i 1.06000i 0.847996 + 0.530002i \(0.177809\pi\)
−0.847996 + 0.530002i \(0.822191\pi\)
\(44\) −1.28298 + 2.22219i −0.193417 + 0.335008i
\(45\) 1.19656i 0.178372i
\(46\) −4.11023 7.11913i −0.606020 1.04966i
\(47\) −10.5209 −1.53463 −0.767313 0.641273i \(-0.778407\pi\)
−0.767313 + 0.641273i \(0.778407\pi\)
\(48\) 1.34292 0.193834
\(49\) 3.07374 + 5.32387i 0.439105 + 0.760552i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 2.76005i 0.386484i
\(52\) −1.66565 + 0.961662i −0.230984 + 0.133359i
\(53\) 2.61745 + 4.53356i 0.359534 + 0.622732i 0.987883 0.155200i \(-0.0496022\pi\)
−0.628349 + 0.777932i \(0.716269\pi\)
\(54\) 4.88062 2.81783i 0.664168 0.383458i
\(55\) 2.22219 + 1.28298i 0.299640 + 0.172997i
\(56\) −0.799622 0.461662i −0.106854 0.0616922i
\(57\) 8.44966 4.87842i 1.11919 0.646162i
\(58\) 2.87842 + 4.98556i 0.377955 + 0.654637i
\(59\) −3.68685 + 2.12860i −0.479987 + 0.277120i −0.720411 0.693547i \(-0.756047\pi\)
0.240424 + 0.970668i \(0.422713\pi\)
\(60\) 1.34292i 0.173371i
\(61\) 3.49339 + 2.01691i 0.447283 + 0.258239i 0.706682 0.707531i \(-0.250191\pi\)
−0.259399 + 0.965770i \(0.583524\pi\)
\(62\) 5.26786 + 9.12420i 0.669019 + 1.15877i
\(63\) −1.10481 −0.139193
\(64\) −1.00000 −0.125000
\(65\) 0.961662 + 1.66565i 0.119280 + 0.206598i
\(66\) 3.44589i 0.424160i
\(67\) 1.66204 2.87874i 0.203050 0.351694i −0.746459 0.665431i \(-0.768248\pi\)
0.949510 + 0.313737i \(0.101581\pi\)
\(68\) 2.05525i 0.249236i
\(69\) −9.56044 5.51972i −1.15094 0.664497i
\(70\) −0.461662 + 0.799622i −0.0551792 + 0.0955731i
\(71\) −7.86679 + 13.6257i −0.933616 + 1.61707i −0.156533 + 0.987673i \(0.550032\pi\)
−0.777083 + 0.629398i \(0.783302\pi\)
\(72\) −1.03625 + 0.598279i −0.122123 + 0.0705078i
\(73\) 7.08485 0.829219 0.414609 0.910000i \(-0.363918\pi\)
0.414609 + 0.910000i \(0.363918\pi\)
\(74\) 5.73517 + 2.02678i 0.666700 + 0.235608i
\(75\) −1.34292 −0.155067
\(76\) −6.29199 + 3.63268i −0.721741 + 0.416698i
\(77\) 1.18461 2.05180i 0.134999 0.233825i
\(78\) −1.29144 + 2.23684i −0.146227 + 0.253272i
\(79\) 12.0757 + 6.97191i 1.35862 + 0.784401i 0.989438 0.144955i \(-0.0463036\pi\)
0.369185 + 0.929356i \(0.379637\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.98929 3.44555i 0.221032 0.382839i
\(82\) 3.00193i 0.331508i
\(83\) 2.86398 + 4.96056i 0.314363 + 0.544492i 0.979302 0.202405i \(-0.0648759\pi\)
−0.664939 + 0.746897i \(0.731543\pi\)
\(84\) −1.23995 −0.135290
\(85\) 2.05525 0.222923
\(86\) −3.47546 6.01967i −0.374768 0.649118i
\(87\) 6.69523 + 3.86549i 0.717804 + 0.414424i
\(88\) 2.56596i 0.273533i
\(89\) −3.60036 + 2.07867i −0.381638 + 0.220339i −0.678530 0.734572i \(-0.737383\pi\)
0.296893 + 0.954911i \(0.404050\pi\)
\(90\) 0.598279 + 1.03625i 0.0630641 + 0.109230i
\(91\) 1.53793 0.887926i 0.161219 0.0930799i
\(92\) 7.11913 + 4.11023i 0.742220 + 0.428521i
\(93\) 12.2531 + 7.07433i 1.27059 + 0.733574i
\(94\) 9.11134 5.26043i 0.939763 0.542572i
\(95\) 3.63268 + 6.29199i 0.372706 + 0.645545i
\(96\) −1.16301 + 0.671462i −0.118699 + 0.0685308i
\(97\) 9.92333i 1.00756i −0.863832 0.503781i \(-0.831942\pi\)
0.863832 0.503781i \(-0.168058\pi\)
\(98\) −5.32387 3.07374i −0.537792 0.310494i
\(99\) −1.53516 2.65898i −0.154290 0.267237i
\(100\) 1.00000 0.100000
\(101\) 16.4846 1.64028 0.820140 0.572163i \(-0.193896\pi\)
0.820140 + 0.572163i \(0.193896\pi\)
\(102\) 1.38002 + 2.39027i 0.136643 + 0.236672i
\(103\) 5.94687i 0.585963i 0.956118 + 0.292981i \(0.0946474\pi\)
−0.956118 + 0.292981i \(0.905353\pi\)
\(104\) 0.961662 1.66565i 0.0942987 0.163330i
\(105\) 1.23995i 0.121007i
\(106\) −4.53356 2.61745i −0.440338 0.254229i
\(107\) 1.86802 3.23550i 0.180588 0.312788i −0.761493 0.648173i \(-0.775533\pi\)
0.942081 + 0.335385i \(0.108867\pi\)
\(108\) −2.81783 + 4.88062i −0.271146 + 0.469638i
\(109\) −5.02919 + 2.90360i −0.481709 + 0.278115i −0.721128 0.692801i \(-0.756376\pi\)
0.239419 + 0.970916i \(0.423043\pi\)
\(110\) −2.56596 −0.244655
\(111\) 8.03094 1.49380i 0.762263 0.141785i
\(112\) 0.923324 0.0872459
\(113\) −4.34573 + 2.50901i −0.408812 + 0.236028i −0.690279 0.723543i \(-0.742512\pi\)
0.281467 + 0.959571i \(0.409179\pi\)
\(114\) −4.87842 + 8.44966i −0.456906 + 0.791384i
\(115\) 4.11023 7.11913i 0.383281 0.663862i
\(116\) −4.98556 2.87842i −0.462898 0.267254i
\(117\) 2.30137i 0.212762i
\(118\) 2.12860 3.68685i 0.195954 0.339402i
\(119\) 1.89766i 0.173959i
\(120\) 0.671462 + 1.16301i 0.0612958 + 0.106167i
\(121\) −4.41583 −0.401439
\(122\) −4.03382 −0.365205
\(123\) −2.01568 3.49126i −0.181748 0.314797i
\(124\) −9.12420 5.26786i −0.819378 0.473068i
\(125\) 1.00000i 0.0894427i
\(126\) 0.956794 0.552405i 0.0852380 0.0492122i
\(127\) −2.85853 4.95113i −0.253654 0.439342i 0.710875 0.703318i \(-0.248299\pi\)
−0.964529 + 0.263977i \(0.914966\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −8.08395 4.66727i −0.711752 0.410930i
\(130\) −1.66565 0.961662i −0.146087 0.0843433i
\(131\) −5.09112 + 2.93936i −0.444813 + 0.256813i −0.705637 0.708573i \(-0.749339\pi\)
0.260824 + 0.965386i \(0.416006\pi\)
\(132\) −1.72295 2.98423i −0.149963 0.259744i
\(133\) 5.80955 3.35415i 0.503752 0.290841i
\(134\) 3.32408i 0.287157i
\(135\) 4.88062 + 2.81783i 0.420057 + 0.242520i
\(136\) −1.02763 1.77990i −0.0881182 0.152625i
\(137\) −10.4012 −0.888636 −0.444318 0.895869i \(-0.646554\pi\)
−0.444318 + 0.895869i \(0.646554\pi\)
\(138\) 11.0394 0.939740
\(139\) 7.32003 + 12.6787i 0.620877 + 1.07539i 0.989323 + 0.145741i \(0.0465565\pi\)
−0.368446 + 0.929649i \(0.620110\pi\)
\(140\) 0.923324i 0.0780351i
\(141\) 7.06436 12.2358i 0.594926 1.03044i
\(142\) 15.7336i 1.32033i
\(143\) 4.27399 + 2.46759i 0.357409 + 0.206350i
\(144\) 0.598279 1.03625i 0.0498566 0.0863541i
\(145\) −2.87842 + 4.98556i −0.239039 + 0.414028i
\(146\) −6.13566 + 3.54242i −0.507791 + 0.293173i
\(147\) −8.25558 −0.680909
\(148\) −5.98019 + 1.11235i −0.491569 + 0.0914343i
\(149\) 19.9932 1.63791 0.818953 0.573860i \(-0.194555\pi\)
0.818953 + 0.573860i \(0.194555\pi\)
\(150\) 1.16301 0.671462i 0.0949590 0.0548246i
\(151\) −7.15059 + 12.3852i −0.581907 + 1.00789i 0.413347 + 0.910574i \(0.364360\pi\)
−0.995253 + 0.0973182i \(0.968974\pi\)
\(152\) 3.63268 6.29199i 0.294650 0.510348i
\(153\) −2.12975 1.22961i −0.172180 0.0994084i
\(154\) 2.36922i 0.190917i
\(155\) −5.26786 + 9.12420i −0.423125 + 0.732874i
\(156\) 2.58288i 0.206796i
\(157\) −4.54457 7.87142i −0.362696 0.628208i 0.625708 0.780058i \(-0.284810\pi\)
−0.988404 + 0.151850i \(0.951477\pi\)
\(158\) −13.9438 −1.10931
\(159\) −7.03007 −0.557520
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −6.57326 3.79508i −0.518046 0.299094i
\(162\) 3.97858i 0.312587i
\(163\) −7.21054 + 4.16301i −0.564773 + 0.326072i −0.755059 0.655657i \(-0.772392\pi\)
0.190286 + 0.981729i \(0.439058\pi\)
\(164\) 1.50097 + 2.59975i 0.117206 + 0.203006i
\(165\) −2.98423 + 1.72295i −0.232322 + 0.134131i
\(166\) −4.96056 2.86398i −0.385014 0.222288i
\(167\) 6.46115 + 3.73035i 0.499979 + 0.288663i 0.728705 0.684828i \(-0.240123\pi\)
−0.228726 + 0.973491i \(0.573456\pi\)
\(168\) 1.07383 0.619977i 0.0828479 0.0478322i
\(169\) −4.65041 8.05475i −0.357724 0.619596i
\(170\) −1.77990 + 1.02763i −0.136512 + 0.0788154i
\(171\) 8.69343i 0.664803i
\(172\) 6.01967 + 3.47546i 0.458995 + 0.265001i
\(173\) −1.76710 3.06071i −0.134350 0.232701i 0.790999 0.611818i \(-0.209561\pi\)
−0.925349 + 0.379116i \(0.876228\pi\)
\(174\) −7.73098 −0.586084
\(175\) −0.923324 −0.0697967
\(176\) 1.28298 + 2.22219i 0.0967084 + 0.167504i
\(177\) 5.71710i 0.429723i
\(178\) 2.07867 3.60036i 0.155803 0.269858i
\(179\) 17.0164i 1.27187i −0.771743 0.635934i \(-0.780615\pi\)
0.771743 0.635934i \(-0.219385\pi\)
\(180\) −1.03625 0.598279i −0.0772375 0.0445931i
\(181\) 4.13726 7.16595i 0.307520 0.532641i −0.670299 0.742091i \(-0.733834\pi\)
0.977819 + 0.209450i \(0.0671675\pi\)
\(182\) −0.887926 + 1.53793i −0.0658174 + 0.113999i
\(183\) −4.69136 + 2.70856i −0.346795 + 0.200222i
\(184\) −8.22046 −0.606020
\(185\) 1.11235 + 5.98019i 0.0817813 + 0.439672i
\(186\) −14.1487 −1.03743
\(187\) 4.56716 2.63685i 0.333984 0.192826i
\(188\) −5.26043 + 9.11134i −0.383657 + 0.664513i
\(189\) 2.60177 4.50639i 0.189251 0.327792i
\(190\) −6.29199 3.63268i −0.456469 0.263543i
\(191\) 9.40975i 0.680866i 0.940269 + 0.340433i \(0.110574\pi\)
−0.940269 + 0.340433i \(0.889426\pi\)
\(192\) 0.671462 1.16301i 0.0484586 0.0839327i
\(193\) 14.4344i 1.03901i −0.854467 0.519505i \(-0.826116\pi\)
0.854467 0.519505i \(-0.173884\pi\)
\(194\) 4.96167 + 8.59386i 0.356227 + 0.617003i
\(195\) −2.58288 −0.184964
\(196\) 6.14747 0.439105
\(197\) 0.351202 + 0.608300i 0.0250221 + 0.0433396i 0.878265 0.478174i \(-0.158701\pi\)
−0.853243 + 0.521513i \(0.825368\pi\)
\(198\) 2.65898 + 1.53516i 0.188965 + 0.109099i
\(199\) 14.3972i 1.02059i −0.859998 0.510297i \(-0.829536\pi\)
0.859998 0.510297i \(-0.170464\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 2.23199 + 3.86592i 0.157433 + 0.272681i
\(202\) −14.2761 + 8.24230i −1.00446 + 0.579926i
\(203\) 4.60329 + 2.65771i 0.323088 + 0.186535i
\(204\) −2.39027 1.38002i −0.167352 0.0966210i
\(205\) 2.59975 1.50097i 0.181574 0.104832i
\(206\) −2.97344 5.15014i −0.207169 0.358828i
\(207\) −8.51845 + 4.91813i −0.592073 + 0.341834i
\(208\) 1.92332i 0.133359i
\(209\) 16.1450 + 9.32134i 1.11678 + 0.644771i
\(210\) −0.619977 1.07383i −0.0427825 0.0741014i
\(211\) −11.5889 −0.797810 −0.398905 0.916992i \(-0.630610\pi\)
−0.398905 + 0.916992i \(0.630610\pi\)
\(212\) 5.23490 0.359534
\(213\) −10.5645 18.2982i −0.723867 1.25377i
\(214\) 3.73604i 0.255390i
\(215\) 3.47546 6.01967i 0.237024 0.410538i
\(216\) 5.63565i 0.383458i
\(217\) 8.42460 + 4.86394i 0.571899 + 0.330186i
\(218\) 2.90360 5.02919i 0.196657 0.340620i
\(219\) −4.75720 + 8.23972i −0.321462 + 0.556788i
\(220\) 2.22219 1.28298i 0.149820 0.0864986i
\(221\) 3.95292 0.265902
\(222\) −6.20810 + 5.30913i −0.416660 + 0.356326i
\(223\) 9.39729 0.629289 0.314645 0.949210i \(-0.398115\pi\)
0.314645 + 0.949210i \(0.398115\pi\)
\(224\) −0.799622 + 0.461662i −0.0534270 + 0.0308461i
\(225\) −0.598279 + 1.03625i −0.0398853 + 0.0690833i
\(226\) 2.50901 4.34573i 0.166897 0.289074i
\(227\) −4.32885 2.49926i −0.287316 0.165882i 0.349415 0.936968i \(-0.386380\pi\)
−0.636731 + 0.771086i \(0.719714\pi\)
\(228\) 9.75683i 0.646162i
\(229\) −13.2423 + 22.9363i −0.875076 + 1.51568i −0.0183940 + 0.999831i \(0.505855\pi\)
−0.856682 + 0.515845i \(0.827478\pi\)
\(230\) 8.22046i 0.542041i
\(231\) 1.59084 + 2.75541i 0.104669 + 0.181293i
\(232\) 5.75683 0.377955
\(233\) −19.9818 −1.30905 −0.654525 0.756040i \(-0.727131\pi\)
−0.654525 + 0.756040i \(0.727131\pi\)
\(234\) 1.15068 + 1.99304i 0.0752226 + 0.130289i
\(235\) 9.11134 + 5.26043i 0.594358 + 0.343153i
\(236\) 4.25720i 0.277120i
\(237\) −16.2167 + 9.36274i −1.05339 + 0.608175i
\(238\) 0.948832 + 1.64343i 0.0615037 + 0.106527i
\(239\) −6.87303 + 3.96815i −0.444580 + 0.256678i −0.705538 0.708672i \(-0.749295\pi\)
0.260959 + 0.965350i \(0.415961\pi\)
\(240\) −1.16301 0.671462i −0.0750717 0.0433427i
\(241\) 6.39989 + 3.69498i 0.412253 + 0.238014i 0.691757 0.722130i \(-0.256837\pi\)
−0.279504 + 0.960144i \(0.590170\pi\)
\(242\) 3.82422 2.20791i 0.245830 0.141930i
\(243\) −5.78202 10.0148i −0.370917 0.642447i
\(244\) 3.49339 2.01691i 0.223642 0.129120i
\(245\) 6.14747i 0.392748i
\(246\) 3.49126 + 2.01568i 0.222595 + 0.128515i
\(247\) 6.98683 + 12.1015i 0.444561 + 0.770003i
\(248\) 10.5357 0.669019
\(249\) −7.69221 −0.487474
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 15.1646i 0.957182i −0.878038 0.478591i \(-0.841148\pi\)
0.878038 0.478591i \(-0.158852\pi\)
\(252\) −0.552405 + 0.956794i −0.0347983 + 0.0602724i
\(253\) 21.0934i 1.32613i
\(254\) 4.95113 + 2.85853i 0.310661 + 0.179360i
\(255\) −1.38002 + 2.39027i −0.0864204 + 0.149685i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.38654 + 3.10992i −0.336003 + 0.193991i −0.658503 0.752578i \(-0.728810\pi\)
0.322500 + 0.946569i \(0.395477\pi\)
\(258\) 9.33454 0.581143
\(259\) 5.52166 1.02706i 0.343099 0.0638182i
\(260\) 1.92332 0.119280
\(261\) 5.96551 3.44419i 0.369256 0.213190i
\(262\) 2.93936 5.09112i 0.181594 0.314530i
\(263\) 13.9347 24.1355i 0.859247 1.48826i −0.0134004 0.999910i \(-0.504266\pi\)
0.872648 0.488350i \(-0.162401\pi\)
\(264\) 2.98423 + 1.72295i 0.183667 + 0.106040i
\(265\) 5.23490i 0.321577i
\(266\) −3.35415 + 5.80955i −0.205656 + 0.356206i
\(267\) 5.58299i 0.341673i
\(268\) −1.66204 2.87874i −0.101525 0.175847i
\(269\) −10.8811 −0.663434 −0.331717 0.943379i \(-0.607628\pi\)
−0.331717 + 0.943379i \(0.607628\pi\)
\(270\) −5.63565 −0.342975
\(271\) 12.0081 + 20.7986i 0.729439 + 1.26343i 0.957120 + 0.289690i \(0.0935523\pi\)
−0.227681 + 0.973736i \(0.573114\pi\)
\(272\) 1.77990 + 1.02763i 0.107922 + 0.0623090i
\(273\) 2.38483i 0.144337i
\(274\) 9.00772 5.20061i 0.544176 0.314180i
\(275\) −1.28298 2.22219i −0.0773667 0.134003i
\(276\) −9.56044 + 5.51972i −0.575471 + 0.332248i
\(277\) 4.54885 + 2.62628i 0.273314 + 0.157798i 0.630393 0.776277i \(-0.282894\pi\)
−0.357079 + 0.934074i \(0.616227\pi\)
\(278\) −12.6787 7.32003i −0.760415 0.439026i
\(279\) 10.9176 6.30330i 0.653622 0.377369i
\(280\) 0.461662 + 0.799622i 0.0275896 + 0.0477866i
\(281\) 16.7463 9.66850i 0.999002 0.576774i 0.0910494 0.995846i \(-0.470978\pi\)
0.907953 + 0.419072i \(0.137645\pi\)
\(282\) 14.1287i 0.841353i
\(283\) −0.882827 0.509701i −0.0524786 0.0302986i 0.473531 0.880777i \(-0.342979\pi\)
−0.526010 + 0.850479i \(0.676312\pi\)
\(284\) 7.86679 + 13.6257i 0.466808 + 0.808535i
\(285\) −9.75683 −0.577945
\(286\) −4.93518 −0.291823
\(287\) −1.38588 2.40041i −0.0818058 0.141692i
\(288\) 1.19656i 0.0705078i
\(289\) −6.38797 + 11.0643i −0.375763 + 0.650840i
\(290\) 5.75683i 0.338053i
\(291\) 11.5409 + 6.66313i 0.676539 + 0.390600i
\(292\) 3.54242 6.13566i 0.207305 0.359062i
\(293\) −6.44390 + 11.1612i −0.376457 + 0.652042i −0.990544 0.137196i \(-0.956191\pi\)
0.614087 + 0.789238i \(0.289524\pi\)
\(294\) 7.14954 4.12779i 0.416970 0.240738i
\(295\) 4.25720 0.247864
\(296\) 4.62282 3.95342i 0.268696 0.229788i
\(297\) 14.4609 0.839106
\(298\) −17.3146 + 9.99660i −1.00301 + 0.579087i
\(299\) 7.90531 13.6924i 0.457176 0.791852i
\(300\) −0.671462 + 1.16301i −0.0387669 + 0.0671462i
\(301\) −5.55811 3.20897i −0.320364 0.184962i
\(302\) 14.3012i 0.822940i
\(303\) −11.0688 + 19.1717i −0.635885 + 1.10138i
\(304\) 7.26537i 0.416698i
\(305\) −2.01691 3.49339i −0.115488 0.200031i
\(306\) 2.45923 0.140585
\(307\) −24.3287 −1.38851 −0.694255 0.719729i \(-0.744266\pi\)
−0.694255 + 0.719729i \(0.744266\pi\)
\(308\) −1.18461 2.05180i −0.0674993 0.116912i
\(309\) −6.91625 3.99310i −0.393452 0.227159i
\(310\) 10.5357i 0.598389i
\(311\) −5.48120 + 3.16457i −0.310810 + 0.179446i −0.647289 0.762245i \(-0.724097\pi\)
0.336479 + 0.941691i \(0.390764\pi\)
\(312\) 1.29144 + 2.23684i 0.0731133 + 0.126636i
\(313\) 10.7348 6.19774i 0.606766 0.350317i −0.164932 0.986305i \(-0.552741\pi\)
0.771699 + 0.635988i \(0.219407\pi\)
\(314\) 7.87142 + 4.54457i 0.444210 + 0.256465i
\(315\) 0.956794 + 0.552405i 0.0539092 + 0.0311245i
\(316\) 12.0757 6.97191i 0.679312 0.392201i
\(317\) 15.4949 + 26.8379i 0.870280 + 1.50737i 0.861708 + 0.507405i \(0.169395\pi\)
0.00857192 + 0.999963i \(0.497271\pi\)
\(318\) 6.08822 3.51503i 0.341410 0.197113i
\(319\) 14.7718i 0.827064i
\(320\) 0.866025 + 0.500000i 0.0484123 + 0.0279508i
\(321\) 2.50861 + 4.34503i 0.140017 + 0.242516i
\(322\) 7.59015 0.422983
\(323\) 14.9322 0.830848
\(324\) −1.98929 3.44555i −0.110516 0.191419i
\(325\) 1.92332i 0.106687i
\(326\) 4.16301 7.21054i 0.230568 0.399355i
\(327\) 7.79863i 0.431265i
\(328\) −2.59975 1.50097i −0.143547 0.0828770i
\(329\) 4.85709 8.41272i 0.267780 0.463808i
\(330\) 1.72295 2.98423i 0.0948451 0.164276i
\(331\) 2.81641 1.62606i 0.154804 0.0893761i −0.420597 0.907248i \(-0.638179\pi\)
0.575401 + 0.817871i \(0.304846\pi\)
\(332\) 5.72796 0.314363
\(333\) 2.42515 6.86246i 0.132898 0.376061i
\(334\) −7.46070 −0.408231
\(335\) −2.87874 + 1.66204i −0.157282 + 0.0908069i
\(336\) −0.619977 + 1.07383i −0.0338225 + 0.0585823i
\(337\) −15.2430 + 26.4016i −0.830339 + 1.43819i 0.0674306 + 0.997724i \(0.478520\pi\)
−0.897770 + 0.440465i \(0.854813\pi\)
\(338\) 8.05475 + 4.65041i 0.438121 + 0.252949i
\(339\) 6.73881i 0.366002i
\(340\) 1.02763 1.77990i 0.0557309 0.0965287i
\(341\) 27.0343i 1.46399i
\(342\) 4.34672 + 7.52873i 0.235044 + 0.407107i
\(343\) −12.1394 −0.655465
\(344\) −6.95091 −0.374768
\(345\) 5.51972 + 9.56044i 0.297172 + 0.514717i
\(346\) 3.06071 + 1.76710i 0.164545 + 0.0949999i
\(347\) 15.8277i 0.849676i 0.905270 + 0.424838i \(0.139669\pi\)
−0.905270 + 0.424838i \(0.860331\pi\)
\(348\) 6.69523 3.86549i 0.358902 0.207212i
\(349\) −1.51935 2.63159i −0.0813289 0.140866i 0.822492 0.568777i \(-0.192583\pi\)
−0.903821 + 0.427911i \(0.859250\pi\)
\(350\) 0.799622 0.461662i 0.0427416 0.0246769i
\(351\) 9.38701 + 5.41959i 0.501042 + 0.289277i
\(352\) −2.22219 1.28298i −0.118443 0.0683832i
\(353\) 19.1232 11.0408i 1.01782 0.587641i 0.104352 0.994540i \(-0.466723\pi\)
0.913473 + 0.406899i \(0.133390\pi\)
\(354\) 2.85855 + 4.95115i 0.151930 + 0.263151i
\(355\) 13.6257 7.86679i 0.723176 0.417526i
\(356\) 4.15734i 0.220339i
\(357\) 2.20699 + 1.27421i 0.116807 + 0.0674383i
\(358\) 8.50822 + 14.7367i 0.449673 + 0.778857i
\(359\) −10.5058 −0.554477 −0.277239 0.960801i \(-0.589419\pi\)
−0.277239 + 0.960801i \(0.589419\pi\)
\(360\) 1.19656 0.0630641
\(361\) 16.8928 + 29.2592i 0.889095 + 1.53996i
\(362\) 8.27452i 0.434899i
\(363\) 2.96506 5.13563i 0.155625 0.269551i
\(364\) 1.77585i 0.0930799i
\(365\) −6.13566 3.54242i −0.321155 0.185419i
\(366\) 2.70856 4.69136i 0.141579 0.245221i
\(367\) 6.16031 10.6700i 0.321566 0.556968i −0.659246 0.751928i \(-0.729124\pi\)
0.980811 + 0.194959i \(0.0624575\pi\)
\(368\) 7.11913 4.11023i 0.371110 0.214261i
\(369\) −3.59198 −0.186991
\(370\) −3.95342 4.62282i −0.205528 0.240329i
\(371\) −4.83351 −0.250943
\(372\) 12.2531 7.07433i 0.635294 0.366787i
\(373\) −13.2072 + 22.8755i −0.683841 + 1.18445i 0.289959 + 0.957039i \(0.406358\pi\)
−0.973800 + 0.227408i \(0.926975\pi\)
\(374\) −2.63685 + 4.56716i −0.136348 + 0.236162i
\(375\) 1.16301 + 0.671462i 0.0600573 + 0.0346741i
\(376\) 10.5209i 0.542572i
\(377\) −5.53613 + 9.58885i −0.285125 + 0.493851i
\(378\) 5.20354i 0.267641i
\(379\) 1.42044 + 2.46028i 0.0729631 + 0.126376i 0.900199 0.435479i \(-0.143421\pi\)
−0.827236 + 0.561855i \(0.810088\pi\)
\(380\) 7.26537 0.372706
\(381\) 7.67759 0.393335
\(382\) −4.70488 8.14908i −0.240722 0.416943i
\(383\) −19.1202 11.0391i −0.976998 0.564070i −0.0756355 0.997136i \(-0.524099\pi\)
−0.901362 + 0.433065i \(0.857432\pi\)
\(384\) 1.34292i 0.0685308i
\(385\) −2.05180 + 1.18461i −0.104570 + 0.0603732i
\(386\) 7.21720 + 12.5006i 0.367346 + 0.636261i
\(387\) −7.20288 + 4.15858i −0.366143 + 0.211393i
\(388\) −8.59386 4.96167i −0.436287 0.251890i
\(389\) −2.65801 1.53460i −0.134766 0.0778074i 0.431101 0.902304i \(-0.358125\pi\)
−0.565867 + 0.824496i \(0.691459\pi\)
\(390\) 2.23684 1.29144i 0.113267 0.0653945i
\(391\) −8.44756 14.6316i −0.427212 0.739952i
\(392\) −5.32387 + 3.07374i −0.268896 + 0.155247i
\(393\) 7.89467i 0.398233i
\(394\) −0.608300 0.351202i −0.0306457 0.0176933i
\(395\) −6.97191 12.0757i −0.350795 0.607595i
\(396\) −3.07032 −0.154290
\(397\) 31.2700 1.56940 0.784698 0.619878i \(-0.212818\pi\)
0.784698 + 0.619878i \(0.212818\pi\)
\(398\) 7.19862 + 12.4684i 0.360834 + 0.624984i
\(399\) 9.00872i 0.451000i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 3.17832i 0.158717i 0.996846 + 0.0793587i \(0.0252873\pi\)
−0.996846 + 0.0793587i \(0.974713\pi\)
\(402\) −3.86592 2.23199i −0.192815 0.111322i
\(403\) −10.1318 + 17.5488i −0.504701 + 0.874168i
\(404\) 8.24230 14.2761i 0.410070 0.710262i
\(405\) −3.44555 + 1.98929i −0.171211 + 0.0988485i
\(406\) −5.31542 −0.263800
\(407\) 10.1443 + 11.8620i 0.502835 + 0.587978i
\(408\) 2.76005 0.136643
\(409\) −0.0108400 + 0.00625847i −0.000536003 + 0.000309461i −0.500268 0.865871i \(-0.666765\pi\)
0.499732 + 0.866180i \(0.333432\pi\)
\(410\) −1.50097 + 2.59975i −0.0741274 + 0.128392i
\(411\) 6.98402 12.0967i 0.344496 0.596685i
\(412\) 5.15014 + 2.97344i 0.253729 + 0.146491i
\(413\) 3.93078i 0.193421i
\(414\) 4.91813 8.51845i 0.241713 0.418659i
\(415\) 5.72796i 0.281174i
\(416\) −0.961662 1.66565i −0.0471494 0.0816651i
\(417\) −19.6605 −0.962777
\(418\) −18.6427 −0.911843
\(419\) −1.64658 2.85196i −0.0804408 0.139327i 0.822999 0.568043i \(-0.192299\pi\)
−0.903439 + 0.428716i \(0.858966\pi\)
\(420\) 1.07383 + 0.619977i 0.0523976 + 0.0302518i
\(421\) 19.3554i 0.943326i −0.881779 0.471663i \(-0.843654\pi\)
0.881779 0.471663i \(-0.156346\pi\)
\(422\) 10.0362 5.79443i 0.488557 0.282068i
\(423\) −6.29441 10.9022i −0.306045 0.530085i
\(424\) −4.53356 + 2.61745i −0.220169 + 0.127115i
\(425\) −1.77990 1.02763i −0.0863379 0.0498472i
\(426\) 18.2982 + 10.5645i 0.886552 + 0.511851i
\(427\) −3.22554 + 1.86226i −0.156095 + 0.0901213i
\(428\) −1.86802 3.23550i −0.0902941 0.156394i
\(429\) −5.73964 + 3.31378i −0.277113 + 0.159991i
\(430\) 6.95091i 0.335203i
\(431\) 3.15630 + 1.82229i 0.152034 + 0.0877766i 0.574087 0.818794i \(-0.305357\pi\)
−0.422053 + 0.906571i \(0.638691\pi\)
\(432\) 2.81783 + 4.88062i 0.135573 + 0.234819i
\(433\) −23.7592 −1.14179 −0.570897 0.821022i \(-0.693404\pi\)
−0.570897 + 0.821022i \(0.693404\pi\)
\(434\) −9.72789 −0.466954
\(435\) −3.86549 6.69523i −0.185336 0.321012i
\(436\) 5.80721i 0.278115i
\(437\) 29.8623 51.7231i 1.42851 2.47425i
\(438\) 9.51440i 0.454616i
\(439\) 20.3096 + 11.7258i 0.969324 + 0.559640i 0.899030 0.437887i \(-0.144273\pi\)
0.0702940 + 0.997526i \(0.477606\pi\)
\(440\) −1.28298 + 2.22219i −0.0611638 + 0.105939i
\(441\) −3.67790 + 6.37031i −0.175138 + 0.303348i
\(442\) −3.42333 + 1.97646i −0.162831 + 0.0940106i
\(443\) −38.9584 −1.85097 −0.925486 0.378783i \(-0.876343\pi\)
−0.925486 + 0.378783i \(0.876343\pi\)
\(444\) 2.72180 7.70189i 0.129171 0.365516i
\(445\) 4.15734 0.197077
\(446\) −8.13829 + 4.69865i −0.385359 + 0.222487i
\(447\) −13.4247 + 23.2522i −0.634965 + 1.09979i
\(448\) 0.461662 0.799622i 0.0218115 0.0377786i
\(449\) 12.2385 + 7.06587i 0.577568 + 0.333459i 0.760166 0.649728i \(-0.225117\pi\)
−0.182598 + 0.983188i \(0.558451\pi\)
\(450\) 1.19656i 0.0564063i
\(451\) 3.85142 6.67086i 0.181356 0.314119i
\(452\) 5.01802i 0.236028i
\(453\) −9.60269 16.6323i −0.451174 0.781456i
\(454\) 4.99853 0.234593
\(455\) −1.77585 −0.0832532
\(456\) 4.87842 + 8.44966i 0.228453 + 0.395692i
\(457\) −25.4320 14.6832i −1.18966 0.686851i −0.231431 0.972851i \(-0.574341\pi\)
−0.958229 + 0.286000i \(0.907674\pi\)
\(458\) 26.4846i 1.23754i
\(459\) 10.0309 5.79135i 0.468203 0.270317i
\(460\) −4.11023 7.11913i −0.191641 0.331931i
\(461\) −25.1231 + 14.5048i −1.17010 + 0.675558i −0.953704 0.300747i \(-0.902764\pi\)
−0.216397 + 0.976305i \(0.569431\pi\)
\(462\) −2.75541 1.59084i −0.128193 0.0740125i
\(463\) 28.0943 + 16.2203i 1.30566 + 0.753820i 0.981368 0.192138i \(-0.0615422\pi\)
0.324287 + 0.945959i \(0.394876\pi\)
\(464\) −4.98556 + 2.87842i −0.231449 + 0.133627i
\(465\) −7.07433 12.2531i −0.328064 0.568224i
\(466\) 17.3047 9.99090i 0.801627 0.462819i
\(467\) 0.495692i 0.0229379i −0.999934 0.0114689i \(-0.996349\pi\)
0.999934 0.0114689i \(-0.00365076\pi\)
\(468\) −1.99304 1.15068i −0.0921285 0.0531904i
\(469\) 1.53460 + 2.65801i 0.0708613 + 0.122735i
\(470\) −10.5209 −0.485291
\(471\) 12.2060 0.562423
\(472\) −2.12860 3.68685i −0.0979769 0.169701i
\(473\) 17.8358i 0.820091i
\(474\) 9.36274 16.2167i 0.430045 0.744860i
\(475\) 7.26537i 0.333358i
\(476\) −1.64343 0.948832i −0.0753263 0.0434897i
\(477\) −3.13193 + 5.42466i −0.143401 + 0.248378i
\(478\) 3.96815 6.87303i 0.181499 0.314365i
\(479\) 25.6937 14.8343i 1.17398 0.677795i 0.219363 0.975643i \(-0.429602\pi\)
0.954613 + 0.297848i \(0.0962688\pi\)
\(480\) 1.34292 0.0612958
\(481\) 2.13940 + 11.5018i 0.0975483 + 0.524439i
\(482\) −7.38995 −0.336603
\(483\) 8.82739 5.09649i 0.401660 0.231899i
\(484\) −2.20791 + 3.82422i −0.100360 + 0.173828i
\(485\) −4.96167 + 8.59386i −0.225298 + 0.390227i
\(486\) 10.0148 + 5.78202i 0.454278 + 0.262278i
\(487\) 34.7629i 1.57526i −0.616151 0.787628i \(-0.711309\pi\)
0.616151 0.787628i \(-0.288691\pi\)
\(488\) −2.01691 + 3.49339i −0.0913013 + 0.158139i
\(489\) 11.1812i 0.505631i
\(490\) 3.07374 + 5.32387i 0.138857 + 0.240508i
\(491\) −33.6299 −1.51770 −0.758848 0.651268i \(-0.774237\pi\)
−0.758848 + 0.651268i \(0.774237\pi\)
\(492\) −4.03136 −0.181748
\(493\) 5.91587 + 10.2466i 0.266438 + 0.461483i
\(494\) −12.1015 6.98683i −0.544474 0.314352i
\(495\) 3.07032i 0.138001i
\(496\) −9.12420 + 5.26786i −0.409689 + 0.236534i
\(497\) −7.26360 12.5809i −0.325817 0.564331i
\(498\) 6.66165 3.84610i 0.298516 0.172348i
\(499\) −5.78065 3.33746i −0.258777 0.149405i 0.364999 0.931008i \(-0.381069\pi\)
−0.623777 + 0.781603i \(0.714403\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) −8.67683 + 5.00957i −0.387652 + 0.223811i
\(502\) 7.58231 + 13.1329i 0.338415 + 0.586152i
\(503\) −30.6980 + 17.7235i −1.36876 + 0.790252i −0.990769 0.135559i \(-0.956717\pi\)
−0.377987 + 0.925811i \(0.623384\pi\)
\(504\) 1.10481i 0.0492122i
\(505\) −14.2761 8.24230i −0.635277 0.366778i
\(506\) 10.5467 + 18.2674i 0.468858 + 0.812086i
\(507\) 12.4903 0.554713
\(508\) −5.71707 −0.253654
\(509\) −17.0193 29.4782i −0.754366 1.30660i −0.945689 0.325073i \(-0.894611\pi\)
0.191323 0.981527i \(-0.438722\pi\)
\(510\) 2.76005i 0.122217i
\(511\) −3.27081 + 5.66520i −0.144692 + 0.250614i
\(512\) 1.00000i 0.0441942i
\(513\) 35.4595 + 20.4726i 1.56558 + 0.903885i
\(514\) 3.10992 5.38654i 0.137173 0.237590i
\(515\) 2.97344 5.15014i 0.131025 0.226942i
\(516\) −8.08395 + 4.66727i −0.355876 + 0.205465i
\(517\) 26.9962 1.18729
\(518\) −4.26837 + 3.65028i −0.187541 + 0.160384i
\(519\) 4.74616 0.208333
\(520\) −1.66565 + 0.961662i −0.0730435 + 0.0421717i
\(521\) 5.22902 9.05693i 0.229087 0.396791i −0.728450 0.685099i \(-0.759759\pi\)
0.957538 + 0.288307i \(0.0930925\pi\)
\(522\) −3.44419 + 5.96551i −0.150748 + 0.261103i
\(523\) −8.39138 4.84477i −0.366929 0.211847i 0.305187 0.952293i \(-0.401281\pi\)
−0.672116 + 0.740446i \(0.734614\pi\)
\(524\) 5.87872i 0.256813i
\(525\) 0.619977 1.07383i 0.0270580 0.0468658i
\(526\) 27.8693i 1.21516i
\(527\) 10.8268 + 18.7525i 0.471622 + 0.816874i
\(528\) −3.44589 −0.149963
\(529\) −44.5760 −1.93809
\(530\) 2.61745 + 4.53356i 0.113695 + 0.196925i
\(531\) −4.41153 2.54700i −0.191444 0.110530i
\(532\) 6.70829i 0.290841i
\(533\) 5.00016 2.88684i 0.216581 0.125043i
\(534\) 2.79149 + 4.83501i 0.120800 + 0.209231i
\(535\) −3.23550 + 1.86802i −0.139883 + 0.0807615i
\(536\) 2.87874 + 1.66204i 0.124343 + 0.0717892i
\(537\) 19.7902 + 11.4259i 0.854011 + 0.493063i
\(538\) 9.42333 5.44056i 0.406268 0.234559i
\(539\) −7.88710 13.6609i −0.339721 0.588415i
\(540\) 4.88062 2.81783i 0.210028 0.121260i
\(541\) 9.38662i 0.403562i 0.979431 + 0.201781i \(0.0646730\pi\)
−0.979431 + 0.201781i \(0.935327\pi\)
\(542\) −20.7986 12.0081i −0.893377 0.515791i
\(543\) 5.55602 + 9.62331i 0.238432 + 0.412976i
\(544\) −2.05525 −0.0881182
\(545\) 5.80721 0.248753
\(546\) −1.19242 2.06533i −0.0510307 0.0883878i
\(547\) 24.0289i 1.02740i −0.857970 0.513700i \(-0.828274\pi\)
0.857970 0.513700i \(-0.171726\pi\)
\(548\) −5.20061 + 9.00772i −0.222159 + 0.384791i
\(549\) 4.82670i 0.205999i
\(550\) 2.22219 + 1.28298i 0.0947545 + 0.0547065i
\(551\) −20.9128 + 36.2220i −0.890913 + 1.54311i
\(552\) 5.51972 9.56044i 0.234935 0.406919i
\(553\) −11.1498 + 6.43734i −0.474137 + 0.273743i
\(554\) −5.25256 −0.223160
\(555\) −7.70189 2.72180i −0.326927 0.115534i
\(556\) 14.6401 0.620877
\(557\) 15.7183 9.07495i 0.666005 0.384518i −0.128556 0.991702i \(-0.541034\pi\)
0.794561 + 0.607184i \(0.207701\pi\)
\(558\) −6.30330 + 10.9176i −0.266840 + 0.462180i
\(559\) 6.68443 11.5778i 0.282721 0.489688i
\(560\) −0.799622 0.461662i −0.0337902 0.0195088i
\(561\) 7.08218i 0.299010i
\(562\) −9.66850 + 16.7463i −0.407841 + 0.706401i
\(563\) 19.4195i 0.818436i −0.912437 0.409218i \(-0.865802\pi\)
0.912437 0.409218i \(-0.134198\pi\)
\(564\) −7.06436 12.2358i −0.297463 0.515221i
\(565\) 5.01802 0.211110
\(566\) 1.01940 0.0428486
\(567\) 1.83676 + 3.18136i 0.0771366 + 0.133605i
\(568\) −13.6257 7.86679i −0.571721 0.330083i
\(569\) 10.1824i 0.426867i 0.976958 + 0.213433i \(0.0684646\pi\)
−0.976958 + 0.213433i \(0.931535\pi\)
\(570\) 8.44966 4.87842i 0.353918 0.204334i
\(571\) −7.42714 12.8642i −0.310816 0.538349i 0.667723 0.744410i \(-0.267269\pi\)
−0.978539 + 0.206060i \(0.933936\pi\)
\(572\) 4.27399 2.46759i 0.178705 0.103175i
\(573\) −10.9436 6.31829i −0.457175 0.263950i
\(574\) 2.40041 + 1.38588i 0.100191 + 0.0578454i
\(575\) −7.11913 + 4.11023i −0.296888 + 0.171408i
\(576\) −0.598279 1.03625i −0.0249283 0.0431771i
\(577\) −38.8951 + 22.4561i −1.61922 + 0.934859i −0.632102 + 0.774885i \(0.717808\pi\)
−0.987121 + 0.159974i \(0.948859\pi\)
\(578\) 12.7759i 0.531409i
\(579\) 16.7873 + 9.69214i 0.697656 + 0.402792i
\(580\) 2.87842 + 4.98556i 0.119520 + 0.207014i
\(581\) −5.28876 −0.219415
\(582\) −13.3263 −0.552392
\(583\) −6.71628 11.6329i −0.278160 0.481787i
\(584\) 7.08485i 0.293173i
\(585\) −1.15068 + 1.99304i −0.0475749 + 0.0824022i
\(586\) 12.8878i 0.532390i
\(587\) −4.80132 2.77204i −0.198172 0.114415i 0.397631 0.917546i \(-0.369833\pi\)
−0.595802 + 0.803131i \(0.703166\pi\)
\(588\) −4.12779 + 7.14954i −0.170227 + 0.294842i
\(589\) −38.2730 + 66.2907i −1.57701 + 2.73146i
\(590\) −3.68685 + 2.12860i −0.151785 + 0.0876332i
\(591\) −0.943274 −0.0388011
\(592\) −2.02678 + 5.73517i −0.0833000 + 0.235714i
\(593\) 4.98431 0.204681 0.102340 0.994749i \(-0.467367\pi\)
0.102340 + 0.994749i \(0.467367\pi\)
\(594\) −12.5235 + 7.23044i −0.513845 + 0.296669i
\(595\) −0.948832 + 1.64343i −0.0388983 + 0.0673739i
\(596\) 9.99660 17.3146i 0.409477 0.709234i
\(597\) 16.7441 + 9.66720i 0.685289 + 0.395652i
\(598\) 15.8106i 0.646544i
\(599\) 21.9749 38.0617i 0.897870 1.55516i 0.0676592 0.997708i \(-0.478447\pi\)
0.830211 0.557449i \(-0.188220\pi\)
\(600\) 1.34292i 0.0548246i
\(601\) 23.2651 + 40.2964i 0.949005 + 1.64372i 0.747527 + 0.664231i \(0.231241\pi\)
0.201477 + 0.979493i \(0.435426\pi\)
\(602\) 6.41795 0.261576
\(603\) 3.97745 0.161974
\(604\) 7.15059 + 12.3852i 0.290953 + 0.503946i
\(605\) 3.82422 + 2.20791i 0.155477 + 0.0897644i
\(606\) 22.1376i 0.899277i
\(607\) 26.3275 15.2002i 1.06860 0.616957i 0.140803 0.990038i \(-0.455032\pi\)
0.927799 + 0.373080i \(0.121698\pi\)
\(608\) −3.63268 6.29199i −0.147325 0.255174i
\(609\) −6.18187 + 3.56910i −0.250502 + 0.144627i
\(610\) 3.49339 + 2.01691i 0.141443 + 0.0816624i
\(611\) 17.5241 + 10.1175i 0.708947 + 0.409311i
\(612\) −2.12975 + 1.22961i −0.0860902 + 0.0497042i
\(613\) 14.1066 + 24.4333i 0.569759 + 0.986852i 0.996589 + 0.0825200i \(0.0262968\pi\)
−0.426830 + 0.904332i \(0.640370\pi\)
\(614\) 21.0692 12.1643i 0.850285 0.490913i
\(615\) 4.03136i 0.162560i
\(616\) 2.05180 + 1.18461i 0.0826695 + 0.0477292i
\(617\) 11.8816 + 20.5796i 0.478336 + 0.828503i 0.999692 0.0248368i \(-0.00790662\pi\)
−0.521355 + 0.853340i \(0.674573\pi\)
\(618\) 7.98619 0.321252
\(619\) 2.84179 0.114221 0.0571106 0.998368i \(-0.481811\pi\)
0.0571106 + 0.998368i \(0.481811\pi\)
\(620\) 5.26786 + 9.12420i 0.211562 + 0.366437i
\(621\) 46.3277i 1.85907i
\(622\) 3.16457 5.48120i 0.126888 0.219776i
\(623\) 3.83857i 0.153789i
\(624\) −2.23684 1.29144i −0.0895451 0.0516989i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −6.19774 + 10.7348i −0.247711 + 0.429049i
\(627\) −21.6815 + 12.5178i −0.865877 + 0.499914i
\(628\) −9.08913 −0.362696
\(629\) 11.7872 + 4.16554i 0.469987 + 0.166091i
\(630\) −1.10481 −0.0440167
\(631\) −0.988858 + 0.570917i −0.0393658 + 0.0227279i −0.519554 0.854438i \(-0.673902\pi\)
0.480188 + 0.877166i \(0.340568\pi\)
\(632\) −6.97191 + 12.0757i −0.277328 + 0.480346i
\(633\) 7.78148 13.4779i 0.309286 0.535699i
\(634\) −26.8379 15.4949i −1.06587 0.615381i
\(635\) 5.71707i 0.226875i
\(636\) −3.51503 + 6.08822i −0.139380 + 0.241413i
\(637\) 11.8236i 0.468467i
\(638\) −7.38591 12.7928i −0.292411 0.506471i
\(639\) −18.8261 −0.744750
\(640\) −1.00000 −0.0395285
\(641\) −19.8079 34.3082i −0.782364 1.35509i −0.930561 0.366136i \(-0.880681\pi\)
0.148198 0.988958i \(-0.452653\pi\)
\(642\) −4.34503 2.50861i −0.171485 0.0990068i
\(643\) 27.6189i 1.08918i −0.838702 0.544591i \(-0.816685\pi\)
0.838702 0.544591i \(-0.183315\pi\)
\(644\) −6.57326 + 3.79508i −0.259023 + 0.149547i
\(645\) 4.66727 + 8.08395i 0.183774 + 0.318305i
\(646\) −12.9316 + 7.46609i −0.508789 + 0.293749i
\(647\) −29.5607 17.0669i −1.16215 0.670969i −0.210333 0.977630i \(-0.567455\pi\)
−0.951819 + 0.306661i \(0.900788\pi\)
\(648\) 3.44555 + 1.98929i 0.135354 + 0.0781466i
\(649\) 9.46032 5.46192i 0.371350 0.214399i
\(650\) 0.961662 + 1.66565i 0.0377195 + 0.0653321i
\(651\) −11.3136 + 6.53190i −0.443414 + 0.256005i
\(652\) 8.32601i 0.326072i
\(653\) −2.94777 1.70190i −0.115355 0.0666004i 0.441212 0.897403i \(-0.354549\pi\)
−0.556568 + 0.830802i \(0.687882\pi\)
\(654\) 3.89932 + 6.75381i 0.152475 + 0.264095i
\(655\) 5.87872 0.229700
\(656\) 3.00193 0.117206
\(657\) 4.23871 + 7.34167i 0.165368 + 0.286426i
\(658\) 9.71417i 0.378698i
\(659\) 18.4772 32.0035i 0.719771 1.24668i −0.241319 0.970446i \(-0.577580\pi\)
0.961090 0.276235i \(-0.0890867\pi\)
\(660\) 3.44589i 0.134131i
\(661\) −5.34346 3.08505i −0.207836 0.119994i 0.392469 0.919765i \(-0.371621\pi\)
−0.600305 + 0.799771i \(0.704954\pi\)
\(662\) −1.62606 + 2.81641i −0.0631985 + 0.109463i
\(663\) −2.65423 + 4.59727i −0.103082 + 0.178543i
\(664\) −4.96056 + 2.86398i −0.192507 + 0.111144i
\(665\) −6.70829 −0.260136
\(666\) 1.33099 + 7.15564i 0.0515747 + 0.277276i
\(667\) 47.3238 1.83239
\(668\) 6.46115 3.73035i 0.249990 0.144332i
\(669\) −6.30992 + 10.9291i −0.243956 + 0.422544i
\(670\) 1.66204 2.87874i 0.0642102 0.111215i
\(671\) −8.96393 5.17532i −0.346048 0.199791i
\(672\) 1.23995i 0.0478322i
\(673\) 9.15112 15.8502i 0.352750 0.610980i −0.633981 0.773349i \(-0.718580\pi\)
0.986730 + 0.162369i \(0.0519134\pi\)
\(674\) 30.4860i 1.17428i
\(675\) −2.81783 4.88062i −0.108458 0.187855i
\(676\) −9.30082 −0.357724
\(677\) −12.6160 −0.484874 −0.242437 0.970167i \(-0.577947\pi\)
−0.242437 + 0.970167i \(0.577947\pi\)
\(678\) 3.36941 + 5.83598i 0.129401 + 0.224130i
\(679\) 7.93492 + 4.58123i 0.304514 + 0.175811i
\(680\) 2.05525i 0.0788154i
\(681\) 5.81331 3.35632i 0.222767 0.128614i
\(682\) −13.5171 23.4124i −0.517598 0.896506i
\(683\) −14.5068 + 8.37553i −0.555089 + 0.320481i −0.751172 0.660107i \(-0.770511\pi\)
0.196083 + 0.980587i \(0.437178\pi\)
\(684\) −7.52873 4.34672i −0.287868 0.166201i
\(685\) 9.00772 + 5.20061i 0.344167 + 0.198705i
\(686\) 10.5130 6.06969i 0.401389 0.231742i
\(687\) −17.7834 30.8017i −0.678479 1.17516i
\(688\) 6.01967 3.47546i 0.229498 0.132501i
\(689\) 10.0684i 0.383576i
\(690\) −9.56044 5.51972i −0.363960 0.210132i
\(691\) −8.24768 14.2854i −0.313756 0.543442i 0.665416 0.746473i \(-0.268254\pi\)
−0.979172 + 0.203031i \(0.934921\pi\)
\(692\) −3.53420 −0.134350
\(693\) 2.83490 0.107689
\(694\) −7.91385 13.7072i −0.300406 0.520318i
\(695\) 14.6401i 0.555329i
\(696\) −3.86549 + 6.69523i −0.146521 + 0.253782i
\(697\) 6.16973i 0.233695i
\(698\) 2.63159 + 1.51935i 0.0996071 + 0.0575082i
\(699\) 13.4170 23.2389i 0.507478 0.878977i
\(700\) −0.461662 + 0.799622i −0.0174492 + 0.0302229i
\(701\) −8.87777 + 5.12559i −0.335309 + 0.193591i −0.658196 0.752847i \(-0.728680\pi\)
0.322887 + 0.946438i \(0.395347\pi\)
\(702\) −10.8392 −0.409099
\(703\) 8.08161 + 43.4483i 0.304804 + 1.63868i
\(704\) 2.56596 0.0967084
\(705\) −12.2358 + 7.06436i −0.460828 + 0.266059i
\(706\) −11.0408 + 19.1232i −0.415525 + 0.719711i
\(707\) −7.61032 + 13.1815i −0.286215 + 0.495740i
\(708\) −4.95115 2.85855i −0.186076 0.107431i
\(709\) 49.6789i 1.86573i 0.360225 + 0.932865i \(0.382700\pi\)
−0.360225 + 0.932865i \(0.617300\pi\)
\(710\) −7.86679 + 13.6257i −0.295235 + 0.511363i
\(711\) 16.6846i 0.625721i
\(712\) −2.07867 3.60036i −0.0779014 0.134929i
\(713\) 86.6085 3.24351
\(714\) −2.54842 −0.0953721
\(715\) −2.46759 4.27399i −0.0922827 0.159838i
\(716\) −14.7367 8.50822i −0.550735 0.317967i
\(717\) 10.6578i 0.398024i
\(718\) 9.09833 5.25292i 0.339547 0.196037i
\(719\) 4.45385 + 7.71430i 0.166101 + 0.287695i 0.937046 0.349207i \(-0.113549\pi\)
−0.770945 + 0.636902i \(0.780216\pi\)
\(720\) −1.03625 + 0.598279i −0.0386187 + 0.0222965i
\(721\) −4.75525 2.74545i −0.177095 0.102246i
\(722\) −29.2592 16.8928i −1.08891 0.628685i
\(723\) −8.59456 + 4.96207i −0.319635 + 0.184541i
\(724\) −4.13726 7.16595i −0.153760 0.266320i
\(725\) 4.98556 2.87842i 0.185159 0.106902i
\(726\) 5.93012i 0.220087i
\(727\) 33.3490 + 19.2541i 1.23685 + 0.714094i 0.968448 0.249214i \(-0.0801722\pi\)
0.268399 + 0.963308i \(0.413506\pi\)
\(728\) 0.887926 + 1.53793i 0.0329087 + 0.0569996i
\(729\) 27.4653 1.01724
\(730\) 7.08485 0.262222
\(731\) −7.14294 12.3719i −0.264191 0.457593i
\(732\) 5.41712i 0.200222i
\(733\) −5.24691 + 9.08791i −0.193799 + 0.335670i −0.946506 0.322686i \(-0.895414\pi\)
0.752707 + 0.658356i \(0.228748\pi\)
\(734\) 12.3206i 0.454763i
\(735\) 7.14954 + 4.12779i 0.263715 + 0.152256i
\(736\) −4.11023 + 7.11913i −0.151505 + 0.262415i
\(737\) −4.26474 + 7.38674i −0.157094 + 0.272094i
\(738\) 3.11075 1.79599i 0.114508 0.0661114i
\(739\) 0.0900634 0.00331304 0.00165652 0.999999i \(-0.499473\pi\)
0.00165652 + 0.999999i \(0.499473\pi\)
\(740\) 5.73517 + 2.02678i 0.210829 + 0.0745057i
\(741\) −18.7656 −0.689370
\(742\) 4.18594 2.41675i 0.153671 0.0887218i
\(743\) 14.8898 25.7899i 0.546255 0.946141i −0.452272 0.891880i \(-0.649386\pi\)
0.998527 0.0542607i \(-0.0172802\pi\)
\(744\) −7.07433 + 12.2531i −0.259358 + 0.449221i
\(745\) −17.3146 9.99660i −0.634358 0.366247i
\(746\) 26.4143i 0.967097i
\(747\) −3.42692 + 5.93559i −0.125384 + 0.217172i
\(748\) 5.27371i 0.192826i
\(749\) 1.72479 + 2.98742i 0.0630224 + 0.109158i
\(750\) −1.34292 −0.0490366
\(751\) 45.3962 1.65653 0.828266 0.560335i \(-0.189328\pi\)
0.828266 + 0.560335i \(0.189328\pi\)
\(752\) 5.26043 + 9.11134i 0.191828 + 0.332256i
\(753\) 17.6365 + 10.1825i 0.642711 + 0.371069i
\(754\) 11.0723i 0.403228i
\(755\) 12.3852 7.15059i 0.450743 0.260237i
\(756\) −2.60177 4.50639i −0.0946254 0.163896i
\(757\) 9.16026 5.28868i 0.332935 0.192220i −0.324208 0.945986i \(-0.605098\pi\)
0.657144 + 0.753765i \(0.271765\pi\)
\(758\) −2.46028 1.42044i −0.0893612 0.0515927i
\(759\) 24.5318 + 14.1634i 0.890446 + 0.514099i
\(760\) −6.29199 + 3.63268i −0.228235 + 0.131771i
\(761\) −16.0028 27.7176i −0.580100 1.00476i −0.995467 0.0951083i \(-0.969680\pi\)
0.415367 0.909654i \(-0.363653\pi\)
\(762\) −6.64898 + 3.83879i −0.240867 + 0.139065i
\(763\) 5.36193i 0.194115i
\(764\) 8.14908 + 4.70488i 0.294823 + 0.170216i
\(765\) 1.22961 + 2.12975i 0.0444568 + 0.0770014i
\(766\) 22.0781 0.797716
\(767\) 8.18799 0.295651
\(768\) −0.671462 1.16301i −0.0242293 0.0419663i
\(769\) 18.6714i 0.673309i −0.941628 0.336655i \(-0.890704\pi\)
0.941628 0.336655i \(-0.109296\pi\)
\(770\) 1.18461 2.05180i 0.0426903 0.0739418i
\(771\) 8.35277i 0.300818i
\(772\) −12.5006 7.21720i −0.449905 0.259753i
\(773\) −4.24530 + 7.35307i −0.152693 + 0.264471i −0.932216 0.361901i \(-0.882128\pi\)
0.779524 + 0.626373i \(0.215461\pi\)
\(774\) 4.15858 7.20288i 0.149477 0.258902i
\(775\) 9.12420 5.26786i 0.327751 0.189227i
\(776\) 9.92333 0.356227
\(777\) −2.51311 + 7.11134i −0.0901572 + 0.255118i
\(778\) 3.06920 0.110036
\(779\) 18.8881 10.9051i 0.676738 0.390715i
\(780\) −1.29144 + 2.23684i −0.0462409 + 0.0800916i
\(781\) 20.1859 34.9630i 0.722308 1.25107i
\(782\) 14.6316 + 8.44756i 0.523225 + 0.302084i
\(783\) 32.4435i 1.15944i
\(784\) 3.07374 5.32387i 0.109776 0.190138i
\(785\) 9.08913i 0.324405i
\(786\) 3.94733 + 6.83698i 0.140797 + 0.243867i
\(787\) 11.6067 0.413733 0.206867 0.978369i \(-0.433673\pi\)
0.206867 + 0.978369i \(0.433673\pi\)
\(788\) 0.702404 0.0250221
\(789\) 18.7132 + 32.4122i 0.666206 + 1.15390i
\(790\) 12.0757 + 6.97191i 0.429634 + 0.248050i
\(791\) 4.63326i 0.164740i
\(792\) 2.65898 1.53516i 0.0944827 0.0545496i
\(793\) −3.87918 6.71893i −0.137754 0.238596i
\(794\) −27.0806 + 15.6350i −0.961055 + 0.554865i
\(795\) 6.08822 + 3.51503i 0.215927 + 0.124665i
\(796\) −12.4684 7.19862i −0.441930 0.255148i
\(797\) −32.7557 + 18.9115i −1.16027 + 0.669880i −0.951368 0.308057i \(-0.900321\pi\)
−0.208899 + 0.977937i \(0.566988\pi\)
\(798\) −4.50436 7.80178i −0.159453 0.276180i
\(799\) 18.7261 10.8115i 0.662482 0.382484i
\(800\) 1.00000i 0.0353553i
\(801\) −4.30804 2.48725i −0.152217 0.0878826i
\(802\) −1.58916 2.75250i −0.0561151 0.0971942i
\(803\) −18.1795 −0.641539
\(804\) 4.46398 0.157433
\(805\) 3.79508 + 6.57326i 0.133759 + 0.231677i
\(806\) 20.2636i 0.713755i
\(807\) 7.30625 12.6548i 0.257192 0.445470i
\(808\) 16.4846i 0.579926i
\(809\) 24.0866 + 13.9064i 0.846841 + 0.488924i 0.859584 0.510995i \(-0.170723\pi\)
−0.0127426 + 0.999919i \(0.504056\pi\)
\(810\) 1.98929 3.44555i 0.0698965 0.121064i
\(811\) −22.0688 + 38.2242i −0.774940 + 1.34223i 0.159889 + 0.987135i \(0.448886\pi\)
−0.934828 + 0.355100i \(0.884447\pi\)
\(812\) 4.60329 2.65771i 0.161544 0.0932674i
\(813\) −32.2519 −1.13112
\(814\) −14.7162 5.20063i −0.515804 0.182282i
\(815\) 8.32601 0.291647
\(816\) −2.39027 + 1.38002i −0.0836762 + 0.0483105i
\(817\) 25.2505 43.7351i 0.883403 1.53010i
\(818\) 0.00625847 0.0108400i 0.000218822 0.000379011i
\(819\) 1.84023 + 1.06245i 0.0643027 + 0.0371252i
\(820\) 3.00193i 0.104832i
\(821\) −1.17267 + 2.03112i −0.0409264 + 0.0708866i −0.885763 0.464138i \(-0.846364\pi\)
0.844837 + 0.535024i \(0.179698\pi\)
\(822\) 13.9680i 0.487191i
\(823\) −4.82924 8.36448i −0.168337 0.291568i 0.769499 0.638649i \(-0.220506\pi\)
−0.937835 + 0.347081i \(0.887173\pi\)
\(824\) −5.94687 −0.207169
\(825\) 3.44589 0.119971
\(826\) 1.96539 + 3.40416i 0.0683847 + 0.118446i
\(827\) 9.14985 + 5.28267i 0.318171 + 0.183696i 0.650577 0.759440i \(-0.274527\pi\)
−0.332406 + 0.943136i \(0.607860\pi\)
\(828\) 9.83626i 0.341834i
\(829\) −25.8734 + 14.9380i −0.898621 + 0.518819i −0.876753 0.480942i \(-0.840295\pi\)
−0.0218685 + 0.999761i \(0.506962\pi\)
\(830\) 2.86398 + 4.96056i 0.0994102 + 0.172183i
\(831\) −6.10875 + 3.52689i −0.211910 + 0.122346i
\(832\) 1.66565 + 0.961662i 0.0577459 + 0.0333396i
\(833\) −10.9419 6.31731i −0.379114 0.218882i
\(834\) 17.0265 9.83023i 0.589578 0.340393i
\(835\) −3.73035 6.46115i −0.129094 0.223597i
\(836\) 16.1450 9.32134i 0.558388 0.322385i
\(837\) 59.3757i 2.05232i
\(838\) 2.85196 + 1.64658i 0.0985194 + 0.0568802i
\(839\) 4.14171 + 7.17365i 0.142988 + 0.247662i 0.928620 0.371031i \(-0.120996\pi\)
−0.785633 + 0.618693i \(0.787662\pi\)
\(840\) −1.23995 −0.0427825
\(841\) −4.14112 −0.142797
\(842\) 9.67772 + 16.7623i 0.333516 + 0.577667i
\(843\) 25.9681i 0.894389i
\(844\) −5.79443 + 10.0362i −0.199453 + 0.345462i
\(845\) 9.30082i 0.319958i
\(846\) 10.9022 + 6.29441i 0.374827 + 0.216406i
\(847\) 2.03862 3.53099i 0.0700478 0.121326i
\(848\) 2.61745 4.53356i 0.0898836 0.155683i
\(849\) 1.18557 0.684489i 0.0406886 0.0234916i
\(850\) 2.05525 0.0704946
\(851\) 38.0018 32.4989i 1.30268 1.11405i
\(852\) −21.1290 −0.723867
\(853\) 3.05650 1.76467i 0.104653 0.0604213i −0.446760 0.894654i \(-0.647422\pi\)
0.551413 + 0.834233i \(0.314089\pi\)
\(854\) 1.86226 3.22554i 0.0637254 0.110376i
\(855\) −4.34672 + 7.52873i −0.148655 + 0.257477i
\(856\) 3.23550 + 1.86802i 0.110587 + 0.0638476i
\(857\) 22.4791i 0.767873i −0.923360 0.383936i \(-0.874568\pi\)
0.923360 0.383936i \(-0.125432\pi\)
\(858\) 3.31378 5.73964i 0.113131 0.195948i
\(859\) 39.4974i 1.34763i 0.738898 + 0.673817i \(0.235346\pi\)
−0.738898 + 0.673817i \(0.764654\pi\)
\(860\) −3.47546 6.01967i −0.118512 0.205269i
\(861\) 3.72225 0.126854
\(862\) −3.64458 −0.124135
\(863\) 10.1444 + 17.5705i 0.345318 + 0.598108i 0.985411 0.170189i \(-0.0544378\pi\)
−0.640094 + 0.768297i \(0.721104\pi\)
\(864\) −4.88062 2.81783i −0.166042 0.0958644i
\(865\) 3.53420i 0.120166i
\(866\) 20.5761 11.8796i 0.699203 0.403685i
\(867\) −8.57855 14.8585i −0.291343 0.504621i
\(868\) 8.42460 4.86394i 0.285949 0.165093i
\(869\) −30.9858 17.8897i −1.05112 0.606866i
\(870\) 6.69523 + 3.86549i 0.226989 + 0.131052i
\(871\) −5.53675 + 3.19664i −0.187605 + 0.108314i
\(872\) −2.90360 5.02919i −0.0983284 0.170310i
\(873\) 10.2830 5.93692i 0.348028 0.200934i
\(874\) 59.7247i 2.02022i
\(875\) 0.799622 + 0.461662i 0.0270322 + 0.0156070i
\(876\) 4.75720 + 8.23972i 0.160731 + 0.278394i
\(877\) −52.3779 −1.76868 −0.884338 0.466847i \(-0.845390\pi\)
−0.884338 + 0.466847i \(0.845390\pi\)
\(878\) −23.4515 −0.791450
\(879\) −8.65367 14.9886i −0.291881 0.505553i
\(880\) 2.56596i 0.0864986i
\(881\) 7.78882 13.4906i 0.262412 0.454511i −0.704470 0.709733i \(-0.748815\pi\)
0.966882 + 0.255222i \(0.0821487\pi\)
\(882\) 7.35580i 0.247683i
\(883\) 4.49887 + 2.59742i 0.151399 + 0.0874102i 0.573786 0.819006i \(-0.305474\pi\)
−0.422387 + 0.906416i \(0.638808\pi\)
\(884\) 1.97646 3.42333i 0.0664755 0.115139i
\(885\) −2.85855 + 4.95115i −0.0960891 + 0.166431i
\(886\) 33.7390 19.4792i 1.13348 0.654417i
\(887\) 31.7194 1.06503 0.532516 0.846420i \(-0.321247\pi\)
0.532516 + 0.846420i \(0.321247\pi\)
\(888\) 1.49380 + 8.03094i 0.0501285 + 0.269501i
\(889\) 5.27871 0.177042
\(890\) −3.60036 + 2.07867i −0.120684 + 0.0696772i
\(891\) −5.10444 + 8.84116i −0.171005 + 0.296190i
\(892\) 4.69865 8.13829i 0.157322 0.272490i
\(893\) 66.1972 + 38.2190i 2.21521 + 1.27895i
\(894\) 26.8493i 0.897976i
\(895\) −8.50822 + 14.7367i −0.284398 + 0.492593i
\(896\) 0.923324i 0.0308461i
\(897\) 10.6162 + 18.3878i 0.354465 + 0.613952i
\(898\) −14.1317 −0.471583
\(899\) −60.6524 −2.02287
\(900\) 0.598279 + 1.03625i 0.0199426 + 0.0345416i
\(901\) −9.31760 5.37952i −0.310414 0.179218i
\(902\) 7.70285i 0.256477i
\(903\) 7.46411 4.30941i 0.248390 0.143408i
\(904\) −2.50901 4.34573i −0.0834484 0.144537i
\(905\) −7.16595 + 4.13726i −0.238204 + 0.137527i
\(906\) 16.6323 + 9.60269i 0.552573 + 0.319028i
\(907\) 47.4891 + 27.4179i 1.57685 + 0.910396i 0.995295 + 0.0968892i \(0.0308893\pi\)
0.581556 + 0.813506i \(0.302444\pi\)
\(908\) −4.32885 + 2.49926i −0.143658 + 0.0829410i
\(909\) 9.86239 + 17.0822i 0.327115 + 0.566579i
\(910\) 1.53793 0.887926i 0.0509820 0.0294345i
\(911\) 21.0065i 0.695975i −0.937499 0.347987i \(-0.886865\pi\)
0.937499 0.347987i \(-0.113135\pi\)
\(912\) −8.44966 4.87842i −0.279796 0.161541i
\(913\) −7.34887 12.7286i −0.243212 0.421256i
\(914\) 29.3664 0.971354
\(915\) 5.41712 0.179084
\(916\) 13.2423 + 22.9363i 0.437538 + 0.757838i
\(917\) 5.42796i 0.179247i
\(918\) −5.79135 + 10.0309i −0.191143 + 0.331069i
\(919\) 31.6976i 1.04561i 0.852453 + 0.522804i \(0.175114\pi\)
−0.852453 + 0.522804i \(0.824886\pi\)
\(920\) 7.11913 + 4.11023i 0.234711 + 0.135510i
\(921\) 16.3358 28.2944i 0.538282 0.932331i
\(922\) 14.5048 25.1231i 0.477692 0.827386i
\(923\) 26.2066 15.1304i 0.862601 0.498023i
\(924\) 3.18168 0.104669
\(925\) 2.02678 5.73517i 0.0666400 0.188571i
\(926\) −32.4406 −1.06606
\(927\) −6.16244 + 3.55789i −0.202401 + 0.116856i
\(928\) 2.87842 4.98556i 0.0944886 0.163659i
\(929\) −0.610310 + 1.05709i −0.0200236 + 0.0346819i −0.875864 0.482559i \(-0.839707\pi\)
0.855840 + 0.517241i \(0.173041\pi\)
\(930\) 12.2531 + 7.07433i 0.401795 + 0.231977i
\(931\) 44.6637i 1.46379i
\(932\) −9.99090 + 17.3047i −0.327263 + 0.566836i
\(933\) 8.49955i 0.278263i
\(934\) 0.247846 + 0.429282i 0.00810977 + 0.0140465i
\(935\) −5.27371 −0.172469
\(936\) 2.30137 0.0752226
\(937\) 15.1797 + 26.2920i 0.495900 + 0.858923i 0.999989 0.00472828i \(-0.00150506\pi\)
−0.504089 + 0.863652i \(0.668172\pi\)
\(938\) −2.65801 1.53460i −0.0867870 0.0501065i
\(939\) 16.6462i 0.543227i
\(940\) 9.11134 5.26043i 0.297179 0.171576i
\(941\) 19.5570 + 33.8738i 0.637541 + 1.10425i 0.985971 + 0.166918i \(0.0533816\pi\)
−0.348430 + 0.937335i \(0.613285\pi\)
\(942\) −10.5707 + 6.10300i −0.344412 + 0.198847i
\(943\) −21.3711 12.3386i −0.695940 0.401801i
\(944\) 3.68685 + 2.12860i 0.119997 + 0.0692801i
\(945\) −4.50639 + 2.60177i −0.146593 + 0.0846355i
\(946\) 8.91790 + 15.4463i 0.289946 + 0.502201i
\(947\) 7.13906 4.12174i 0.231988 0.133938i −0.379501 0.925191i \(-0.623904\pi\)
0.611489 + 0.791253i \(0.290571\pi\)
\(948\) 18.7255i 0.608175i
\(949\) −11.8009 6.81323i −0.383072 0.221167i
\(950\) 3.63268 + 6.29199i 0.117860 + 0.204139i
\(951\) −41.6169 −1.34952
\(952\) 1.89766 0.0615037
\(953\) 29.6054 + 51.2780i 0.959012 + 1.66106i 0.724908 + 0.688845i \(0.241882\pi\)
0.234103 + 0.972212i \(0.424785\pi\)
\(954\) 6.26386i 0.202800i
\(955\) 4.70488 8.14908i 0.152246 0.263698i
\(956\) 7.93630i 0.256678i
\(957\) −17.1797 9.91871i −0.555341 0.320626i
\(958\) −14.8343 + 25.6937i −0.479274 + 0.830127i
\(959\) 4.80185 8.31704i 0.155060 0.268571i
\(960\) −1.16301 + 0.671462i −0.0375358 + 0.0216713i
\(961\) −80.0014 −2.58069
\(962\) −7.60370 8.89119i −0.245153 0.286663i
\(963\) 4.47038 0.144056
\(964\) 6.39989 3.69498i 0.206127 0.119007i
\(965\) −7.21720 + 12.5006i −0.232330 + 0.402407i
\(966\) −5.09649 + 8.82739i −0.163977 + 0.284017i
\(967\) −37.1087 21.4247i −1.19333 0.688972i −0.234273 0.972171i \(-0.575271\pi\)
−0.959061 + 0.283199i \(0.908604\pi\)
\(968\) 4.41583i 0.141930i
\(969\) −10.0264 + 17.3662i −0.322094 + 0.557883i
\(970\) 9.92333i 0.318619i
\(971\) −24.5335 42.4933i −0.787318 1.36367i −0.927604 0.373564i \(-0.878136\pi\)
0.140286 0.990111i \(-0.455198\pi\)
\(972\) −11.5640 −0.370917
\(973\) −13.5175 −0.433352
\(974\) 17.3814 + 30.1055i 0.556937 + 0.964644i
\(975\) 2.23684 + 1.29144i 0.0716361 + 0.0413591i
\(976\) 4.03382i 0.129120i
\(977\) −27.5869 + 15.9273i −0.882584 + 0.509560i −0.871510 0.490378i \(-0.836859\pi\)
−0.0110747 + 0.999939i \(0.503525\pi\)
\(978\) 5.59060 + 9.68320i 0.178768 + 0.309634i
\(979\) 9.23840 5.33379i 0.295261 0.170469i
\(980\) −5.32387 3.07374i −0.170065 0.0981869i
\(981\) −6.01771 3.47433i −0.192131 0.110927i
\(982\) 29.1243 16.8149i 0.929395 0.536587i
\(983\) 18.3044 + 31.7042i 0.583821 + 1.01121i 0.995021 + 0.0996629i \(0.0317764\pi\)
−0.411200 + 0.911545i \(0.634890\pi\)
\(984\) 3.49126 2.01568i 0.111297 0.0642576i
\(985\) 0.702404i 0.0223804i
\(986\) −10.2466 5.91587i −0.326318 0.188400i
\(987\) 6.52269 + 11.2976i 0.207620 + 0.359608i
\(988\) 13.9737 0.444561
\(989\) −57.1397 −1.81694
\(990\) −1.53516 2.65898i −0.0487907 0.0845079i
\(991\) 25.6983i 0.816334i −0.912907 0.408167i \(-0.866168\pi\)
0.912907 0.408167i \(-0.133832\pi\)
\(992\) 5.26786 9.12420i 0.167255 0.289694i
\(993\) 4.36734i 0.138593i
\(994\) 12.5809 + 7.26360i 0.399042 + 0.230387i
\(995\) −7.19862 + 12.4684i −0.228212 + 0.395274i
\(996\) −3.84610 + 6.66165i −0.121868 + 0.211082i
\(997\) 26.8778 15.5179i 0.851229 0.491458i −0.00983602 0.999952i \(-0.503131\pi\)
0.861065 + 0.508494i \(0.169798\pi\)
\(998\) 6.67491 0.211291
\(999\) 22.2801 + 26.0526i 0.704911 + 0.824269i
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 370.2.l.c.11.1 12
37.27 even 6 inner 370.2.l.c.101.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.l.c.11.1 12 1.1 even 1 trivial
370.2.l.c.101.1 yes 12 37.27 even 6 inner