Properties

Label 124.3.n.a.7.7
Level $124$
Weight $3$
Character 124.7
Analytic conductor $3.379$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,3,Mod(7,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([15, 28]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.n (of order \(30\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.37875527807\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 7.7
Character \(\chi\) \(=\) 124.7
Dual form 124.3.n.a.71.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.60673 - 1.19097i) q^{2} +(0.931035 + 4.38017i) q^{3} +(1.16319 + 3.82714i) q^{4} +(-0.973390 + 1.68596i) q^{5} +(3.72072 - 8.14661i) q^{6} +(-1.13057 + 2.53929i) q^{7} +(2.68905 - 7.53452i) q^{8} +(-10.0972 + 4.49556i) q^{9} +O(q^{10})\) \(q+(-1.60673 - 1.19097i) q^{2} +(0.931035 + 4.38017i) q^{3} +(1.16319 + 3.82714i) q^{4} +(-0.973390 + 1.68596i) q^{5} +(3.72072 - 8.14661i) q^{6} +(-1.13057 + 2.53929i) q^{7} +(2.68905 - 7.53452i) q^{8} +(-10.0972 + 4.49556i) q^{9} +(3.57190 - 1.54962i) q^{10} +(-12.6802 + 1.33274i) q^{11} +(-15.6806 + 8.65819i) q^{12} +(-4.93216 - 5.47772i) q^{13} +(4.84073 - 2.73350i) q^{14} +(-8.29106 - 2.69393i) q^{15} +(-13.2940 + 8.90341i) q^{16} +(-0.437066 + 4.15841i) q^{17} +(21.5776 + 4.80225i) q^{18} +(17.1611 + 15.4519i) q^{19} +(-7.58465 - 1.76420i) q^{20} +(-12.1751 - 2.58791i) q^{21} +(21.9610 + 12.9603i) q^{22} +(-7.50904 + 10.3353i) q^{23} +(35.5061 + 4.76361i) q^{24} +(10.6050 + 18.3684i) q^{25} +(1.40089 + 14.6753i) q^{26} +(-5.40310 - 7.43672i) q^{27} +(-11.0333 - 1.37314i) q^{28} +(-14.8909 - 45.8294i) q^{29} +(10.1132 + 14.2028i) q^{30} +(1.12489 + 30.9796i) q^{31} +(31.9635 + 1.52726i) q^{32} +(-17.6434 - 54.3007i) q^{33} +(5.65478 - 6.16093i) q^{34} +(-3.18067 - 4.37781i) q^{35} +(-28.9501 - 33.4141i) q^{36} +(7.46297 + 12.9262i) q^{37} +(-9.17060 - 45.2654i) q^{38} +(19.4014 - 26.7037i) q^{39} +(10.0854 + 11.8677i) q^{40} +(25.6656 + 5.45538i) q^{41} +(16.4801 + 18.6583i) q^{42} +(-39.2538 - 35.3443i) q^{43} +(-19.8501 - 46.9787i) q^{44} +(2.24917 - 21.3994i) q^{45} +(24.3740 - 7.66308i) q^{46} +(16.4571 + 5.34723i) q^{47} +(-51.3756 - 49.9405i) q^{48} +(27.6176 + 30.6724i) q^{49} +(4.83675 - 42.1434i) q^{50} +(-18.6215 + 1.95720i) q^{51} +(15.2269 - 25.2477i) q^{52} +(31.5797 - 14.0602i) q^{53} +(-0.175551 + 18.3838i) q^{54} +(10.0958 - 22.6756i) q^{55} +(16.0922 + 15.3466i) q^{56} +(-51.7045 + 89.5548i) q^{57} +(-30.6556 + 91.3703i) q^{58} +(11.9352 + 56.1509i) q^{59} +(0.665924 - 34.8646i) q^{60} +107.434 q^{61} +(35.0883 - 51.1157i) q^{62} -30.7223i q^{63} +(-49.5380 - 40.5214i) q^{64} +(14.0361 - 2.98347i) q^{65} +(-36.3221 + 108.259i) q^{66} +(-40.8447 - 23.5817i) q^{67} +(-16.4232 + 3.16432i) q^{68} +(-52.2616 - 23.2684i) q^{69} +(-0.103343 + 10.8221i) q^{70} +(15.7127 + 35.2912i) q^{71} +(6.72003 + 88.1663i) q^{72} +(13.9500 + 132.726i) q^{73} +(3.40372 - 29.6572i) q^{74} +(-70.5833 + 63.5535i) q^{75} +(-39.1749 + 83.6514i) q^{76} +(10.9516 - 33.7055i) q^{77} +(-62.9760 + 19.7993i) q^{78} +(107.810 + 11.3313i) q^{79} +(-2.07059 - 31.0796i) q^{80} +(-39.0179 + 43.3338i) q^{81} +(-34.7406 - 39.3322i) q^{82} +(19.3403 - 90.9891i) q^{83} +(-4.25778 - 49.6062i) q^{84} +(-6.58548 - 4.78463i) q^{85} +(20.9766 + 103.539i) q^{86} +(186.877 - 107.893i) q^{87} +(-24.0561 + 99.1231i) q^{88} +(72.7316 - 52.8426i) q^{89} +(-29.0998 + 31.7045i) q^{90} +(19.4857 - 6.33127i) q^{91} +(-48.2891 - 16.7162i) q^{92} +(-134.649 + 33.7703i) q^{93} +(-20.0738 - 28.1914i) q^{94} +(-42.7558 + 13.8922i) q^{95} +(23.0695 + 141.428i) q^{96} +(-94.9092 + 68.9555i) q^{97} +(-7.84427 - 82.1741i) q^{98} +(122.043 - 70.4616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 5 q^{6} - 27 q^{8} - 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 6 q^{2} - 10 q^{4} - 8 q^{5} - 5 q^{6} - 27 q^{8} - 96 q^{9} - 4 q^{10} + 27 q^{12} - 26 q^{13} + 10 q^{14} + 46 q^{16} - 18 q^{17} - 11 q^{18} + 143 q^{20} + 90 q^{21} + 77 q^{22} - 54 q^{24} - 464 q^{25} - 27 q^{26} - 52 q^{28} - 12 q^{29} + 206 q^{30} + 154 q^{32} + 72 q^{33} - 168 q^{34} + 23 q^{36} - 48 q^{37} - 78 q^{38} + 85 q^{40} - 18 q^{41} - 91 q^{42} - 493 q^{44} - 30 q^{45} + 198 q^{46} - 314 q^{48} + 48 q^{49} - 563 q^{50} - 551 q^{52} + 46 q^{53} - 600 q^{54} - 90 q^{56} - 44 q^{57} - 125 q^{58} - 77 q^{60} + 208 q^{61} - 17 q^{62} - 529 q^{64} + 132 q^{65} + 788 q^{66} + 364 q^{68} + 36 q^{69} + 586 q^{70} + 1113 q^{72} + 214 q^{73} + 351 q^{74} + 824 q^{76} + 456 q^{77} + 123 q^{78} + 410 q^{80} + 90 q^{81} - 718 q^{82} - 412 q^{84} + 394 q^{85} + 680 q^{86} - 141 q^{88} + 12 q^{89} + 193 q^{90} - 520 q^{92} + 82 q^{93} - 876 q^{94} + 888 q^{96} - 548 q^{97} + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{14}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60673 1.19097i −0.803367 0.595484i
\(3\) 0.931035 + 4.38017i 0.310345 + 1.46006i 0.806195 + 0.591650i \(0.201523\pi\)
−0.495850 + 0.868408i \(0.665143\pi\)
\(4\) 1.16319 + 3.82714i 0.290799 + 0.956784i
\(5\) −0.973390 + 1.68596i −0.194678 + 0.337192i −0.946795 0.321838i \(-0.895700\pi\)
0.752117 + 0.659030i \(0.229033\pi\)
\(6\) 3.72072 8.14661i 0.620120 1.35777i
\(7\) −1.13057 + 2.53929i −0.161509 + 0.362756i −0.976113 0.217261i \(-0.930288\pi\)
0.814604 + 0.580017i \(0.196954\pi\)
\(8\) 2.68905 7.53452i 0.336131 0.941815i
\(9\) −10.0972 + 4.49556i −1.12191 + 0.499507i
\(10\) 3.57190 1.54962i 0.357190 0.154962i
\(11\) −12.6802 + 1.33274i −1.15275 + 0.121158i −0.661557 0.749895i \(-0.730104\pi\)
−0.491189 + 0.871053i \(0.663437\pi\)
\(12\) −15.6806 + 8.65819i −1.30671 + 0.721516i
\(13\) −4.93216 5.47772i −0.379397 0.421363i 0.522957 0.852359i \(-0.324829\pi\)
−0.902354 + 0.430996i \(0.858162\pi\)
\(14\) 4.84073 2.73350i 0.345767 0.195250i
\(15\) −8.29106 2.69393i −0.552738 0.179595i
\(16\) −13.2940 + 8.90341i −0.830872 + 0.556463i
\(17\) −0.437066 + 4.15841i −0.0257098 + 0.244612i 0.974118 + 0.226041i \(0.0725784\pi\)
−0.999828 + 0.0185711i \(0.994088\pi\)
\(18\) 21.5776 + 4.80225i 1.19875 + 0.266792i
\(19\) 17.1611 + 15.4519i 0.903215 + 0.813259i 0.983010 0.183553i \(-0.0587598\pi\)
−0.0797947 + 0.996811i \(0.525426\pi\)
\(20\) −7.58465 1.76420i −0.379232 0.0882099i
\(21\) −12.1751 2.58791i −0.579769 0.123234i
\(22\) 21.9610 + 12.9603i 0.998227 + 0.589107i
\(23\) −7.50904 + 10.3353i −0.326480 + 0.449361i −0.940432 0.339982i \(-0.889579\pi\)
0.613952 + 0.789343i \(0.289579\pi\)
\(24\) 35.5061 + 4.76361i 1.47942 + 0.198484i
\(25\) 10.6050 + 18.3684i 0.424201 + 0.734738i
\(26\) 1.40089 + 14.6753i 0.0538804 + 0.564434i
\(27\) −5.40310 7.43672i −0.200115 0.275434i
\(28\) −11.0333 1.37314i −0.394046 0.0490407i
\(29\) −14.8909 45.8294i −0.513479 1.58033i −0.786033 0.618185i \(-0.787868\pi\)
0.272554 0.962140i \(-0.412132\pi\)
\(30\) 10.1132 + 14.2028i 0.337105 + 0.473427i
\(31\) 1.12489 + 30.9796i 0.0362867 + 0.999341i
\(32\) 31.9635 + 1.52726i 0.998860 + 0.0477268i
\(33\) −17.6434 54.3007i −0.534647 1.64548i
\(34\) 5.65478 6.16093i 0.166317 0.181204i
\(35\) −3.18067 4.37781i −0.0908762 0.125080i
\(36\) −28.9501 33.4141i −0.804170 0.928170i
\(37\) 7.46297 + 12.9262i 0.201702 + 0.349358i 0.949077 0.315044i \(-0.102019\pi\)
−0.747375 + 0.664402i \(0.768686\pi\)
\(38\) −9.17060 45.2654i −0.241331 1.19120i
\(39\) 19.4014 26.7037i 0.497471 0.684709i
\(40\) 10.0854 + 11.8677i 0.252135 + 0.296692i
\(41\) 25.6656 + 5.45538i 0.625989 + 0.133058i 0.509975 0.860189i \(-0.329655\pi\)
0.116015 + 0.993248i \(0.462988\pi\)
\(42\) 16.4801 + 18.6583i 0.392384 + 0.444245i
\(43\) −39.2538 35.3443i −0.912880 0.821961i 0.0716042 0.997433i \(-0.477188\pi\)
−0.984484 + 0.175472i \(0.943855\pi\)
\(44\) −19.8501 46.9787i −0.451139 1.06770i
\(45\) 2.24917 21.3994i 0.0499815 0.475542i
\(46\) 24.3740 7.66308i 0.529871 0.166589i
\(47\) 16.4571 + 5.34723i 0.350151 + 0.113771i 0.478811 0.877918i \(-0.341068\pi\)
−0.128661 + 0.991689i \(0.541068\pi\)
\(48\) −51.3756 49.9405i −1.07033 1.04043i
\(49\) 27.6176 + 30.6724i 0.563624 + 0.625968i
\(50\) 4.83675 42.1434i 0.0967350 0.842869i
\(51\) −18.6215 + 1.95720i −0.365127 + 0.0383764i
\(52\) 15.2269 25.2477i 0.292825 0.485533i
\(53\) 31.5797 14.0602i 0.595843 0.265287i −0.0865785 0.996245i \(-0.527593\pi\)
0.682422 + 0.730958i \(0.260927\pi\)
\(54\) −0.175551 + 18.3838i −0.00325095 + 0.340440i
\(55\) 10.0958 22.6756i 0.183561 0.412284i
\(56\) 16.0922 + 15.3466i 0.287361 + 0.274046i
\(57\) −51.7045 + 89.5548i −0.907097 + 1.57114i
\(58\) −30.6556 + 91.3703i −0.528546 + 1.57535i
\(59\) 11.9352 + 56.1509i 0.202292 + 0.951710i 0.955742 + 0.294205i \(0.0950549\pi\)
−0.753450 + 0.657505i \(0.771612\pi\)
\(60\) 0.665924 34.8646i 0.0110987 0.581077i
\(61\) 107.434 1.76122 0.880610 0.473842i \(-0.157133\pi\)
0.880610 + 0.473842i \(0.157133\pi\)
\(62\) 35.0883 51.1157i 0.565940 0.824447i
\(63\) 30.7223i 0.487655i
\(64\) −49.5380 40.5214i −0.774031 0.633147i
\(65\) 14.0361 2.98347i 0.215941 0.0458996i
\(66\) −36.3221 + 108.259i −0.550335 + 1.64030i
\(67\) −40.8447 23.5817i −0.609622 0.351965i 0.163195 0.986594i \(-0.447820\pi\)
−0.772818 + 0.634628i \(0.781153\pi\)
\(68\) −16.4232 + 3.16432i −0.241517 + 0.0465341i
\(69\) −52.2616 23.2684i −0.757415 0.337223i
\(70\) −0.103343 + 10.8221i −0.00147632 + 0.154601i
\(71\) 15.7127 + 35.2912i 0.221305 + 0.497060i 0.989742 0.142866i \(-0.0456318\pi\)
−0.768437 + 0.639926i \(0.778965\pi\)
\(72\) 6.72003 + 88.1663i 0.0933337 + 1.22453i
\(73\) 13.9500 + 132.726i 0.191097 + 1.81816i 0.498842 + 0.866693i \(0.333759\pi\)
−0.307745 + 0.951469i \(0.599574\pi\)
\(74\) 3.40372 29.6572i 0.0459962 0.400773i
\(75\) −70.5833 + 63.5535i −0.941111 + 0.847380i
\(76\) −39.1749 + 83.6514i −0.515459 + 1.10068i
\(77\) 10.9516 33.7055i 0.142228 0.437734i
\(78\) −62.9760 + 19.7993i −0.807385 + 0.253838i
\(79\) 107.810 + 11.3313i 1.36468 + 0.143434i 0.758387 0.651805i \(-0.225988\pi\)
0.606296 + 0.795239i \(0.292655\pi\)
\(80\) −2.07059 31.0796i −0.0258824 0.388495i
\(81\) −39.0179 + 43.3338i −0.481703 + 0.534985i
\(82\) −34.7406 39.3322i −0.423665 0.479661i
\(83\) 19.3403 90.9891i 0.233016 1.09625i −0.693634 0.720328i \(-0.743991\pi\)
0.926650 0.375926i \(-0.122675\pi\)
\(84\) −4.25778 49.6062i −0.0506878 0.590550i
\(85\) −6.58548 4.78463i −0.0774762 0.0562897i
\(86\) 20.9766 + 103.539i 0.243914 + 1.20394i
\(87\) 186.877 107.893i 2.14801 1.24015i
\(88\) −24.0561 + 99.1231i −0.273365 + 1.12640i
\(89\) 72.7316 52.8426i 0.817209 0.593737i −0.0987023 0.995117i \(-0.531469\pi\)
0.915912 + 0.401380i \(0.131469\pi\)
\(90\) −29.0998 + 31.7045i −0.323331 + 0.352272i
\(91\) 19.4857 6.33127i 0.214128 0.0695744i
\(92\) −48.2891 16.7162i −0.524882 0.181697i
\(93\) −134.649 + 33.7703i −1.44784 + 0.363121i
\(94\) −20.0738 28.1914i −0.213551 0.299909i
\(95\) −42.7558 + 13.8922i −0.450061 + 0.146234i
\(96\) 23.0695 + 141.428i 0.240307 + 1.47321i
\(97\) −94.9092 + 68.9555i −0.978445 + 0.710882i −0.957361 0.288896i \(-0.906712\pi\)
−0.0210845 + 0.999778i \(0.506712\pi\)
\(98\) −7.84427 82.1741i −0.0800435 0.838511i
\(99\) 122.043 70.4616i 1.23276 0.711733i
\(100\) −57.9628 + 61.9529i −0.579628 + 0.619529i
\(101\) −25.9127 18.8267i −0.256561 0.186403i 0.452068 0.891983i \(-0.350686\pi\)
−0.708630 + 0.705581i \(0.750686\pi\)
\(102\) 32.2507 + 19.0329i 0.316184 + 0.186597i
\(103\) 10.7235 50.4500i 0.104111 0.489806i −0.894937 0.446193i \(-0.852780\pi\)
0.999048 0.0436135i \(-0.0138870\pi\)
\(104\) −54.5348 + 22.4316i −0.524373 + 0.215688i
\(105\) 16.2143 18.0078i 0.154422 0.171503i
\(106\) −67.4854 15.0194i −0.636655 0.141692i
\(107\) −141.977 14.9224i −1.32689 0.139461i −0.585573 0.810620i \(-0.699130\pi\)
−0.741314 + 0.671158i \(0.765797\pi\)
\(108\) 22.1765 29.3287i 0.205338 0.271562i
\(109\) 42.2717 130.099i 0.387814 1.19357i −0.546605 0.837391i \(-0.684080\pi\)
0.934419 0.356177i \(-0.115920\pi\)
\(110\) −43.2272 + 24.4099i −0.392975 + 0.221908i
\(111\) −49.6709 + 44.7239i −0.447486 + 0.402918i
\(112\) −7.57866 43.8231i −0.0676666 0.391278i
\(113\) −7.59941 72.3035i −0.0672514 0.639854i −0.975284 0.220955i \(-0.929083\pi\)
0.908033 0.418899i \(-0.137584\pi\)
\(114\) 189.732 82.3125i 1.66432 0.722039i
\(115\) −10.1157 22.7202i −0.0879626 0.197567i
\(116\) 158.075 110.298i 1.36271 0.950845i
\(117\) 74.4264 + 33.1368i 0.636123 + 0.283220i
\(118\) 47.6971 104.434i 0.404213 0.885035i
\(119\) −10.0653 5.81119i −0.0845822 0.0488335i
\(120\) −42.5926 + 55.2251i −0.354938 + 0.460209i
\(121\) 40.6556 8.64161i 0.335997 0.0714183i
\(122\) −172.619 127.951i −1.41491 1.04878i
\(123\) 117.499i 0.955275i
\(124\) −117.255 + 40.3404i −0.945602 + 0.325326i
\(125\) −89.9608 −0.719686
\(126\) −36.5892 + 49.3625i −0.290390 + 0.391766i
\(127\) −20.7638 97.6860i −0.163495 0.769181i −0.981115 0.193424i \(-0.938041\pi\)
0.817621 0.575757i \(-0.195293\pi\)
\(128\) 31.3348 + 124.105i 0.244803 + 0.969573i
\(129\) 118.268 204.846i 0.916803 1.58795i
\(130\) −26.1056 11.9229i −0.200812 0.0917148i
\(131\) −72.4368 + 162.696i −0.552953 + 1.24195i 0.393564 + 0.919297i \(0.371242\pi\)
−0.946517 + 0.322655i \(0.895425\pi\)
\(132\) 187.294 130.686i 1.41889 0.990044i
\(133\) −58.6387 + 26.1076i −0.440892 + 0.196298i
\(134\) 37.5416 + 86.5342i 0.280161 + 0.645778i
\(135\) 17.7973 1.87058i 0.131832 0.0138561i
\(136\) 30.1563 + 14.4753i 0.221738 + 0.106436i
\(137\) 56.1100 + 62.3165i 0.409562 + 0.454865i 0.912269 0.409592i \(-0.134329\pi\)
−0.502707 + 0.864457i \(0.667662\pi\)
\(138\) 56.2587 + 99.6280i 0.407672 + 0.721942i
\(139\) 59.1897 + 19.2319i 0.425825 + 0.138359i 0.514087 0.857738i \(-0.328131\pi\)
−0.0882611 + 0.996097i \(0.528131\pi\)
\(140\) 13.0548 17.2651i 0.0932482 0.123322i
\(141\) −8.09969 + 77.0634i −0.0574446 + 0.546549i
\(142\) 16.7846 75.4170i 0.118202 0.531105i
\(143\) 69.8412 + 62.8853i 0.488400 + 0.439757i
\(144\) 94.2059 149.663i 0.654208 1.03933i
\(145\) 91.7613 + 19.5045i 0.632836 + 0.134514i
\(146\) 135.658 229.869i 0.929165 1.57445i
\(147\) −108.638 + 149.527i −0.739032 + 1.01719i
\(148\) −40.7896 + 43.5976i −0.275606 + 0.294578i
\(149\) 140.369 + 243.126i 0.942072 + 1.63172i 0.761511 + 0.648152i \(0.224458\pi\)
0.180561 + 0.983564i \(0.442209\pi\)
\(150\) 189.099 18.0512i 1.26066 0.120341i
\(151\) −127.521 175.518i −0.844510 1.16237i −0.985046 0.172293i \(-0.944883\pi\)
0.140536 0.990076i \(-0.455117\pi\)
\(152\) 162.570 87.7496i 1.06954 0.577300i
\(153\) −14.2812 43.9531i −0.0933414 0.287275i
\(154\) −57.7384 + 41.1128i −0.374925 + 0.266966i
\(155\) −53.3253 28.2587i −0.344034 0.182314i
\(156\) 124.766 + 43.1901i 0.799783 + 0.276860i
\(157\) 18.1138 + 55.7484i 0.115374 + 0.355085i 0.992025 0.126042i \(-0.0402274\pi\)
−0.876651 + 0.481127i \(0.840227\pi\)
\(158\) −159.727 146.604i −1.01093 0.927876i
\(159\) 90.9879 + 125.234i 0.572251 + 0.787636i
\(160\) −33.6879 + 52.4027i −0.210549 + 0.327517i
\(161\) −17.7549 30.7524i −0.110279 0.191009i
\(162\) 114.301 23.1569i 0.705560 0.142944i
\(163\) −115.724 + 159.280i −0.709963 + 0.977180i 0.289835 + 0.957077i \(0.406400\pi\)
−0.999798 + 0.0201036i \(0.993600\pi\)
\(164\) 8.97552 + 104.571i 0.0547288 + 0.637630i
\(165\) 108.723 + 23.1097i 0.658926 + 0.140059i
\(166\) −139.440 + 123.162i −0.839999 + 0.741938i
\(167\) −42.8530 38.5850i −0.256605 0.231048i 0.530780 0.847509i \(-0.321899\pi\)
−0.787385 + 0.616462i \(0.788566\pi\)
\(168\) −52.2382 + 84.7748i −0.310942 + 0.504612i
\(169\) 11.9861 114.040i 0.0709237 0.674794i
\(170\) 4.88278 + 15.5307i 0.0287222 + 0.0913572i
\(171\) −242.744 78.8723i −1.41955 0.461241i
\(172\) 89.6077 191.342i 0.520975 1.11245i
\(173\) −190.181 211.217i −1.09931 1.22091i −0.973460 0.228859i \(-0.926500\pi\)
−0.125851 0.992049i \(-0.540166\pi\)
\(174\) −428.759 49.2082i −2.46413 0.282805i
\(175\) −58.6325 + 6.16253i −0.335043 + 0.0352144i
\(176\) 156.704 130.614i 0.890365 0.742128i
\(177\) −234.839 + 104.557i −1.32677 + 0.590717i
\(178\) −179.794 1.71690i −1.01008 0.00964553i
\(179\) 87.4498 196.415i 0.488546 1.09729i −0.486174 0.873862i \(-0.661608\pi\)
0.974720 0.223431i \(-0.0717256\pi\)
\(180\) 84.5147 16.2838i 0.469526 0.0904655i
\(181\) 37.1897 64.4144i 0.205468 0.355881i −0.744814 0.667272i \(-0.767462\pi\)
0.950282 + 0.311392i \(0.100795\pi\)
\(182\) −38.8486 13.0341i −0.213454 0.0716160i
\(183\) 100.025 + 470.581i 0.546586 + 2.57148i
\(184\) 57.6794 + 84.3692i 0.313475 + 0.458528i
\(185\) −29.0575 −0.157068
\(186\) 256.564 + 106.102i 1.37938 + 0.570442i
\(187\) 53.3120i 0.285091i
\(188\) −1.32180 + 69.2034i −0.00703088 + 0.368103i
\(189\) 24.9926 5.31234i 0.132236 0.0281076i
\(190\) 85.2423 + 28.5996i 0.448644 + 0.150524i
\(191\) −115.643 66.7666i −0.605462 0.349564i 0.165725 0.986172i \(-0.447003\pi\)
−0.771187 + 0.636608i \(0.780337\pi\)
\(192\) 131.369 254.712i 0.684215 1.32662i
\(193\) −155.662 69.3053i −0.806540 0.359095i −0.0383077 0.999266i \(-0.512197\pi\)
−0.768232 + 0.640171i \(0.778863\pi\)
\(194\) 234.618 + 2.24043i 1.20937 + 0.0115486i
\(195\) 26.1363 + 58.7030i 0.134032 + 0.301041i
\(196\) −85.2630 + 141.374i −0.435015 + 0.721297i
\(197\) 5.60674 + 53.3445i 0.0284606 + 0.270784i 0.999493 + 0.0318369i \(0.0101357\pi\)
−0.971032 + 0.238948i \(0.923198\pi\)
\(198\) −280.008 32.1362i −1.41418 0.162304i
\(199\) 93.5387 84.2226i 0.470044 0.423229i −0.399765 0.916617i \(-0.630908\pi\)
0.869809 + 0.493388i \(0.164242\pi\)
\(200\) 166.915 30.5101i 0.834574 0.152551i
\(201\) 65.2641 200.862i 0.324697 0.999314i
\(202\) 19.2129 + 61.1107i 0.0951133 + 0.302528i
\(203\) 133.209 + 14.0009i 0.656204 + 0.0689698i
\(204\) −29.1508 68.9903i −0.142896 0.338188i
\(205\) −34.1802 + 37.9609i −0.166732 + 0.185175i
\(206\) −77.3141 + 68.2885i −0.375311 + 0.331498i
\(207\) 29.3572 138.115i 0.141822 0.667222i
\(208\) 114.338 + 28.9075i 0.549703 + 0.138979i
\(209\) −238.200 173.062i −1.13971 0.828048i
\(210\) −47.4987 + 9.62305i −0.226184 + 0.0458240i
\(211\) 339.321 195.907i 1.60816 0.928470i 0.618374 0.785884i \(-0.287792\pi\)
0.989782 0.142586i \(-0.0455416\pi\)
\(212\) 90.5436 + 104.505i 0.427092 + 0.492949i
\(213\) −139.953 + 101.682i −0.657055 + 0.477379i
\(214\) 210.347 + 193.066i 0.982931 + 0.902178i
\(215\) 97.7985 31.7766i 0.454877 0.147798i
\(216\) −70.5614 + 20.7120i −0.326673 + 0.0958890i
\(217\) −79.9380 32.1680i −0.368378 0.148240i
\(218\) −222.863 + 158.690i −1.02231 + 0.727937i
\(219\) −568.374 + 184.676i −2.59532 + 0.843269i
\(220\) 98.5261 + 12.2620i 0.447846 + 0.0557364i
\(221\) 24.9343 18.1158i 0.112825 0.0819720i
\(222\) 133.073 12.7030i 0.599427 0.0572208i
\(223\) 296.848 171.385i 1.33116 0.768545i 0.345681 0.938352i \(-0.387648\pi\)
0.985477 + 0.169807i \(0.0543145\pi\)
\(224\) −40.0150 + 79.4381i −0.178639 + 0.354634i
\(225\) −189.657 137.794i −0.842922 0.612419i
\(226\) −73.9009 + 125.223i −0.326995 + 0.554085i
\(227\) −55.7879 + 262.461i −0.245762 + 1.15622i 0.666146 + 0.745822i \(0.267943\pi\)
−0.911907 + 0.410396i \(0.865390\pi\)
\(228\) −402.881 93.7106i −1.76702 0.411011i
\(229\) 82.2978 91.4009i 0.359379 0.399131i −0.536158 0.844118i \(-0.680125\pi\)
0.895537 + 0.444987i \(0.146792\pi\)
\(230\) −10.8058 + 48.5529i −0.0469818 + 0.211099i
\(231\) 157.832 + 16.5888i 0.683257 + 0.0718132i
\(232\) −385.345 11.0420i −1.66097 0.0475947i
\(233\) −34.0681 + 104.851i −0.146215 + 0.450004i −0.997165 0.0752425i \(-0.976027\pi\)
0.850950 + 0.525247i \(0.176027\pi\)
\(234\) −80.1187 141.881i −0.342388 0.606331i
\(235\) −25.0344 + 22.5411i −0.106529 + 0.0959194i
\(236\) −201.014 + 110.992i −0.851755 + 0.470306i
\(237\) 50.7418 + 482.776i 0.214100 + 2.03703i
\(238\) 9.25130 + 21.3245i 0.0388710 + 0.0895986i
\(239\) 127.734 + 286.896i 0.534453 + 1.20040i 0.955939 + 0.293567i \(0.0948423\pi\)
−0.421485 + 0.906835i \(0.638491\pi\)
\(240\) 134.206 38.0057i 0.559193 0.158357i
\(241\) −186.520 83.0438i −0.773940 0.344580i −0.0185262 0.999828i \(-0.505897\pi\)
−0.755414 + 0.655248i \(0.772564\pi\)
\(242\) −75.6146 34.5347i −0.312457 0.142705i
\(243\) −297.784 171.925i −1.22545 0.707512i
\(244\) 124.967 + 411.166i 0.512160 + 1.68511i
\(245\) −78.5952 + 16.7059i −0.320797 + 0.0681874i
\(246\) 139.937 188.789i 0.568850 0.767436i
\(247\) 170.215i 0.689129i
\(248\) 236.441 + 74.8302i 0.953392 + 0.301735i
\(249\) 416.555 1.67291
\(250\) 144.543 + 107.140i 0.578173 + 0.428561i
\(251\) 22.2739 + 104.790i 0.0887405 + 0.417491i 0.999984 + 0.00562351i \(0.00179003\pi\)
−0.911244 + 0.411868i \(0.864877\pi\)
\(252\) 117.578 35.7359i 0.466580 0.141809i
\(253\) 81.4419 141.061i 0.321905 0.557555i
\(254\) −82.9789 + 181.685i −0.326689 + 0.715294i
\(255\) 14.8262 33.3002i 0.0581420 0.130589i
\(256\) 97.4587 236.723i 0.380698 0.924699i
\(257\) 259.937 115.731i 1.01143 0.450316i 0.166982 0.985960i \(-0.446598\pi\)
0.844444 + 0.535644i \(0.179931\pi\)
\(258\) −433.989 + 188.280i −1.68213 + 0.729766i
\(259\) −41.2609 + 4.33670i −0.159309 + 0.0167440i
\(260\) 27.7449 + 50.2479i 0.106711 + 0.193261i
\(261\) 356.385 + 395.806i 1.36546 + 1.51650i
\(262\) 310.152 175.139i 1.18379 0.668470i
\(263\) 184.992 + 60.1075i 0.703391 + 0.228545i 0.638807 0.769367i \(-0.279428\pi\)
0.0645834 + 0.997912i \(0.479428\pi\)
\(264\) −456.574 13.0830i −1.72945 0.0495569i
\(265\) −7.03444 + 66.9282i −0.0265450 + 0.252559i
\(266\) 125.310 + 27.8887i 0.471091 + 0.104845i
\(267\) 299.176 + 269.379i 1.12051 + 1.00891i
\(268\) 42.7401 183.748i 0.159478 0.685628i
\(269\) −339.900 72.2479i −1.26357 0.268579i −0.473059 0.881031i \(-0.656850\pi\)
−0.790508 + 0.612451i \(0.790184\pi\)
\(270\) −30.8234 18.1905i −0.114161 0.0673724i
\(271\) 125.277 172.429i 0.462277 0.636270i −0.512702 0.858567i \(-0.671355\pi\)
0.974979 + 0.222297i \(0.0713553\pi\)
\(272\) −31.2136 59.1731i −0.114756 0.217548i
\(273\) 45.8739 + 79.4560i 0.168036 + 0.291047i
\(274\) −15.9370 166.951i −0.0581643 0.609311i
\(275\) −158.954 218.782i −0.578016 0.795570i
\(276\) 28.2609 227.078i 0.102394 0.822746i
\(277\) 161.922 + 498.346i 0.584557 + 1.79908i 0.601041 + 0.799218i \(0.294753\pi\)
−0.0164840 + 0.999864i \(0.505247\pi\)
\(278\) −72.1976 101.394i −0.259704 0.364725i
\(279\) −150.629 307.750i −0.539888 1.10305i
\(280\) −41.5377 + 12.1926i −0.148349 + 0.0435451i
\(281\) 119.638 + 368.209i 0.425759 + 1.31035i 0.902266 + 0.431181i \(0.141903\pi\)
−0.476507 + 0.879171i \(0.658097\pi\)
\(282\) 104.794 114.174i 0.371610 0.404872i
\(283\) −104.316 143.578i −0.368606 0.507343i 0.583915 0.811815i \(-0.301520\pi\)
−0.952521 + 0.304472i \(0.901520\pi\)
\(284\) −116.788 + 101.185i −0.411224 + 0.356286i
\(285\) −100.657 174.344i −0.353183 0.611732i
\(286\) −37.3220 184.219i −0.130496 0.644121i
\(287\) −42.8694 + 59.0047i −0.149371 + 0.205591i
\(288\) −329.608 + 128.273i −1.14447 + 0.445392i
\(289\) 265.583 + 56.4515i 0.918973 + 0.195334i
\(290\) −124.207 140.623i −0.428300 0.484907i
\(291\) −390.401 351.519i −1.34158 1.20797i
\(292\) −491.733 + 207.775i −1.68402 + 0.711557i
\(293\) 8.49106 80.7870i 0.0289797 0.275724i −0.970430 0.241381i \(-0.922400\pi\)
0.999410 0.0343425i \(-0.0109337\pi\)
\(294\) 352.634 110.866i 1.19943 0.377096i
\(295\) −106.286 34.5344i −0.360291 0.117066i
\(296\) 117.461 21.4706i 0.396829 0.0725358i
\(297\) 78.4236 + 87.0983i 0.264053 + 0.293260i
\(298\) 64.0195 557.813i 0.214830 1.87186i
\(299\) 93.6497 9.84298i 0.313210 0.0329197i
\(300\) −325.330 196.207i −1.08443 0.654023i
\(301\) 134.129 59.7179i 0.445610 0.198398i
\(302\) −4.14327 + 433.884i −0.0137194 + 1.43670i
\(303\) 58.3385 131.030i 0.192536 0.432444i
\(304\) −365.713 52.6250i −1.20300 0.173108i
\(305\) −104.576 + 181.130i −0.342871 + 0.593870i
\(306\) −29.4006 + 87.6295i −0.0960802 + 0.286371i
\(307\) −23.8190 112.060i −0.0775865 0.365016i 0.922177 0.386768i \(-0.126409\pi\)
−0.999763 + 0.0217527i \(0.993075\pi\)
\(308\) 141.734 + 2.70717i 0.460177 + 0.00878951i
\(309\) 230.964 0.747456
\(310\) 52.0245 + 108.913i 0.167821 + 0.351332i
\(311\) 152.293i 0.489689i −0.969562 0.244845i \(-0.921263\pi\)
0.969562 0.244845i \(-0.0787370\pi\)
\(312\) −149.028 217.987i −0.477654 0.698678i
\(313\) 286.840 60.9697i 0.916421 0.194791i 0.274522 0.961581i \(-0.411480\pi\)
0.641899 + 0.766789i \(0.278147\pi\)
\(314\) 37.2905 111.146i 0.118760 0.353967i
\(315\) 51.7965 + 29.9047i 0.164433 + 0.0949357i
\(316\) 82.0375 + 425.784i 0.259612 + 1.34742i
\(317\) −10.3888 4.62539i −0.0327722 0.0145911i 0.390285 0.920694i \(-0.372376\pi\)
−0.423057 + 0.906103i \(0.639043\pi\)
\(318\) 2.95628 309.582i 0.00929647 0.973527i
\(319\) 249.898 + 561.281i 0.783381 + 1.75950i
\(320\) 116.537 44.0760i 0.364179 0.137738i
\(321\) −66.8229 635.777i −0.208171 1.98061i
\(322\) −8.09767 + 70.5564i −0.0251480 + 0.219119i
\(323\) −71.7559 + 64.6093i −0.222154 + 0.200029i
\(324\) −211.230 98.9214i −0.651944 0.305313i
\(325\) 48.3115 148.687i 0.148651 0.457500i
\(326\) 375.635 118.098i 1.15226 0.362263i
\(327\) 609.212 + 64.0308i 1.86303 + 0.195813i
\(328\) 110.120 178.708i 0.335731 0.544841i
\(329\) −32.1840 + 35.7440i −0.0978237 + 0.108644i
\(330\) −147.166 166.616i −0.445957 0.504898i
\(331\) 18.1270 85.2806i 0.0547642 0.257645i −0.942245 0.334923i \(-0.891290\pi\)
0.997010 + 0.0772780i \(0.0246229\pi\)
\(332\) 370.724 31.8199i 1.11664 0.0958430i
\(333\) −133.466 96.9686i −0.400798 0.291197i
\(334\) 22.8999 + 113.032i 0.0685626 + 0.338420i
\(335\) 79.5156 45.9084i 0.237360 0.137040i
\(336\) 184.897 73.9967i 0.550289 0.220228i
\(337\) 227.924 165.597i 0.676333 0.491385i −0.195806 0.980643i \(-0.562732\pi\)
0.872139 + 0.489258i \(0.162732\pi\)
\(338\) −155.077 + 168.957i −0.458807 + 0.499874i
\(339\) 309.627 100.604i 0.913353 0.296766i
\(340\) 10.6512 30.7690i 0.0313272 0.0904970i
\(341\) −55.5517 391.328i −0.162908 1.14759i
\(342\) 296.091 + 415.827i 0.865762 + 1.21587i
\(343\) −238.644 + 77.5402i −0.695755 + 0.226065i
\(344\) −371.858 + 200.716i −1.08098 + 0.583478i
\(345\) 90.1005 65.4618i 0.261161 0.189744i
\(346\) 54.0174 + 565.869i 0.156120 + 1.63546i
\(347\) 242.862 140.216i 0.699889 0.404081i −0.107417 0.994214i \(-0.534258\pi\)
0.807306 + 0.590133i \(0.200925\pi\)
\(348\) 630.297 + 589.703i 1.81120 + 1.69455i
\(349\) −156.636 113.803i −0.448814 0.326082i 0.340314 0.940312i \(-0.389467\pi\)
−0.789127 + 0.614230i \(0.789467\pi\)
\(350\) 101.546 + 59.9279i 0.290132 + 0.171222i
\(351\) −14.0873 + 66.2758i −0.0401349 + 0.188820i
\(352\) −407.340 + 23.2333i −1.15721 + 0.0660036i
\(353\) 12.7175 14.1242i 0.0360270 0.0400120i −0.724862 0.688894i \(-0.758097\pi\)
0.760889 + 0.648882i \(0.224763\pi\)
\(354\) 501.847 + 111.690i 1.41765 + 0.315508i
\(355\) −74.7942 7.86119i −0.210688 0.0221442i
\(356\) 286.837 + 216.888i 0.805722 + 0.609235i
\(357\) 16.0829 49.4981i 0.0450502 0.138650i
\(358\) −374.433 + 211.438i −1.04590 + 0.590608i
\(359\) −198.377 + 178.619i −0.552582 + 0.497547i −0.897457 0.441101i \(-0.854588\pi\)
0.344875 + 0.938649i \(0.387921\pi\)
\(360\) −155.186 74.4905i −0.431073 0.206918i
\(361\) 18.0065 + 171.321i 0.0498796 + 0.474573i
\(362\) −136.469 + 59.2052i −0.376987 + 0.163550i
\(363\) 75.7035 + 170.033i 0.208550 + 0.468410i
\(364\) 46.8963 + 67.2098i 0.128836 + 0.184642i
\(365\) −237.349 105.675i −0.650272 0.289520i
\(366\) 399.733 875.226i 1.09217 2.39133i
\(367\) −514.994 297.332i −1.40325 0.810168i −0.408528 0.912746i \(-0.633958\pi\)
−0.994725 + 0.102578i \(0.967291\pi\)
\(368\) 7.80543 204.253i 0.0212104 0.555036i
\(369\) −283.675 + 60.2970i −0.768767 + 0.163407i
\(370\) 46.6878 + 34.6066i 0.126183 + 0.0935313i
\(371\) 96.0861i 0.258992i
\(372\) −285.866 476.038i −0.768457 1.27967i
\(373\) −406.698 −1.09034 −0.545172 0.838325i \(-0.683535\pi\)
−0.545172 + 0.838325i \(0.683535\pi\)
\(374\) −63.4928 + 85.6582i −0.169767 + 0.229033i
\(375\) −83.7566 394.044i −0.223351 1.05078i
\(376\) 84.5428 109.617i 0.224848 0.291535i
\(377\) −177.596 + 307.606i −0.471078 + 0.815931i
\(378\) −46.4833 21.2298i −0.122972 0.0561636i
\(379\) 47.2020 106.018i 0.124544 0.279730i −0.840503 0.541806i \(-0.817741\pi\)
0.965047 + 0.262077i \(0.0844073\pi\)
\(380\) −102.901 147.473i −0.270791 0.388086i
\(381\) 408.550 181.898i 1.07231 0.477423i
\(382\) 106.291 + 245.004i 0.278249 + 0.641371i
\(383\) −229.082 + 24.0775i −0.598125 + 0.0628655i −0.398753 0.917058i \(-0.630557\pi\)
−0.199372 + 0.979924i \(0.563890\pi\)
\(384\) −514.429 + 252.798i −1.33966 + 0.658329i
\(385\) 46.1660 + 51.2725i 0.119912 + 0.133175i
\(386\) 167.568 + 296.744i 0.434113 + 0.768766i
\(387\) 555.246 + 180.410i 1.43474 + 0.466177i
\(388\) −374.300 283.022i −0.964691 0.729437i
\(389\) −23.2427 + 221.140i −0.0597499 + 0.568482i 0.923163 + 0.384409i \(0.125595\pi\)
−0.982913 + 0.184073i \(0.941072\pi\)
\(390\) 27.9193 125.448i 0.0715880 0.321660i
\(391\) −39.6965 35.7429i −0.101525 0.0914140i
\(392\) 305.367 125.605i 0.778998 0.320422i
\(393\) −780.077 165.810i −1.98493 0.421910i
\(394\) 54.5231 92.3880i 0.138383 0.234487i
\(395\) −124.045 + 170.734i −0.314039 + 0.432237i
\(396\) 411.626 + 385.115i 1.03946 + 0.972513i
\(397\) −280.531 485.893i −0.706626 1.22391i −0.966101 0.258163i \(-0.916883\pi\)
0.259475 0.965750i \(-0.416450\pi\)
\(398\) −250.598 + 23.9219i −0.629644 + 0.0601053i
\(399\) −168.951 232.540i −0.423435 0.582808i
\(400\) −304.524 149.768i −0.761311 0.374421i
\(401\) 99.6779 + 306.777i 0.248573 + 0.765030i 0.995028 + 0.0995940i \(0.0317544\pi\)
−0.746455 + 0.665436i \(0.768246\pi\)
\(402\) −344.082 + 245.005i −0.855926 + 0.609465i
\(403\) 164.149 158.958i 0.407318 0.394437i
\(404\) 41.9108 121.071i 0.103740 0.299680i
\(405\) −35.0795 107.963i −0.0866159 0.266576i
\(406\) −197.358 181.144i −0.486103 0.446167i
\(407\) −111.859 153.961i −0.274839 0.378283i
\(408\) −35.3276 + 145.567i −0.0865871 + 0.356782i
\(409\) 376.592 + 652.277i 0.920764 + 1.59481i 0.798236 + 0.602345i \(0.205767\pi\)
0.122528 + 0.992465i \(0.460900\pi\)
\(410\) 100.129 20.2857i 0.244216 0.0494772i
\(411\) −220.717 + 303.790i −0.537023 + 0.739149i
\(412\) 205.553 17.6429i 0.498914 0.0428226i
\(413\) −156.077 33.1752i −0.377911 0.0803274i
\(414\) −211.660 + 186.951i −0.511255 + 0.451571i
\(415\) 134.578 + 121.175i 0.324285 + 0.291988i
\(416\) −149.283 182.620i −0.358854 0.438990i
\(417\) −29.1314 + 277.167i −0.0698595 + 0.664669i
\(418\) 176.612 + 561.753i 0.422517 + 1.34391i
\(419\) 265.116 + 86.1415i 0.632736 + 0.205588i 0.607787 0.794100i \(-0.292058\pi\)
0.0249492 + 0.999689i \(0.492058\pi\)
\(420\) 87.7785 + 41.1077i 0.208997 + 0.0978755i
\(421\) 192.838 + 214.169i 0.458049 + 0.508714i 0.927284 0.374359i \(-0.122137\pi\)
−0.469235 + 0.883073i \(0.655470\pi\)
\(422\) −778.518 89.3495i −1.84483 0.211729i
\(423\) −190.209 + 19.9918i −0.449667 + 0.0472619i
\(424\) −21.0174 275.747i −0.0495693 0.650346i
\(425\) −81.0186 + 36.0718i −0.190632 + 0.0848748i
\(426\) 345.967 + 3.30373i 0.812128 + 0.00775523i
\(427\) −121.462 + 272.807i −0.284454 + 0.638893i
\(428\) −108.037 560.723i −0.252422 1.31010i
\(429\) −210.424 + 364.465i −0.490499 + 0.849569i
\(430\) −194.981 65.4181i −0.453445 0.152135i
\(431\) 96.4661 + 453.837i 0.223819 + 1.05299i 0.936274 + 0.351269i \(0.114250\pi\)
−0.712455 + 0.701718i \(0.752417\pi\)
\(432\) 138.041 + 50.7575i 0.319539 + 0.117494i
\(433\) 206.318 0.476485 0.238243 0.971206i \(-0.423429\pi\)
0.238243 + 0.971206i \(0.423429\pi\)
\(434\) 90.1281 + 146.889i 0.207668 + 0.338454i
\(435\) 420.090i 0.965723i
\(436\) 547.076 + 10.4493i 1.25476 + 0.0239663i
\(437\) −288.564 + 61.3361i −0.660328 + 0.140357i
\(438\) 1133.17 + 380.190i 2.58715 + 0.868013i
\(439\) 368.310 + 212.644i 0.838974 + 0.484382i 0.856915 0.515457i \(-0.172378\pi\)
−0.0179411 + 0.999839i \(0.505711\pi\)
\(440\) −143.702 137.043i −0.326595 0.311462i
\(441\) −416.750 185.549i −0.945011 0.420746i
\(442\) −61.6381 0.588599i −0.139453 0.00133167i
\(443\) −144.318 324.144i −0.325775 0.731702i 0.674202 0.738547i \(-0.264488\pi\)
−0.999977 + 0.00684525i \(0.997821\pi\)
\(444\) −228.941 138.075i −0.515634 0.310979i
\(445\) 18.2944 + 174.059i 0.0411109 + 0.391144i
\(446\) −681.071 78.1656i −1.52707 0.175259i
\(447\) −934.245 + 841.198i −2.09003 + 1.88187i
\(448\) 158.902 79.9794i 0.354691 0.178525i
\(449\) −198.349 + 610.455i −0.441757 + 1.35959i 0.444245 + 0.895905i \(0.353472\pi\)
−0.886002 + 0.463682i \(0.846528\pi\)
\(450\) 140.621 + 447.274i 0.312491 + 0.993943i
\(451\) −332.715 34.9698i −0.737728 0.0775383i
\(452\) 267.876 113.187i 0.592646 0.250414i
\(453\) 650.071 721.977i 1.43504 1.59377i
\(454\) 402.219 355.264i 0.885946 0.782521i
\(455\) −8.29287 + 39.0149i −0.0182261 + 0.0857470i
\(456\) 535.717 + 630.386i 1.17482 + 1.38243i
\(457\) −258.106 187.525i −0.564784 0.410339i 0.268423 0.963301i \(-0.413498\pi\)
−0.833207 + 0.552962i \(0.813498\pi\)
\(458\) −241.086 + 48.8431i −0.526389 + 0.106644i
\(459\) 33.2864 19.2179i 0.0725195 0.0418691i
\(460\) 75.1869 65.1422i 0.163450 0.141613i
\(461\) 402.528 292.453i 0.873162 0.634389i −0.0582716 0.998301i \(-0.518559\pi\)
0.931434 + 0.363911i \(0.118559\pi\)
\(462\) −233.838 214.627i −0.506143 0.464561i
\(463\) −344.220 + 111.844i −0.743456 + 0.241563i −0.656163 0.754619i \(-0.727822\pi\)
−0.0872927 + 0.996183i \(0.527822\pi\)
\(464\) 605.997 + 476.675i 1.30603 + 1.02732i
\(465\) 74.1303 259.884i 0.159420 0.558890i
\(466\) 179.612 127.894i 0.385435 0.274450i
\(467\) 455.997 148.162i 0.976439 0.317264i 0.223027 0.974812i \(-0.428406\pi\)
0.753413 + 0.657548i \(0.228406\pi\)
\(468\) −40.2466 + 323.384i −0.0859970 + 0.690992i
\(469\) 106.058 77.0559i 0.226137 0.164298i
\(470\) 67.0693 6.40238i 0.142701 0.0136221i
\(471\) −227.323 + 131.245i −0.482639 + 0.278652i
\(472\) 455.165 + 61.0663i 0.964332 + 0.129378i
\(473\) 544.852 + 395.858i 1.15191 + 0.836909i
\(474\) 493.442 836.125i 1.04102 1.76398i
\(475\) −101.834 + 479.090i −0.214387 + 1.00861i
\(476\) 10.5324 45.2808i 0.0221268 0.0951276i
\(477\) −255.658 + 283.937i −0.535971 + 0.595256i
\(478\) 136.449 613.093i 0.285457 1.28262i
\(479\) −311.191 32.7075i −0.649668 0.0682828i −0.226038 0.974118i \(-0.572577\pi\)
−0.423629 + 0.905836i \(0.639244\pi\)
\(480\) −260.897 98.7701i −0.543536 0.205771i
\(481\) 33.9978 104.634i 0.0706814 0.217535i
\(482\) 200.785 + 355.568i 0.416566 + 0.737693i
\(483\) 118.170 106.401i 0.244659 0.220292i
\(484\) 80.3630 + 145.543i 0.166039 + 0.300708i
\(485\) −23.8727 227.134i −0.0492221 0.468317i
\(486\) 273.702 + 630.889i 0.563172 + 1.29813i
\(487\) 58.2140 + 130.751i 0.119536 + 0.268482i 0.963397 0.268080i \(-0.0863893\pi\)
−0.843861 + 0.536562i \(0.819723\pi\)
\(488\) 288.897 809.467i 0.592001 1.65874i
\(489\) −805.419 358.596i −1.64707 0.733324i
\(490\) 146.178 + 66.7623i 0.298322 + 0.136250i
\(491\) −182.159 105.170i −0.370997 0.214195i 0.302897 0.953023i \(-0.402046\pi\)
−0.673894 + 0.738828i \(0.735379\pi\)
\(492\) −449.684 + 136.674i −0.913992 + 0.277792i
\(493\) 197.086 41.8919i 0.399768 0.0849734i
\(494\) −202.720 + 273.490i −0.410365 + 0.553624i
\(495\) 274.346i 0.554235i
\(496\) −290.778 401.826i −0.586246 0.810133i
\(497\) −107.379 −0.216054
\(498\) −669.293 496.103i −1.34396 0.996191i
\(499\) −9.12993 42.9530i −0.0182965 0.0860781i 0.968052 0.250749i \(-0.0806770\pi\)
−0.986349 + 0.164671i \(0.947344\pi\)
\(500\) −104.642 344.292i −0.209284 0.688585i
\(501\) 129.111 223.627i 0.257707 0.446362i
\(502\) 89.0136 194.898i 0.177318 0.388242i
\(503\) 20.5014 46.0470i 0.0407583 0.0915447i −0.892019 0.451998i \(-0.850711\pi\)
0.932777 + 0.360453i \(0.117378\pi\)
\(504\) −231.477 82.6137i −0.459281 0.163916i
\(505\) 56.9642 25.3621i 0.112800 0.0502220i
\(506\) −298.855 + 129.654i −0.590623 + 0.256233i
\(507\) 510.676 53.6742i 1.00725 0.105866i
\(508\) 349.706 193.094i 0.688397 0.380106i
\(509\) 79.7336 + 88.5531i 0.156647 + 0.173975i 0.816360 0.577543i \(-0.195989\pi\)
−0.659712 + 0.751518i \(0.729322\pi\)
\(510\) −63.4812 + 35.8471i −0.124473 + 0.0702884i
\(511\) −352.801 114.632i −0.690413 0.224329i
\(512\) −438.520 + 264.281i −0.856484 + 0.516174i
\(513\) 22.1886 211.110i 0.0432526 0.411521i
\(514\) −555.481 123.627i −1.08070 0.240519i
\(515\) 74.6186 + 67.1869i 0.144891 + 0.130460i
\(516\) 921.540 + 214.351i 1.78593 + 0.415410i
\(517\) −215.806 45.8709i −0.417419 0.0887252i
\(518\) 71.4602 + 42.1725i 0.137954 + 0.0814140i
\(519\) 748.103 1029.68i 1.44143 1.98396i
\(520\) 15.2648 113.778i 0.0293555 0.218804i
\(521\) −310.832 538.377i −0.596606 1.03335i −0.993318 0.115409i \(-0.963182\pi\)
0.396712 0.917943i \(-0.370151\pi\)
\(522\) −101.225 1060.40i −0.193917 2.03141i
\(523\) −27.2396 37.4921i −0.0520834 0.0716866i 0.782181 0.623051i \(-0.214107\pi\)
−0.834264 + 0.551365i \(0.814107\pi\)
\(524\) −706.917 87.9789i −1.34908 0.167899i
\(525\) −81.5819 251.083i −0.155394 0.478254i
\(526\) −225.647 316.896i −0.428986 0.602464i
\(527\) −129.317 8.86239i −0.245384 0.0168167i
\(528\) 718.011 + 564.785i 1.35987 + 1.06967i
\(529\) 113.037 + 347.892i 0.213681 + 0.657642i
\(530\) 91.0118 99.1581i 0.171720 0.187091i
\(531\) −372.942 513.311i −0.702340 0.966688i
\(532\) −168.126 194.050i −0.316026 0.364756i
\(533\) −96.7036 167.496i −0.181433 0.314250i
\(534\) −159.874 789.129i −0.299390 1.47777i
\(535\) 163.357 224.842i 0.305341 0.420266i
\(536\) −287.510 + 244.333i −0.536399 + 0.455845i
\(537\) 941.753 + 200.176i 1.75373 + 0.372767i
\(538\) 460.084 + 520.892i 0.855174 + 0.968202i
\(539\) −391.075 352.126i −0.725557 0.653294i
\(540\) 27.8607 + 65.9370i 0.0515939 + 0.122106i
\(541\) 70.6467 672.159i 0.130585 1.24244i −0.711342 0.702846i \(-0.751912\pi\)
0.841927 0.539591i \(-0.181421\pi\)
\(542\) −406.645 + 127.847i −0.750267 + 0.235880i
\(543\) 316.771 + 102.925i 0.583372 + 0.189549i
\(544\) −20.3211 + 132.250i −0.0373550 + 0.243106i
\(545\) 178.195 + 197.905i 0.326963 + 0.363129i
\(546\) 20.9222 182.299i 0.0383191 0.333881i
\(547\) 652.301 68.5596i 1.19251 0.125338i 0.512595 0.858631i \(-0.328684\pi\)
0.679913 + 0.733293i \(0.262018\pi\)
\(548\) −173.227 + 287.227i −0.316107 + 0.524136i
\(549\) −1084.79 + 482.978i −1.97593 + 0.879741i
\(550\) −5.16457 + 540.834i −0.00939013 + 0.983334i
\(551\) 452.609 1016.58i 0.821431 1.84496i
\(552\) −315.850 + 331.196i −0.572192 + 0.599994i
\(553\) −150.660 + 260.950i −0.272441 + 0.471881i
\(554\) 333.347 993.554i 0.601710 1.79342i
\(555\) −27.0536 127.277i −0.0487452 0.229328i
\(556\) −4.75402 + 248.898i −0.00855039 + 0.447658i
\(557\) 966.750 1.73564 0.867819 0.496881i \(-0.165522\pi\)
0.867819 + 0.496881i \(0.165522\pi\)
\(558\) −124.499 + 673.866i −0.223117 + 1.20765i
\(559\) 389.345i 0.696503i
\(560\) 81.2611 + 29.8797i 0.145109 + 0.0533566i
\(561\) 233.516 49.6353i 0.416249 0.0884765i
\(562\) 246.298 734.099i 0.438252 1.30623i
\(563\) 642.394 + 370.886i 1.14102 + 0.658768i 0.946683 0.322167i \(-0.104411\pi\)
0.194336 + 0.980935i \(0.437745\pi\)
\(564\) −304.354 + 58.6410i −0.539634 + 0.103973i
\(565\) 129.298 + 57.5672i 0.228846 + 0.101889i
\(566\) −3.38931 + 354.928i −0.00598817 + 0.627082i
\(567\) −65.9249 148.070i −0.116270 0.261146i
\(568\) 308.155 23.4875i 0.542526 0.0413513i
\(569\) −61.7209 587.236i −0.108473 1.03205i −0.904409 0.426668i \(-0.859687\pi\)
0.795936 0.605381i \(-0.206979\pi\)
\(570\) −45.9079 + 400.003i −0.0805401 + 0.701760i
\(571\) −508.060 + 457.459i −0.889773 + 0.801155i −0.980865 0.194687i \(-0.937631\pi\)
0.0910926 + 0.995842i \(0.470964\pi\)
\(572\) −159.432 + 340.440i −0.278727 + 0.595174i
\(573\) 184.782 568.699i 0.322481 0.992495i
\(574\) 139.152 43.7488i 0.242426 0.0762175i
\(575\) −269.477 28.3232i −0.468656 0.0492577i
\(576\) 682.361 + 186.451i 1.18466 + 0.323701i
\(577\) 328.184 364.486i 0.568777 0.631691i −0.388297 0.921534i \(-0.626937\pi\)
0.957074 + 0.289843i \(0.0936033\pi\)
\(578\) −359.490 407.004i −0.621955 0.704159i
\(579\) 158.642 746.353i 0.273994 1.28904i
\(580\) 32.0899 + 373.870i 0.0553274 + 0.644604i
\(581\) 209.182 + 151.980i 0.360039 + 0.261583i
\(582\) 208.624 + 1029.75i 0.358460 + 1.76933i
\(583\) −381.699 + 220.374i −0.654715 + 0.378000i
\(584\) 1037.54 + 251.800i 1.77661 + 0.431164i
\(585\) −128.313 + 93.2250i −0.219339 + 0.159359i
\(586\) −109.858 + 119.691i −0.187470 + 0.204250i
\(587\) 51.3250 16.6765i 0.0874362 0.0284097i −0.264972 0.964256i \(-0.585363\pi\)
0.352408 + 0.935846i \(0.385363\pi\)
\(588\) −698.627 241.842i −1.18814 0.411297i
\(589\) −459.390 + 549.025i −0.779948 + 0.932131i
\(590\) 129.644 + 182.071i 0.219736 + 0.308594i
\(591\) −228.438 + 74.2241i −0.386528 + 0.125591i
\(592\) −214.300 105.395i −0.361993 0.178032i
\(593\) −343.634 + 249.665i −0.579485 + 0.421020i −0.838538 0.544843i \(-0.816589\pi\)
0.259054 + 0.965863i \(0.416589\pi\)
\(594\) −22.2748 233.344i −0.0374997 0.392835i
\(595\) 19.5949 11.3131i 0.0329326 0.0190136i
\(596\) −767.199 + 820.012i −1.28725 + 1.37586i
\(597\) 455.998 + 331.302i 0.763815 + 0.554944i
\(598\) −162.193 95.7186i −0.271226 0.160065i
\(599\) −137.772 + 648.167i −0.230004 + 1.08208i 0.699889 + 0.714251i \(0.253233\pi\)
−0.929893 + 0.367831i \(0.880101\pi\)
\(600\) 289.043 + 702.710i 0.481739 + 1.17118i
\(601\) −266.017 + 295.442i −0.442624 + 0.491584i −0.922633 0.385680i \(-0.873967\pi\)
0.480008 + 0.877264i \(0.340634\pi\)
\(602\) −286.631 63.7920i −0.476132 0.105967i
\(603\) 518.430 + 54.4891i 0.859750 + 0.0903634i
\(604\) 523.398 692.201i 0.866553 1.14603i
\(605\) −25.0043 + 76.9554i −0.0413295 + 0.127199i
\(606\) −249.788 + 141.052i −0.412191 + 0.232759i
\(607\) 124.255 111.880i 0.204703 0.184315i −0.560402 0.828221i \(-0.689353\pi\)
0.765105 + 0.643905i \(0.222687\pi\)
\(608\) 524.930 + 520.107i 0.863372 + 0.855439i
\(609\) 62.6964 + 596.516i 0.102950 + 0.979501i
\(610\) 383.745 166.482i 0.629091 0.272922i
\(611\) −51.8784 116.521i −0.0849073 0.190705i
\(612\) 151.603 105.782i 0.247717 0.172847i
\(613\) −853.826 380.148i −1.39287 0.620144i −0.433202 0.901297i \(-0.642616\pi\)
−0.959663 + 0.281153i \(0.909283\pi\)
\(614\) −95.1886 + 208.418i −0.155030 + 0.339443i
\(615\) −198.098 114.372i −0.322111 0.185971i
\(616\) −224.505 173.151i −0.364457 0.281089i
\(617\) 901.418 191.602i 1.46097 0.310538i 0.592214 0.805781i \(-0.298254\pi\)
0.868755 + 0.495242i \(0.164921\pi\)
\(618\) −371.098 275.070i −0.600482 0.445098i
\(619\) 958.561i 1.54856i 0.632841 + 0.774282i \(0.281889\pi\)
−0.632841 + 0.774282i \(0.718111\pi\)
\(620\) 46.1222 236.954i 0.0743907 0.382183i
\(621\) 117.433 0.189103
\(622\) −181.376 + 244.695i −0.291602 + 0.393400i
\(623\) 51.9550 + 244.429i 0.0833948 + 0.392342i
\(624\) −20.1672 + 527.736i −0.0323192 + 0.845730i
\(625\) −177.559 + 307.541i −0.284094 + 0.492065i
\(626\) −533.488 243.655i −0.852218 0.389225i
\(627\) 536.270 1204.48i 0.855295 1.92102i
\(628\) −192.287 + 134.170i −0.306189 + 0.213647i
\(629\) −57.0144 + 25.3845i −0.0906429 + 0.0403568i
\(630\) −47.6077 109.737i −0.0755678 0.174186i
\(631\) 310.608 32.6463i 0.492248 0.0517373i 0.144847 0.989454i \(-0.453731\pi\)
0.347401 + 0.937717i \(0.387064\pi\)
\(632\) 375.282 781.826i 0.593801 1.23707i
\(633\) 1174.03 + 1303.89i 1.85470 + 2.05986i
\(634\) 11.1834 + 19.8045i 0.0176394 + 0.0312374i
\(635\) 184.906 + 60.0797i 0.291191 + 0.0946136i
\(636\) −373.451 + 493.895i −0.587188 + 0.776564i
\(637\) 31.8006 302.563i 0.0499225 0.474981i
\(638\) 266.947 1199.45i 0.418412 1.88002i
\(639\) −317.308 285.705i −0.496569 0.447113i
\(640\) −239.738 67.9737i −0.374590 0.106209i
\(641\) 791.733 + 168.288i 1.23515 + 0.262540i 0.778808 0.627263i \(-0.215825\pi\)
0.456346 + 0.889803i \(0.349158\pi\)
\(642\) −649.823 + 1101.11i −1.01219 + 1.71512i
\(643\) −41.5388 + 57.1732i −0.0646015 + 0.0889163i −0.840095 0.542439i \(-0.817501\pi\)
0.775494 + 0.631355i \(0.217501\pi\)
\(644\) 97.0412 103.721i 0.150685 0.161058i
\(645\) 230.241 + 398.789i 0.356963 + 0.618278i
\(646\) 192.240 18.3511i 0.297585 0.0284073i
\(647\) 396.694 + 546.003i 0.613129 + 0.843899i 0.996830 0.0795579i \(-0.0253509\pi\)
−0.383702 + 0.923457i \(0.625351\pi\)
\(648\) 221.578 + 410.508i 0.341942 + 0.633501i
\(649\) −226.176 696.099i −0.348499 1.07257i
\(650\) −254.706 + 181.364i −0.391855 + 0.279021i
\(651\) 66.4766 380.092i 0.102115 0.583858i
\(652\) −744.197 257.618i −1.14141 0.395119i
\(653\) 281.933 + 867.701i 0.431751 + 1.32879i 0.896380 + 0.443287i \(0.146188\pi\)
−0.464629 + 0.885505i \(0.653812\pi\)
\(654\) −902.584 828.432i −1.38010 1.26672i
\(655\) −203.789 280.492i −0.311129 0.428232i
\(656\) −389.768 + 155.987i −0.594159 + 0.237785i
\(657\) −737.533 1277.45i −1.12258 1.94436i
\(658\) 94.2810 19.1010i 0.143284 0.0290288i
\(659\) 683.346 940.545i 1.03694 1.42723i 0.137340 0.990524i \(-0.456145\pi\)
0.899604 0.436707i \(-0.143855\pi\)
\(660\) 38.0215 + 442.978i 0.0576084 + 0.671179i
\(661\) −758.545 161.234i −1.14757 0.243924i −0.405404 0.914138i \(-0.632869\pi\)
−0.742168 + 0.670214i \(0.766202\pi\)
\(662\) −130.692 + 115.435i −0.197419 + 0.174373i
\(663\) 102.565 + 92.3500i 0.154698 + 0.139291i
\(664\) −633.552 390.394i −0.954145 0.587943i
\(665\) 13.0619 124.275i 0.0196419 0.186880i
\(666\) 98.9578 + 314.756i 0.148585 + 0.472607i
\(667\) 585.477 + 190.233i 0.877777 + 0.285207i
\(668\) 97.8237 208.886i 0.146443 0.312704i
\(669\) 1027.07 + 1140.68i 1.53524 + 1.70505i
\(670\) −182.436 20.9379i −0.272292 0.0312506i
\(671\) −1362.29 + 143.182i −2.03024 + 0.213387i
\(672\) −385.208 101.313i −0.573226 0.150764i
\(673\) 279.281 124.344i 0.414979 0.184760i −0.188618 0.982051i \(-0.560401\pi\)
0.603596 + 0.797290i \(0.293734\pi\)
\(674\) −563.434 5.38039i −0.835956 0.00798277i
\(675\) 79.3011 178.113i 0.117483 0.263871i
\(676\) 450.390 86.7784i 0.666257 0.128370i
\(677\) −284.189 + 492.230i −0.419777 + 0.727076i −0.995917 0.0902756i \(-0.971225\pi\)
0.576139 + 0.817351i \(0.304559\pi\)
\(678\) −617.304 207.112i −0.910478 0.305474i
\(679\) −67.7972 318.961i −0.0998487 0.469751i
\(680\) −53.7586 + 36.7523i −0.0790567 + 0.0540475i
\(681\) −1201.57 −1.76442
\(682\) −376.802 + 694.921i −0.552496 + 1.01895i
\(683\) 192.240i 0.281463i 0.990048 + 0.140732i \(0.0449455\pi\)
−0.990048 + 0.140732i \(0.955055\pi\)
\(684\) 19.4968 1020.76i 0.0285040 1.49234i
\(685\) −159.680 + 33.9410i −0.233109 + 0.0495490i
\(686\) 475.786 + 159.631i 0.693565 + 0.232698i
\(687\) 476.974 + 275.381i 0.694286 + 0.400846i
\(688\) 836.524 + 120.373i 1.21588 + 0.174961i
\(689\) −232.774 103.638i −0.337843 0.150417i
\(690\) −222.731 2.12691i −0.322798 0.00308248i
\(691\) 98.4155 + 221.045i 0.142425 + 0.319891i 0.970647 0.240508i \(-0.0773142\pi\)
−0.828222 + 0.560400i \(0.810648\pi\)
\(692\) 587.140 973.534i 0.848468 1.40684i
\(693\) 40.9449 + 389.565i 0.0590835 + 0.562142i
\(694\) −557.207 63.9499i −0.802892 0.0921469i
\(695\) −90.0389 + 81.0714i −0.129552 + 0.116650i
\(696\) −310.404 1698.16i −0.445983 2.43988i
\(697\) −33.9032 + 104.343i −0.0486417 + 0.149704i
\(698\) 116.137 + 369.399i 0.166386 + 0.529225i
\(699\) −490.984 51.6045i −0.702409 0.0738262i
\(700\) −91.7858 217.226i −0.131123 0.310324i
\(701\) 2.70631 3.00566i 0.00386064 0.00428768i −0.741211 0.671272i \(-0.765748\pi\)
0.745072 + 0.666984i \(0.232415\pi\)
\(702\) 101.567 89.7100i 0.144682 0.127792i
\(703\) −71.6625 + 337.146i −0.101938 + 0.479581i
\(704\) 682.157 + 447.799i 0.968973 + 0.636077i
\(705\) −122.042 88.6685i −0.173109 0.125771i
\(706\) −37.2552 + 7.54775i −0.0527694 + 0.0106909i
\(707\) 77.1025 44.5151i 0.109056 0.0629634i
\(708\) −673.317 777.140i −0.951012 1.09766i
\(709\) −70.9453 + 51.5448i −0.100064 + 0.0727007i −0.636692 0.771118i \(-0.719698\pi\)
0.536628 + 0.843819i \(0.319698\pi\)
\(710\) 110.812 + 101.708i 0.156073 + 0.143251i
\(711\) −1139.52 + 370.252i −1.60270 + 0.520748i
\(712\) −202.565 690.095i −0.284501 0.969234i
\(713\) −328.630 221.001i −0.460912 0.309959i
\(714\) −84.7916 + 60.3761i −0.118756 + 0.0845604i
\(715\) −174.005 + 56.5376i −0.243363 + 0.0790736i
\(716\) 853.430 + 106.213i 1.19194 + 0.148342i
\(717\) −1137.73 + 826.609i −1.58679 + 1.15287i
\(718\) 531.469 50.7336i 0.740207 0.0706596i
\(719\) −805.577 + 465.100i −1.12041 + 0.646871i −0.941506 0.336995i \(-0.890589\pi\)
−0.178907 + 0.983866i \(0.557256\pi\)
\(720\) 160.627 + 304.508i 0.223093 + 0.422928i
\(721\) 115.984 + 84.2671i 0.160865 + 0.116875i
\(722\) 175.106 296.712i 0.242529 0.410959i
\(723\) 190.090 894.305i 0.262919 1.23694i
\(724\) 289.781 + 67.4035i 0.400251 + 0.0930988i
\(725\) 683.897 759.545i 0.943306 1.04765i
\(726\) 80.8681 363.358i 0.111389 0.500494i
\(727\) 958.401 + 100.732i 1.31830 + 0.138558i 0.737420 0.675434i \(-0.236044\pi\)
0.580875 + 0.813993i \(0.302710\pi\)
\(728\) 4.69481 163.840i 0.00644891 0.225055i
\(729\) 313.644 965.296i 0.430238 1.32414i
\(730\) 255.502 + 452.467i 0.350003 + 0.619817i
\(731\) 164.133 147.786i 0.224532 0.202169i
\(732\) −1684.63 + 930.188i −2.30141 + 1.27075i
\(733\) 68.2132 + 649.005i 0.0930603 + 0.885409i 0.937084 + 0.349104i \(0.113514\pi\)
−0.844024 + 0.536306i \(0.819819\pi\)
\(734\) 473.346 + 1091.07i 0.644886 + 1.48648i
\(735\) −146.350 328.707i −0.199115 0.447220i
\(736\) −255.800 + 318.885i −0.347554 + 0.433267i
\(737\) 549.347 + 244.585i 0.745383 + 0.331866i
\(738\) 527.602 + 240.966i 0.714908 + 0.326513i
\(739\) −627.641 362.368i −0.849311 0.490350i 0.0111075 0.999938i \(-0.496464\pi\)
−0.860418 + 0.509589i \(0.829798\pi\)
\(740\) −33.7995 111.207i −0.0456751 0.150280i
\(741\) 745.571 158.476i 1.00617 0.213868i
\(742\) 114.435 154.385i 0.154226 0.208066i
\(743\) 567.317i 0.763549i −0.924256 0.381774i \(-0.875313\pi\)
0.924256 0.381774i \(-0.124687\pi\)
\(744\) −107.634 + 1105.32i −0.144670 + 1.48565i
\(745\) −546.534 −0.733602
\(746\) 653.456 + 484.364i 0.875946 + 0.649281i
\(747\) 213.764 + 1005.68i 0.286163 + 1.34629i
\(748\) 204.032 62.0122i 0.272770 0.0829040i
\(749\) 198.407 343.650i 0.264895 0.458812i
\(750\) −334.719 + 732.876i −0.446292 + 0.977168i
\(751\) 24.8758 55.8721i 0.0331236 0.0743969i −0.896226 0.443598i \(-0.853702\pi\)
0.929350 + 0.369201i \(0.120369\pi\)
\(752\) −266.388 + 75.4382i −0.354240 + 0.100317i
\(753\) −438.262 + 195.127i −0.582021 + 0.259132i
\(754\) 651.699 282.730i 0.864323 0.374973i
\(755\) 420.043 44.1483i 0.556349 0.0584746i
\(756\) 49.4023 + 89.4707i 0.0653469 + 0.118348i
\(757\) −773.590 859.159i −1.02192 1.13495i −0.990786 0.135437i \(-0.956756\pi\)
−0.0311302 0.999515i \(-0.509911\pi\)
\(758\) −202.105 + 114.126i −0.266629 + 0.150562i
\(759\) 693.699 + 225.396i 0.913964 + 0.296965i
\(760\) −10.3014 + 359.501i −0.0135545 + 0.473028i
\(761\) 123.165 1171.84i 0.161846 1.53987i −0.548582 0.836097i \(-0.684832\pi\)
0.710428 0.703769i \(-0.248501\pi\)
\(762\) −873.067 194.308i −1.14576 0.254997i
\(763\) 282.568 + 254.425i 0.370338 + 0.333454i
\(764\) 121.010 520.245i 0.158390 0.680949i
\(765\) 88.0044 + 18.7059i 0.115038 + 0.0244522i
\(766\) 396.749 + 234.143i 0.517950 + 0.305670i
\(767\) 248.712 342.323i 0.324266 0.446314i
\(768\) 1127.63 + 206.489i 1.46826 + 0.268866i
\(769\) 454.909 + 787.925i 0.591559 + 1.02461i 0.994023 + 0.109174i \(0.0348205\pi\)
−0.402464 + 0.915436i \(0.631846\pi\)
\(770\) −13.1126 137.364i −0.0170294 0.178394i
\(771\) 748.933 + 1030.82i 0.971379 + 1.33699i
\(772\) 84.1755 676.356i 0.109036 0.876109i
\(773\) −82.2452 253.125i −0.106397 0.327458i 0.883658 0.468132i \(-0.155073\pi\)
−0.990056 + 0.140675i \(0.955073\pi\)
\(774\) −677.271 951.152i −0.875027 1.22888i
\(775\) −557.117 + 349.202i −0.718861 + 0.450583i
\(776\) 264.331 + 900.520i 0.340633 + 1.16046i
\(777\) −57.4108 176.692i −0.0738878 0.227403i
\(778\) 300.715 327.631i 0.386523 0.421120i
\(779\) 356.153 + 490.202i 0.457192 + 0.629271i
\(780\) −194.263 + 168.310i −0.249055 + 0.215782i
\(781\) −246.274 426.559i −0.315332 0.546171i
\(782\) 21.2131 + 104.706i 0.0271268 + 0.133896i
\(783\) −260.364 + 358.360i −0.332521 + 0.457676i
\(784\) −640.236 161.867i −0.816627 0.206464i
\(785\) −111.621 23.7259i −0.142193 0.0302240i
\(786\) 1055.90 + 1195.46i 1.34339 + 1.52094i
\(787\) 1125.91 + 1013.77i 1.43064 + 1.28815i 0.896709 + 0.442621i \(0.145951\pi\)
0.533927 + 0.845530i \(0.320716\pi\)
\(788\) −197.635 + 83.5078i −0.250806 + 0.105974i
\(789\) −91.0474 + 866.258i −0.115396 + 1.09792i
\(790\) 402.646 126.590i 0.509678 0.160240i
\(791\) 192.191 + 62.4468i 0.242973 + 0.0789466i
\(792\) −202.714 1109.01i −0.255953 1.40027i
\(793\) −529.884 588.495i −0.668201 0.742113i
\(794\) −127.945 + 1114.80i −0.161139 + 1.40404i
\(795\) −299.706 + 31.5004i −0.376989 + 0.0396232i
\(796\) 431.135 + 260.018i 0.541627 + 0.326656i
\(797\) −27.2883 + 12.1495i −0.0342387 + 0.0152441i −0.423785 0.905763i \(-0.639299\pi\)
0.389546 + 0.921007i \(0.372632\pi\)
\(798\) −5.48936 + 574.845i −0.00687889 + 0.720358i
\(799\) −29.4288 + 66.0982i −0.0368320 + 0.0827261i
\(800\) 310.921 + 603.317i 0.388651 + 0.754146i
\(801\) −496.828 + 860.532i −0.620260 + 1.07432i
\(802\) 205.205 611.623i 0.255867 0.762622i
\(803\) −353.779 1664.40i −0.440572 2.07273i
\(804\) 844.642 + 16.1329i 1.05055 + 0.0200658i
\(805\) 69.1298 0.0858755
\(806\) −453.058 + 59.9070i −0.562107 + 0.0743264i
\(807\) 1556.08i 1.92823i
\(808\) −211.531 + 144.614i −0.261795 + 0.178978i
\(809\) −528.027 + 112.236i −0.652691 + 0.138734i −0.522344 0.852735i \(-0.674942\pi\)
−0.130347 + 0.991468i \(0.541609\pi\)
\(810\) −72.2176 + 215.247i −0.0891575 + 0.265737i
\(811\) −412.385 238.090i −0.508489 0.293576i 0.223723 0.974653i \(-0.428179\pi\)
−0.732212 + 0.681076i \(0.761512\pi\)
\(812\) 101.365 + 526.097i 0.124834 + 0.647902i
\(813\) 871.908 + 388.198i 1.07246 + 0.477489i
\(814\) −3.63441 + 380.596i −0.00446488 + 0.467562i
\(815\) −155.896 350.148i −0.191283 0.429629i
\(816\) 230.127 191.813i 0.282019 0.235065i
\(817\) −127.501 1213.09i −0.156060 1.48482i
\(818\) 171.757 1496.55i 0.209971 1.82952i
\(819\) −168.288 + 151.527i −0.205480 + 0.185015i
\(820\) −185.040 86.6563i −0.225658 0.105678i
\(821\) 415.411 1278.50i 0.505981 1.55725i −0.293133 0.956072i \(-0.594698\pi\)
0.799115 0.601179i \(-0.205302\pi\)
\(822\) 716.437 225.244i 0.871578 0.274020i
\(823\) 33.3198 + 3.50205i 0.0404858 + 0.00425523i 0.124750 0.992188i \(-0.460187\pi\)
−0.0842639 + 0.996443i \(0.526854\pi\)
\(824\) −351.281 216.459i −0.426312 0.262693i
\(825\) 810.311 899.941i 0.982195 1.09084i
\(826\) 211.264 + 239.187i 0.255768 + 0.289572i
\(827\) 59.1855 278.446i 0.0715665 0.336694i −0.927769 0.373156i \(-0.878276\pi\)
0.999335 + 0.0364623i \(0.0116089\pi\)
\(828\) 562.733 48.3003i 0.679629 0.0583337i
\(829\) 318.579 + 231.461i 0.384293 + 0.279205i 0.763113 0.646265i \(-0.223670\pi\)
−0.378820 + 0.925470i \(0.623670\pi\)
\(830\) −71.9164 354.974i −0.0866463 0.427680i
\(831\) −2032.09 + 1173.23i −2.44535 + 1.41182i
\(832\) 22.3645 + 471.213i 0.0268804 + 0.566362i
\(833\) −139.619 + 101.439i −0.167610 + 0.121776i
\(834\) 376.903 410.639i 0.451922 0.492373i
\(835\) 106.765 34.6902i 0.127863 0.0415451i
\(836\) 385.260 1112.93i 0.460838 1.33125i
\(837\) 224.309 175.751i 0.267991 0.209977i
\(838\) −323.380 454.151i −0.385895 0.541947i
\(839\) −1110.03 + 360.672i −1.32304 + 0.429883i −0.883539 0.468358i \(-0.844846\pi\)
−0.439504 + 0.898241i \(0.644846\pi\)
\(840\) −92.0789 170.591i −0.109618 0.203084i
\(841\) −1198.21 + 870.554i −1.42475 + 1.03514i
\(842\) −54.7722 573.777i −0.0650502 0.681445i
\(843\) −1501.43 + 866.852i −1.78106 + 1.02829i
\(844\) 1144.46 + 1070.75i 1.35599 + 1.26866i
\(845\) 180.600 + 131.214i 0.213728 + 0.155283i
\(846\) 329.425 + 194.411i 0.389392 + 0.229801i
\(847\) −24.0202 + 113.006i −0.0283592 + 0.133420i
\(848\) −294.636 + 468.083i −0.347448 + 0.551984i
\(849\) 531.775 590.596i 0.626355 0.695638i
\(850\) 173.136 + 38.5326i 0.203689 + 0.0453325i
\(851\) −189.636 19.9316i −0.222840 0.0234214i
\(852\) −551.942 417.343i −0.647819 0.489839i
\(853\) −350.261 + 1077.99i −0.410622 + 1.26377i 0.505486 + 0.862835i \(0.331313\pi\)
−0.916108 + 0.400931i \(0.868687\pi\)
\(854\) 520.061 293.672i 0.608971 0.343878i
\(855\) 369.260 332.483i 0.431883 0.388869i
\(856\) −494.216 + 1029.60i −0.577355 + 1.20281i
\(857\) −45.8405 436.143i −0.0534895 0.508919i −0.988163 0.153410i \(-0.950974\pi\)
0.934673 0.355508i \(-0.115692\pi\)
\(858\) 772.162 334.991i 0.899955 0.390432i
\(859\) −338.879 761.135i −0.394504 0.886072i −0.996179 0.0873305i \(-0.972166\pi\)
0.601675 0.798741i \(-0.294500\pi\)
\(860\) 235.372 + 337.326i 0.273689 + 0.392239i
\(861\) −298.364 132.840i −0.346532 0.154286i
\(862\) 385.510 844.084i 0.447227 0.979216i
\(863\) 788.691 + 455.351i 0.913894 + 0.527637i 0.881682 0.471844i \(-0.156411\pi\)
0.0322122 + 0.999481i \(0.489745\pi\)
\(864\) −161.344 245.956i −0.186741 0.284671i
\(865\) 541.224 115.041i 0.625692 0.132995i
\(866\) −331.499 245.718i −0.382793 0.283739i
\(867\) 1215.86i 1.40238i
\(868\) 30.1281 343.351i 0.0347098 0.395566i
\(869\) −1382.15 −1.59051
\(870\) 500.313 674.973i 0.575073 0.775831i
\(871\) 72.2786 + 340.044i 0.0829835 + 0.390407i
\(872\) −866.562 668.339i −0.993764 0.766444i
\(873\) 648.322 1122.93i 0.742637 1.28629i
\(874\) 536.694 + 245.119i 0.614067 + 0.280456i
\(875\) 101.707 228.437i 0.116236 0.261071i
\(876\) −1367.91 1960.43i −1.56154 2.23794i
\(877\) 324.421 144.441i 0.369921 0.164699i −0.213352 0.976975i \(-0.568438\pi\)
0.583273 + 0.812276i \(0.301772\pi\)
\(878\) −338.524 780.307i −0.385563 0.888732i
\(879\) 361.767 38.0232i 0.411566 0.0432573i
\(880\) 67.6766 + 391.336i 0.0769052 + 0.444700i
\(881\) −408.209 453.362i −0.463348 0.514600i 0.465507 0.885044i \(-0.345872\pi\)
−0.928855 + 0.370445i \(0.879205\pi\)
\(882\) 448.624 + 794.463i 0.508644 + 0.900752i
\(883\) −993.086 322.673i −1.12467 0.365428i −0.313124 0.949712i \(-0.601375\pi\)
−0.811549 + 0.584284i \(0.801375\pi\)
\(884\) 98.3351 + 74.3547i 0.111239 + 0.0841116i
\(885\) 52.3107 497.704i 0.0591082 0.562377i
\(886\) −154.164 + 692.692i −0.174000 + 0.781819i
\(887\) −501.954 451.962i −0.565901 0.509540i 0.335780 0.941940i \(-0.391000\pi\)
−0.901682 + 0.432401i \(0.857667\pi\)
\(888\) 203.406 + 494.512i 0.229060 + 0.556882i
\(889\) 271.528 + 57.7151i 0.305431 + 0.0649214i
\(890\) 177.905 301.455i 0.199893 0.338713i
\(891\) 437.003 601.483i 0.490463 0.675065i
\(892\) 1001.21 + 936.725i 1.12243 + 1.05014i
\(893\) 199.797 + 346.058i 0.223736 + 0.387523i
\(894\) 2502.92 238.927i 2.79969 0.267256i
\(895\) 246.026 + 338.626i 0.274889 + 0.378353i
\(896\) −350.566 60.7411i −0.391256 0.0677914i
\(897\) 130.305 + 401.038i 0.145268 + 0.447088i
\(898\) 1045.73 744.612i 1.16451 0.829189i
\(899\) 1403.03 512.866i 1.56065 0.570485i
\(900\) 306.749 886.126i 0.340832 0.984585i
\(901\) 44.6656 + 137.467i 0.0495733 + 0.152571i
\(902\) 492.937 + 452.440i 0.546494 + 0.501597i
\(903\) 386.453 + 531.907i 0.427966 + 0.589045i
\(904\) −565.208 137.170i −0.625230 0.151737i
\(905\) 72.4001 + 125.401i 0.0800001 + 0.138564i
\(906\) −1904.34 + 385.812i −2.10192 + 0.425842i
\(907\) −106.278 + 146.279i −0.117175 + 0.161278i −0.863576 0.504219i \(-0.831780\pi\)
0.746400 + 0.665497i \(0.231780\pi\)
\(908\) −1069.37 + 91.7856i −1.17772 + 0.101085i
\(909\) 346.282 + 73.6045i 0.380948 + 0.0809731i
\(910\) 59.7899 52.8100i 0.0657031 0.0580330i
\(911\) 238.685 + 214.913i 0.262004 + 0.235909i 0.789654 0.613553i \(-0.210260\pi\)
−0.527650 + 0.849462i \(0.676927\pi\)
\(912\) −109.985 1650.88i −0.120598 1.81018i
\(913\) −123.974 + 1179.54i −0.135788 + 1.29193i
\(914\) 191.372 + 608.699i 0.209378 + 0.665973i
\(915\) −890.745 289.421i −0.973492 0.316307i
\(916\) 445.532 + 208.648i 0.486389 + 0.227782i
\(917\) −331.238 367.877i −0.361219 0.401174i
\(918\) −76.3704 8.76493i −0.0831922 0.00954786i
\(919\) −222.325 + 23.3673i −0.241920 + 0.0254268i −0.224713 0.974425i \(-0.572144\pi\)
−0.0172077 + 0.999852i \(0.505478\pi\)
\(920\) −198.388 + 15.1211i −0.215639 + 0.0164360i
\(921\) 468.665 208.663i 0.508865 0.226561i
\(922\) −995.058 9.50208i −1.07924 0.0103059i
\(923\) 115.818 260.132i 0.125480 0.281833i
\(924\) 120.102 + 623.342i 0.129980 + 0.674613i
\(925\) −158.290 + 274.166i −0.171124 + 0.296396i
\(926\) 686.272 + 230.251i 0.741115 + 0.248651i
\(927\) 118.524 + 557.612i 0.127858 + 0.601523i
\(928\) −405.972 1487.61i −0.437470 1.60303i
\(929\) 474.252 0.510497 0.255248 0.966875i \(-0.417843\pi\)
0.255248 + 0.966875i \(0.417843\pi\)
\(930\) −428.621 + 329.278i −0.460883 + 0.354062i
\(931\) 953.116i 1.02376i
\(932\) −440.907 8.42144i −0.473076 0.00903589i
\(933\) 667.072 141.790i 0.714975 0.151973i
\(934\) −909.123 305.020i −0.973365 0.326574i
\(935\) 89.8819 + 51.8933i 0.0961304 + 0.0555009i
\(936\) 449.806 471.661i 0.480562 0.503911i
\(937\) −467.413 208.106i −0.498840 0.222098i 0.141864 0.989886i \(-0.454690\pi\)
−0.640703 + 0.767788i \(0.721357\pi\)
\(938\) −262.179 2.50362i −0.279508 0.00266910i
\(939\) 534.116 + 1199.64i 0.568813 + 1.27758i
\(940\) −115.388 69.5904i −0.122753 0.0740323i
\(941\) 55.5276 + 528.309i 0.0590091 + 0.561434i 0.983586 + 0.180439i \(0.0577518\pi\)
−0.924577 + 0.380995i \(0.875581\pi\)
\(942\) 521.557 + 59.8584i 0.553669 + 0.0635439i
\(943\) −249.107 + 224.297i −0.264164 + 0.237854i
\(944\) −658.601 640.204i −0.697671 0.678182i
\(945\) −15.3711 + 47.3075i −0.0162657 + 0.0500608i
\(946\) −403.979 1284.94i −0.427039 1.35829i
\(947\) −1528.39 160.640i −1.61393 0.169631i −0.745869 0.666093i \(-0.767965\pi\)
−0.868058 + 0.496462i \(0.834632\pi\)
\(948\) −1788.63 + 755.758i −1.88674 + 0.797213i
\(949\) 658.231 731.039i 0.693605 0.770326i
\(950\) 734.201 648.490i 0.772843 0.682621i
\(951\) 10.5877 49.8111i 0.0111332 0.0523776i
\(952\) −70.8506 + 60.2105i −0.0744229 + 0.0632463i
\(953\) 297.460 + 216.118i 0.312130 + 0.226776i 0.732810 0.680433i \(-0.238208\pi\)
−0.420680 + 0.907209i \(0.638208\pi\)
\(954\) 748.934 151.731i 0.785046 0.159047i
\(955\) 225.132 129.980i 0.235740 0.136105i
\(956\) −949.411 + 822.573i −0.993107 + 0.860432i
\(957\) −2225.84 + 1617.17i −2.32586 + 1.68983i
\(958\) 461.048 + 423.170i 0.481261 + 0.441723i
\(959\) −221.676 + 72.0268i −0.231153 + 0.0751062i
\(960\) 301.561 + 469.418i 0.314126 + 0.488977i
\(961\) −958.469 + 69.6971i −0.997367 + 0.0725256i
\(962\) −179.242 + 127.629i −0.186322 + 0.132671i
\(963\) 1500.65 487.592i 1.55831 0.506326i
\(964\) 100.862 810.432i 0.104628 0.840697i
\(965\) 268.366 194.979i 0.278099 0.202051i
\(966\) −316.589 + 30.2213i −0.327732 + 0.0312850i
\(967\) 719.225 415.245i 0.743769 0.429415i −0.0796689 0.996821i \(-0.525386\pi\)
0.823438 + 0.567406i \(0.192053\pi\)
\(968\) 44.2145 329.558i 0.0456762 0.340453i
\(969\) −349.807 254.150i −0.360998 0.262280i
\(970\) −232.152 + 393.375i −0.239332 + 0.405542i
\(971\) −144.081 + 677.847i −0.148384 + 0.698092i 0.839558 + 0.543270i \(0.182814\pi\)
−0.987942 + 0.154822i \(0.950519\pi\)
\(972\) 311.602 1339.64i 0.320578 1.37823i
\(973\) −115.753 + 128.557i −0.118965 + 0.132124i
\(974\) 62.1854 279.413i 0.0638454 0.286871i
\(975\) 696.257 + 73.1795i 0.714109 + 0.0750559i
\(976\) −1428.23 + 956.532i −1.46335 + 0.980053i
\(977\) 65.5268 201.671i 0.0670694 0.206418i −0.911905 0.410401i \(-0.865389\pi\)
0.978974 + 0.203983i \(0.0653887\pi\)
\(978\) 867.019 + 1535.40i 0.886523 + 1.56993i
\(979\) −851.827 + 766.988i −0.870099 + 0.783440i
\(980\) −155.357 281.362i −0.158528 0.287104i
\(981\) 158.042 + 1503.67i 0.161103 + 1.53279i
\(982\) 167.428 + 385.926i 0.170497 + 0.393000i
\(983\) −770.812 1731.27i −0.784143 1.76121i −0.635170 0.772372i \(-0.719070\pi\)
−0.148973 0.988841i \(-0.547597\pi\)
\(984\) 885.297 + 315.960i 0.899692 + 0.321098i
\(985\) −95.3944 42.4723i −0.0968471 0.0431191i
\(986\) −366.556 167.414i −0.371761 0.169791i
\(987\) −186.529 107.693i −0.188986 0.109111i
\(988\) 651.436 197.993i 0.659348 0.200398i
\(989\) 660.053 140.299i 0.667394 0.141859i
\(990\) 326.738 440.802i 0.330038 0.445255i
\(991\) 492.719i 0.497194i −0.968607 0.248597i \(-0.920031\pi\)
0.968607 0.248597i \(-0.0799694\pi\)
\(992\) −11.3584 + 991.935i −0.0114500 + 0.999934i
\(993\) 390.421 0.393173
\(994\) 172.530 + 127.885i 0.173571 + 0.128657i
\(995\) 50.9464 + 239.684i 0.0512024 + 0.240889i
\(996\) 484.534 + 1594.21i 0.486480 + 1.60061i
\(997\) 193.403 334.984i 0.193985 0.335992i −0.752582 0.658498i \(-0.771192\pi\)
0.946567 + 0.322506i \(0.104525\pi\)
\(998\) −36.4862 + 79.8875i −0.0365593 + 0.0800476i
\(999\) 55.8058 125.342i 0.0558616 0.125467i
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 124.3.n.a.7.7 240
4.3 odd 2 inner 124.3.n.a.7.18 yes 240
31.9 even 15 inner 124.3.n.a.71.18 yes 240
124.71 odd 30 inner 124.3.n.a.71.7 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.3.n.a.7.7 240 1.1 even 1 trivial
124.3.n.a.7.18 yes 240 4.3 odd 2 inner
124.3.n.a.71.7 yes 240 124.71 odd 30 inner
124.3.n.a.71.18 yes 240 31.9 even 15 inner