Properties

Label 124.3.n.a.7.18
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 7.18
Character \(\chi\) \(=\) 124.7
Dual form 124.3.n.a.71.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.599843 - 1.90793i) q^{2} +(-0.931035 - 4.38017i) q^{3} +(-3.28038 - 2.28891i) q^{4} +(-0.973390 + 1.68596i) q^{5} +(-8.91553 - 0.851069i) q^{6} +(1.13057 - 2.53929i) q^{7} +(-6.33479 + 4.88573i) q^{8} +(-10.0972 + 4.49556i) q^{9} +O(q^{10})\) \(q+(0.599843 - 1.90793i) q^{2} +(-0.931035 - 4.38017i) q^{3} +(-3.28038 - 2.28891i) q^{4} +(-0.973390 + 1.68596i) q^{5} +(-8.91553 - 0.851069i) q^{6} +(1.13057 - 2.53929i) q^{7} +(-6.33479 + 4.88573i) q^{8} +(-10.0972 + 4.49556i) q^{9} +(2.63281 + 2.86847i) q^{10} +(12.6802 - 1.33274i) q^{11} +(-6.97170 + 16.4997i) q^{12} +(-4.93216 - 5.47772i) q^{13} +(-4.16662 - 3.68021i) q^{14} +(8.29106 + 2.69393i) q^{15} +(5.52175 + 15.0170i) q^{16} +(-0.437066 + 4.15841i) q^{17} +(2.52048 + 21.9613i) q^{18} +(-17.1611 - 15.4519i) q^{19} +(7.05211 - 3.30258i) q^{20} +(-12.1751 - 2.58791i) q^{21} +(5.06335 - 24.9924i) q^{22} +(7.50904 - 10.3353i) q^{23} +(27.2983 + 23.1987i) q^{24} +(10.6050 + 18.3684i) q^{25} +(-13.4096 + 6.12443i) q^{26} +(5.40310 + 7.43672i) q^{27} +(-9.52090 + 5.74207i) 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} +(7.67177 + 3.32828i) q^{34} +(3.18067 + 4.37781i) q^{35} +(43.4126 + 8.36447i) q^{36} +(7.46297 + 12.9262i) q^{37} +(-39.7751 + 23.4734i) q^{38} +(-19.4014 + 26.7037i) q^{39} +(-2.07093 - 15.4359i) q^{40} +(25.6656 + 5.45538i) q^{41} +(-12.2407 + 21.6770i) q^{42} +(39.2538 + 35.3443i) q^{43} +(-44.6464 - 24.6520i) q^{44} +(2.24917 - 21.3994i) q^{45} +(-15.2148 - 20.5263i) q^{46} +(-16.4571 - 5.34723i) q^{47} +(60.6361 - 38.1676i) q^{48} +(27.6176 + 30.6724i) q^{49} +(41.4070 - 9.21544i) q^{50} +(18.6215 - 1.95720i) q^{51} +(3.64132 + 29.2583i) q^{52} +(31.5797 - 14.0602i) q^{53} +(17.4297 - 5.84785i) q^{54} +(-10.0958 + 22.6756i) q^{55} +(5.24441 + 21.6095i) q^{56} +(-51.7045 + 89.5548i) q^{57} +(-96.3714 + 0.920277i) q^{58} +(-11.9352 - 56.1509i) q^{59} +(-21.0316 - 27.8146i) q^{60} +107.434 q^{61} +(-59.7816 - 16.4367i) q^{62} +30.7223i q^{63} +(16.2592 - 61.9002i) q^{64} +(14.0361 - 2.98347i) q^{65} +(-114.185 + 1.09038i) q^{66} +(40.8447 + 23.5817i) q^{67} +(10.9520 - 12.6407i) q^{68} +(-52.2616 - 23.2684i) q^{69} +(10.2604 - 3.44248i) q^{70} +(-15.7127 - 35.2912i) q^{71} +(41.9995 - 77.8106i) q^{72} +(13.9500 + 132.726i) q^{73} +(29.1390 - 6.48510i) q^{74} +(70.5833 - 63.5535i) q^{75} +(20.9267 + 89.9683i) q^{76} +(10.9516 - 33.7055i) q^{77} +(39.3109 + 53.0344i) q^{78} +(-107.810 - 11.3313i) q^{79} +(-30.6929 - 5.30795i) q^{80} +(-39.0179 + 43.3338i) q^{81} +(25.8038 - 45.6957i) q^{82} +(-19.3403 + 90.9891i) q^{83} +(34.0156 + 36.3572i) q^{84} +(-6.58548 - 4.78463i) q^{85} +(90.9806 - 53.6925i) q^{86} +(-186.877 + 107.893i) q^{87} +(-73.8151 + 70.3948i) q^{88} +(72.7316 - 52.8426i) q^{89} +(-39.4794 - 17.1275i) 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} +(-36.4488 - 138.584i) q^{96} +(-94.9092 + 68.9555i) q^{97} +(75.0870 - 34.2937i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.599843 1.90793i 0.299921 0.953964i
\(3\) −0.931035 4.38017i −0.310345 1.46006i −0.806195 0.591650i \(-0.798477\pi\)
0.495850 0.868408i \(-0.334857\pi\)
\(4\) −3.28038 2.28891i −0.820094 0.572228i
\(5\) −0.973390 + 1.68596i −0.194678 + 0.337192i −0.946795 0.321838i \(-0.895700\pi\)
0.752117 + 0.659030i \(0.229033\pi\)
\(6\) −8.91553 0.851069i −1.48592 0.141845i
\(7\) 1.13057 2.53929i 0.161509 0.362756i −0.814604 0.580017i \(-0.803046\pi\)
0.976113 + 0.217261i \(0.0697124\pi\)
\(8\) −6.33479 + 4.88573i −0.791849 + 0.610717i
\(9\) −10.0972 + 4.49556i −1.12191 + 0.499507i
\(10\) 2.63281 + 2.86847i 0.263281 + 0.286847i
\(11\) 12.6802 1.33274i 1.15275 0.121158i 0.491189 0.871053i \(-0.336563\pi\)
0.661557 + 0.749895i \(0.269896\pi\)
\(12\) −6.97170 + 16.4997i −0.580975 + 1.37497i
\(13\) −4.93216 5.47772i −0.379397 0.421363i 0.522957 0.852359i \(-0.324829\pi\)
−0.902354 + 0.430996i \(0.858162\pi\)
\(14\) −4.16662 3.68021i −0.297616 0.262872i
\(15\) 8.29106 + 2.69393i 0.552738 + 0.179595i
\(16\) 5.52175 + 15.0170i 0.345109 + 0.938563i
\(17\) −0.437066 + 4.15841i −0.0257098 + 0.244612i 0.974118 + 0.226041i \(0.0725784\pi\)
−0.999828 + 0.0185711i \(0.994088\pi\)
\(18\) 2.52048 + 21.9613i 0.140026 + 1.22007i
\(19\) −17.1611 15.4519i −0.903215 0.813259i 0.0797947 0.996811i \(-0.474574\pi\)
−0.983010 + 0.183553i \(0.941240\pi\)
\(20\) 7.05211 3.30258i 0.352605 0.165129i
\(21\) −12.1751 2.58791i −0.579769 0.123234i
\(22\) 5.06335 24.9924i 0.230152 1.13602i
\(23\) 7.50904 10.3353i 0.326480 0.449361i −0.613952 0.789343i \(-0.710421\pi\)
0.940432 + 0.339982i \(0.110421\pi\)
\(24\) 27.2983 + 23.1987i 1.13743 + 0.966613i
\(25\) 10.6050 + 18.3684i 0.424201 + 0.734738i
\(26\) −13.4096 + 6.12443i −0.515754 + 0.235555i
\(27\) 5.40310 + 7.43672i 0.200115 + 0.275434i
\(28\) −9.52090 + 5.74207i −0.340032 + 0.205074i
\(29\) −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
\(34\) 7.67177 + 3.32828i 0.225640 + 0.0978906i
\(35\) 3.18067 + 4.37781i 0.0908762 + 0.125080i
\(36\) 43.4126 + 8.36447i 1.20590 + 0.232346i
\(37\) 7.46297 + 12.9262i 0.201702 + 0.349358i 0.949077 0.315044i \(-0.102019\pi\)
−0.747375 + 0.664402i \(0.768686\pi\)
\(38\) −39.7751 + 23.4734i −1.04671 + 0.617721i
\(39\) −19.4014 + 26.7037i −0.497471 + 0.684709i
\(40\) −2.07093 15.4359i −0.0517733 0.385898i
\(41\) 25.6656 + 5.45538i 0.625989 + 0.133058i 0.509975 0.860189i \(-0.329655\pi\)
0.116015 + 0.993248i \(0.462988\pi\)
\(42\) −12.2407 + 21.6770i −0.291445 + 0.516118i
\(43\) 39.2538 + 35.3443i 0.912880 + 0.821961i 0.984484 0.175472i \(-0.0561452\pi\)
−0.0716042 + 0.997433i \(0.522812\pi\)
\(44\) −44.6464 24.6520i −1.01469 0.560273i
\(45\) 2.24917 21.3994i 0.0499815 0.475542i
\(46\) −15.2148 20.5263i −0.330756 0.446223i
\(47\) −16.4571 5.34723i −0.350151 0.113771i 0.128661 0.991689i \(-0.458932\pi\)
−0.478811 + 0.877918i \(0.658932\pi\)
\(48\) 60.6361 38.1676i 1.26325 0.795158i
\(49\) 27.6176 + 30.6724i 0.563624 + 0.625968i
\(50\) 41.4070 9.21544i 0.828140 0.184309i
\(51\) 18.6215 1.95720i 0.365127 0.0383764i
\(52\) 3.64132 + 29.2583i 0.0700254 + 0.562659i
\(53\) 31.5797 14.0602i 0.595843 0.265287i −0.0865785 0.996245i \(-0.527593\pi\)
0.682422 + 0.730958i \(0.260927\pi\)
\(54\) 17.4297 5.84785i 0.322773 0.108294i
\(55\) −10.0958 + 22.6756i −0.183561 + 0.412284i
\(56\) 5.24441 + 21.6095i 0.0936501 + 0.385885i
\(57\) −51.7045 + 89.5548i −0.907097 + 1.57114i
\(58\) −96.3714 + 0.920277i −1.66158 + 0.0158668i
\(59\) −11.9352 56.1509i −0.202292 0.951710i −0.955742 0.294205i \(-0.904945\pi\)
0.753450 0.657505i \(-0.228388\pi\)
\(60\) −21.0316 27.8146i −0.350527 0.463577i
\(61\) 107.434 1.76122 0.880610 0.473842i \(-0.157133\pi\)
0.880610 + 0.473842i \(0.157133\pi\)
\(62\) −59.7816 16.4367i −0.964219 0.265108i
\(63\) 30.7223i 0.487655i
\(64\) 16.2592 61.9002i 0.254050 0.967191i
\(65\) 14.0361 2.98347i 0.215941 0.0458996i
\(66\) −114.185 + 1.09038i −1.73008 + 0.0165210i
\(67\) 40.8447 + 23.5817i 0.609622 + 0.351965i 0.772818 0.634628i \(-0.218847\pi\)
−0.163195 + 0.986594i \(0.552180\pi\)
\(68\) 10.9520 12.6407i 0.161058 0.185893i
\(69\) −52.2616 23.2684i −0.757415 0.337223i
\(70\) 10.2604 3.44248i 0.146578 0.0491783i
\(71\) −15.7127 35.2912i −0.221305 0.497060i 0.768437 0.639926i \(-0.221035\pi\)
−0.989742 + 0.142866i \(0.954368\pi\)
\(72\) 41.9995 77.8106i 0.583327 1.08070i
\(73\) 13.9500 + 132.726i 0.191097 + 1.81816i 0.498842 + 0.866693i \(0.333759\pi\)
−0.307745 + 0.951469i \(0.599574\pi\)
\(74\) 29.1390 6.48510i 0.393770 0.0876364i
\(75\) 70.5833 63.5535i 0.941111 0.847380i
\(76\) 20.9267 + 89.9683i 0.275352 + 1.18379i
\(77\) 10.9516 33.7055i 0.142228 0.437734i
\(78\) 39.3109 + 53.0344i 0.503986 + 0.679928i
\(79\) −107.810 11.3313i −1.36468 0.143434i −0.606296 0.795239i \(-0.707345\pi\)
−0.758387 + 0.651805i \(0.774012\pi\)
\(80\) −30.6929 5.30795i −0.383661 0.0663493i
\(81\) −39.0179 + 43.3338i −0.481703 + 0.534985i
\(82\) 25.8038 45.6957i 0.314680 0.557264i
\(83\) −19.3403 + 90.9891i −0.233016 + 1.09625i 0.693634 + 0.720328i \(0.256009\pi\)
−0.926650 + 0.375926i \(0.877325\pi\)
\(84\) 34.0156 + 36.3572i 0.404947 + 0.432823i
\(85\) −6.58548 4.78463i −0.0774762 0.0562897i
\(86\) 90.9806 53.6925i 1.05791 0.624331i
\(87\) −186.877 + 107.893i −2.14801 + 1.24015i
\(88\) −73.8151 + 70.3948i −0.838807 + 0.799941i
\(89\) 72.7316 52.8426i 0.817209 0.593737i −0.0987023 0.995117i \(-0.531469\pi\)
0.915912 + 0.401380i \(0.131469\pi\)
\(90\) −39.4794 17.1275i −0.438660 0.190306i
\(91\) −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
\(96\) −36.4488 138.584i −0.379675 1.44358i
\(97\) −94.9092 + 68.9555i −0.978445 + 0.710882i −0.957361 0.288896i \(-0.906712\pi\)
−0.0210845 + 0.999778i \(0.506712\pi\)
\(98\) 75.0870 34.2937i 0.766194 0.349936i
\(99\) −122.043 + 70.4616i −1.23276 + 0.711733i
\(100\) 7.25530 84.5294i 0.0725530 0.845294i
\(101\) −25.9127 18.8267i −0.256561 0.186403i 0.452068 0.891983i \(-0.350686\pi\)
−0.708630 + 0.705581i \(0.750686\pi\)
\(102\) 7.43577 36.7024i 0.0728997 0.359828i
\(103\) −10.7235 + 50.4500i −0.104111 + 0.489806i 0.894937 + 0.446193i \(0.147220\pi\)
−0.999048 + 0.0436135i \(0.986113\pi\)
\(104\) 58.0069 + 10.6030i 0.557759 + 0.101952i
\(105\) 16.2143 18.0078i 0.154422 0.171503i
\(106\) −7.88297 68.6857i −0.0743676 0.647978i
\(107\) 141.977 + 14.9224i 1.32689 + 0.139461i 0.741314 0.671158i \(-0.234203\pi\)
0.585573 + 0.810620i \(0.300870\pi\)
\(108\) −0.702174 36.7625i −0.00650161 0.340393i
\(109\) 42.2717 130.099i 0.387814 1.19357i −0.546605 0.837391i \(-0.684080\pi\)
0.934419 0.356177i \(-0.115920\pi\)
\(110\) 37.2075 + 32.8639i 0.338250 + 0.298763i
\(111\) 49.6709 44.7239i 0.447486 0.402918i
\(112\) 44.3753 + 2.95637i 0.396208 + 0.0263962i
\(113\) −7.59941 72.3035i −0.0672514 0.639854i −0.975284 0.220955i \(-0.929083\pi\)
0.908033 0.418899i \(-0.137584\pi\)
\(114\) 139.850 + 152.367i 1.22675 + 1.33656i
\(115\) 10.1157 + 22.7202i 0.0879626 + 0.197567i
\(116\) −56.0519 + 184.422i −0.483206 + 1.58984i
\(117\) 74.4264 + 33.1368i 0.636123 + 0.283220i
\(118\) −114.291 10.9101i −0.968569 0.0924588i
\(119\) 10.0653 + 5.81119i 0.0845822 + 0.0488335i
\(120\) −65.6840 + 23.4424i −0.547367 + 0.195354i
\(121\) 40.6556 8.64161i 0.335997 0.0714183i
\(122\) 64.4438 204.977i 0.528227 1.68014i
\(123\) 117.499i 0.955275i
\(124\) −67.2195 + 104.199i −0.542093 + 0.840318i
\(125\) −89.9608 −0.719686
\(126\) 58.6158 + 18.4285i 0.465205 + 0.146258i
\(127\) 20.7638 + 97.6860i 0.163495 + 0.769181i 0.981115 + 0.193424i \(0.0619594\pi\)
−0.817621 + 0.575757i \(0.804707\pi\)
\(128\) −108.348 68.1518i −0.846470 0.532436i
\(129\) 118.268 204.846i 0.916803 1.58795i
\(130\) 2.72722 28.5695i 0.0209787 0.219766i
\(131\) 72.4368 162.696i 0.552953 1.24195i −0.393564 0.919297i \(-0.628758\pi\)
0.946517 0.322655i \(-0.104575\pi\)
\(132\) −66.4127 + 218.511i −0.503127 + 1.65539i
\(133\) −58.6387 + 26.1076i −0.440892 + 0.196298i
\(134\) 69.4925 63.7834i 0.518601 0.475995i
\(135\) −17.7973 + 1.87058i −0.131832 + 0.0138561i
\(136\) −17.5481 28.4780i −0.129031 0.209397i
\(137\) 56.1100 + 62.3165i 0.409562 + 0.454865i 0.912269 0.409592i \(-0.134329\pi\)
−0.502707 + 0.864457i \(0.667662\pi\)
\(138\) −75.7431 + 85.7540i −0.548863 + 0.621406i
\(139\) −59.1897 19.2319i −0.425825 0.138359i 0.0882611 0.996097i \(-0.471869\pi\)
−0.514087 + 0.857738i \(0.671869\pi\)
\(140\) −0.413352 21.6411i −0.00295251 0.154580i
\(141\) −8.09969 + 77.0634i −0.0574446 + 0.546549i
\(142\) −76.7583 + 8.80945i −0.540551 + 0.0620384i
\(143\) −69.8412 62.8853i −0.488400 0.439757i
\(144\) −123.264 126.806i −0.856000 0.880599i
\(145\) 91.7613 + 19.5045i 0.632836 + 0.134514i
\(146\) 261.599 + 52.9990i 1.79177 + 0.363007i
\(147\) 108.638 149.527i 0.739032 1.01719i
\(148\) 5.10570 59.4851i 0.0344980 0.401926i
\(149\) 140.369 + 243.126i 0.942072 + 1.63172i 0.761511 + 0.648152i \(0.224458\pi\)
0.180561 + 0.983564i \(0.442209\pi\)
\(150\) −78.9166 172.790i −0.526111 1.15193i
\(151\) 127.521 + 175.518i 0.844510 + 1.16237i 0.985046 + 0.172293i \(0.0551174\pi\)
−0.140536 + 0.990076i \(0.544883\pi\)
\(152\) 184.206 + 14.0402i 1.21188 + 0.0923694i
\(153\) −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 \(0.840227\pi\)
\(158\) −86.2883 + 198.897i −0.546128 + 1.25884i
\(159\) −90.9879 125.234i −0.572251 0.787636i
\(160\) −28.5381 + 55.3759i −0.178363 + 0.346099i
\(161\) −17.7549 30.7524i −0.110279 0.191009i
\(162\) 59.2732 + 100.437i 0.365884 + 0.619981i
\(163\) 115.724 159.280i 0.709963 0.977180i −0.289835 0.957077i \(-0.593600\pi\)
0.999798 0.0201036i \(-0.00639960\pi\)
\(164\) −71.7058 76.6420i −0.437231 0.467329i
\(165\) 108.723 + 23.1097i 0.658926 + 0.140059i
\(166\) 161.999 + 91.4791i 0.975900 + 0.551079i
\(167\) 42.8530 + 38.5850i 0.256605 + 0.231048i 0.787385 0.616462i \(-0.211434\pi\)
−0.530780 + 0.847509i \(0.678101\pi\)
\(168\) 89.7708 43.0907i 0.534350 0.256492i
\(169\) 11.9861 114.040i 0.0709237 0.674794i
\(170\) −13.0790 + 9.69459i −0.0769352 + 0.0570270i
\(171\) 242.744 + 78.8723i 1.41955 + 0.461241i
\(172\) −47.8673 205.791i −0.278298 1.19646i
\(173\) −190.181 211.217i −1.09931 1.22091i −0.973460 0.228859i \(-0.926500\pi\)
−0.125851 0.992049i \(-0.540166\pi\)
\(174\) 93.7561 + 421.267i 0.538828 + 2.42107i
\(175\) 58.6325 6.16253i 0.335043 0.0352144i
\(176\) 90.0307 + 183.060i 0.511538 + 1.04011i
\(177\) −234.839 + 104.557i −1.32677 + 0.590717i
\(178\) −57.1924 170.464i −0.321305 0.957663i
\(179\) −87.4498 + 196.415i −0.488546 + 1.09729i 0.486174 + 0.873862i \(0.338392\pi\)
−0.974720 + 0.223431i \(0.928274\pi\)
\(180\) −56.3595 + 65.0500i −0.313108 + 0.361389i
\(181\) 37.1897 64.4144i 0.205468 0.355881i −0.744814 0.667272i \(-0.767462\pi\)
0.950282 + 0.311392i \(0.100795\pi\)
\(182\) 0.391281 + 40.9750i 0.00214990 + 0.225137i
\(183\) −100.025 470.581i −0.546586 2.57148i
\(184\) 2.92735 + 102.159i 0.0159095 + 0.555213i
\(185\) −29.0575 −0.157068
\(186\) −16.3368 + 277.157i −0.0878322 + 1.49009i
\(187\) 53.3120i 0.285091i
\(188\) 41.7461 + 55.2098i 0.222054 + 0.293669i
\(189\) 24.9926 5.31234i 0.132236 0.0281076i
\(190\) −0.858556 89.9080i −0.00451872 0.473200i
\(191\) 115.643 + 66.7666i 0.605462 + 0.349564i 0.771187 0.636608i \(-0.219663\pi\)
−0.165725 + 0.986172i \(0.552997\pi\)
\(192\) −286.272 13.5869i −1.49100 0.0707650i
\(193\) −155.662 69.3053i −0.806540 0.359095i −0.0383077 0.999266i \(-0.512197\pi\)
−0.768232 + 0.640171i \(0.778863\pi\)
\(194\) 74.6316 + 222.442i 0.384699 + 1.14661i
\(195\) −26.1363 58.7030i −0.134032 0.301041i
\(196\) −20.3895 163.831i −0.104028 0.835874i
\(197\) 5.60674 + 53.3445i 0.0284606 + 0.270784i 0.999493 + 0.0318369i \(0.0101357\pi\)
−0.971032 + 0.238948i \(0.923198\pi\)
\(198\) 61.2290 + 275.115i 0.309237 + 1.38947i
\(199\) −93.5387 + 84.2226i −0.470044 + 0.423229i −0.869809 0.493388i \(-0.835758\pi\)
0.399765 + 0.916617i \(0.369092\pi\)
\(200\) −156.924 64.5469i −0.784620 0.322735i
\(201\) 65.2641 200.862i 0.324697 0.999314i
\(202\) −51.4635 + 38.1465i −0.254770 + 0.188844i
\(203\) −133.209 14.0009i −0.656204 0.0689698i
\(204\) −65.5653 36.2026i −0.321399 0.177464i
\(205\) −34.1802 + 37.9609i −0.166732 + 0.185175i
\(206\) 89.8226 + 50.7217i 0.436032 + 0.246222i
\(207\) −29.3572 + 138.115i −0.141822 + 0.667222i
\(208\) 55.0248 104.313i 0.264542 0.501504i
\(209\) −238.200 173.062i −1.13971 0.828048i
\(210\) −24.6315 41.7375i −0.117293 0.198750i
\(211\) −339.321 + 195.907i −1.60816 + 0.928470i −0.618374 + 0.785884i \(0.712208\pi\)
−0.989782 + 0.142586i \(0.954458\pi\)
\(212\) −135.776 26.1605i −0.640452 0.123399i
\(213\) −139.953 + 101.682i −0.657055 + 0.477379i
\(214\) 113.635 261.931i 0.531003 1.22398i
\(215\) −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
\(220\) 85.0207 51.2761i 0.386458 0.233073i
\(221\) 24.9343 18.1158i 0.112825 0.0819720i
\(222\) −55.5352 121.596i −0.250159 0.547729i
\(223\) −296.848 + 171.385i −1.33116 + 0.768545i −0.985477 0.169807i \(-0.945685\pi\)
−0.345681 + 0.938352i \(0.612352\pi\)
\(224\) 32.2587 82.8914i 0.144012 0.370051i
\(225\) −189.657 137.794i −0.842922 0.612419i
\(226\) −142.508 28.8716i −0.630568 0.127751i
\(227\) 55.7879 262.461i 0.245762 1.15622i −0.666146 0.745822i \(-0.732057\pi\)
0.911907 0.410396i \(-0.134610\pi\)
\(228\) 374.594 175.426i 1.64295 0.769414i
\(229\) 82.2978 91.4009i 0.359379 0.399131i −0.536158 0.844118i \(-0.680125\pi\)
0.895537 + 0.444987i \(0.146792\pi\)
\(230\) 49.4164 5.67145i 0.214854 0.0246585i
\(231\) −157.832 16.5888i −0.683257 0.0718132i
\(232\) 318.241 + 217.567i 1.37173 + 0.937789i
\(233\) −34.0681 + 104.851i −0.146215 + 0.450004i −0.997165 0.0752425i \(-0.976027\pi\)
0.850950 + 0.525247i \(0.176027\pi\)
\(234\) 107.867 122.123i 0.460969 0.521895i
\(235\) 25.0344 22.5411i 0.106529 0.0959194i
\(236\) −89.3725 + 211.515i −0.378697 + 0.896250i
\(237\) 50.7418 + 482.776i 0.214100 + 2.03703i
\(238\) 17.1249 15.7180i 0.0719534 0.0660421i
\(239\) −127.734 286.896i −0.534453 1.20040i −0.955939 0.293567i \(-0.905158\pi\)
0.421485 0.906835i \(-0.361509\pi\)
\(240\) 5.32642 + 139.382i 0.0221934 + 0.580759i
\(241\) −186.520 83.0438i −0.773940 0.344580i −0.0185262 0.999828i \(-0.505897\pi\)
−0.755414 + 0.655248i \(0.772564\pi\)
\(242\) 7.89939 82.7515i 0.0326421 0.341949i
\(243\) 297.784 + 171.925i 1.22545 + 0.707512i
\(244\) −352.425 245.908i −1.44437 1.00782i
\(245\) −78.5952 + 16.7059i −0.320797 + 0.0681874i
\(246\) −224.179 70.4808i −0.911297 0.286507i
\(247\) 170.215i 0.689129i
\(248\) 158.484 + 190.753i 0.639048 + 0.769167i
\(249\) 416.555 1.67291
\(250\) −53.9623 + 171.639i −0.215849 + 0.686555i
\(251\) −22.2739 104.790i −0.0887405 0.417491i −0.999984 0.00562351i \(-0.998210\pi\)
0.911244 0.411868i \(-0.135123\pi\)
\(252\) 70.3206 100.781i 0.279050 0.399923i
\(253\) 81.4419 141.061i 0.321905 0.557555i
\(254\) 198.833 + 18.9804i 0.782807 + 0.0747261i
\(255\) −14.8262 + 33.3002i −0.0581420 + 0.130589i
\(256\) −195.021 + 165.840i −0.761799 + 0.647813i
\(257\) 259.937 115.731i 1.01143 0.450316i 0.166982 0.985960i \(-0.446598\pi\)
0.844444 + 0.535644i \(0.179931\pi\)
\(258\) −319.888 348.521i −1.23988 1.35086i
\(259\) 41.2609 4.33670i 0.159309 0.0167440i
\(260\) −52.8727 22.3406i −0.203357 0.0859253i
\(261\) 356.385 + 395.806i 1.36546 + 1.51650i
\(262\) −266.961 235.796i −1.01894 0.899985i
\(263\) −184.992 60.1075i −0.703391 0.228545i −0.0645834 0.997912i \(-0.520572\pi\)
−0.638807 + 0.769367i \(0.720572\pi\)
\(264\) 377.066 + 257.783i 1.42828 + 0.976450i
\(265\) −7.03444 + 66.9282i −0.0265450 + 0.252559i
\(266\) 14.6375 + 127.539i 0.0550281 + 0.479469i
\(267\) −299.176 269.379i −1.12051 1.00891i
\(268\) −80.0095 170.847i −0.298543 0.637488i
\(269\) −339.900 72.2479i −1.26357 0.268579i −0.473059 0.881031i \(-0.656850\pi\)
−0.790508 + 0.612451i \(0.790184\pi\)
\(270\) −7.10669 + 35.0781i −0.0263211 + 0.129919i
\(271\) −125.277 + 172.429i −0.462277 + 0.636270i −0.974979 0.222297i \(-0.928645\pi\)
0.512702 + 0.858567i \(0.328645\pi\)
\(272\) −64.8602 + 16.3983i −0.238457 + 0.0602877i
\(273\) 45.8739 + 79.4560i 0.168036 + 0.291047i
\(274\) 152.552 69.6737i 0.556761 0.254284i
\(275\) 158.954 + 218.782i 0.578016 + 0.795570i
\(276\) 118.179 + 195.951i 0.428183 + 0.709969i
\(277\) 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 \(0.658097\pi\)
\(282\) 142.173 + 61.6795i 0.504159 + 0.218722i
\(283\) 104.316 + 143.578i 0.368606 + 0.507343i 0.952521 0.304472i \(-0.0984800\pi\)
−0.583915 + 0.811815i \(0.698480\pi\)
\(284\) −29.2351 + 151.734i −0.102941 + 0.534273i
\(285\) −100.657 174.344i −0.353183 0.611732i
\(286\) −161.874 + 95.5307i −0.565994 + 0.334023i
\(287\) 42.8694 59.0047i 0.149371 0.205591i
\(288\) −315.876 + 159.115i −1.09679 + 0.552483i
\(289\) 265.583 + 56.4515i 0.918973 + 0.195334i
\(290\) 92.2554 163.374i 0.318122 0.563360i
\(291\) 390.401 + 351.519i 1.34158 + 1.20797i
\(292\) 258.037 467.321i 0.883687 1.60042i
\(293\) 8.49106 80.7870i 0.0289797 0.275724i −0.970430 0.241381i \(-0.922400\pi\)
0.999410 0.0343425i \(-0.0109337\pi\)
\(294\) −220.121 296.965i −0.748711 1.01009i
\(295\) 106.286 + 34.5344i 0.360291 + 0.117066i
\(296\) −110.431 45.4230i −0.373076 0.153456i
\(297\) 78.4236 + 87.0983i 0.264053 + 0.293260i
\(298\) 548.065 121.976i 1.83915 0.409316i
\(299\) −93.6497 + 9.84298i −0.313210 + 0.0329197i
\(300\) −377.008 + 46.9203i −1.25669 + 0.156401i
\(301\) 134.129 59.7179i 0.445610 0.198398i
\(302\) 411.367 138.018i 1.36214 0.457013i
\(303\) −58.3385 + 131.030i −0.192536 + 0.432444i
\(304\) 137.282 343.030i 0.451586 1.12839i
\(305\) −104.576 + 181.130i −0.342871 + 0.593870i
\(306\) −92.4258 + 0.882599i −0.302045 + 0.00288431i
\(307\) 23.8190 + 112.060i 0.0775865 + 0.365016i 0.999763 0.0217527i \(-0.00692466\pi\)
−0.922177 + 0.386768i \(0.873591\pi\)
\(308\) −113.074 + 85.4995i −0.367124 + 0.277596i
\(309\) 230.964 0.747456
\(310\) 85.9024 84.7901i 0.277104 0.273516i
\(311\) 152.293i 0.489689i 0.969562 + 0.244845i \(0.0787370\pi\)
−0.969562 + 0.244845i \(0.921263\pi\)
\(312\) −7.56349 263.952i −0.0242420 0.846000i
\(313\) 286.840 60.9697i 0.916421 0.194791i 0.274522 0.961581i \(-0.411480\pi\)
0.641899 + 0.766789i \(0.278147\pi\)
\(314\) 117.229 1.11945i 0.373342 0.00356514i
\(315\) −51.7965 29.9047i −0.164433 0.0949357i
\(316\) 327.721 + 283.939i 1.03709 + 0.898540i
\(317\) −10.3888 4.62539i −0.0327722 0.0145911i 0.390285 0.920694i \(-0.372376\pi\)
−0.423057 + 0.906103i \(0.639043\pi\)
\(318\) −293.516 + 98.4776i −0.923006 + 0.309678i
\(319\) −249.898 561.281i −0.783381 1.75950i
\(320\) 88.5348 + 87.6654i 0.276671 + 0.273955i
\(321\) −66.8229 635.777i −0.208171 1.98061i
\(322\) −69.3235 + 15.4285i −0.215290 + 0.0479145i
\(323\) 71.7559 64.6093i 0.222154 0.200029i
\(324\) 227.181 52.8426i 0.701176 0.163094i
\(325\) 48.3115 148.687i 0.148651 0.457500i
\(326\) −234.479 316.336i −0.719262 0.970356i
\(327\) −609.212 64.0308i −1.86303 0.195813i
\(328\) −189.240 + 90.8364i −0.576950 + 0.276940i
\(329\) −32.1840 + 35.7440i −0.0978237 + 0.108644i
\(330\) 109.308 193.573i 0.331237 0.586585i
\(331\) −18.1270 + 85.2806i −0.0547642 + 0.257645i −0.997010 0.0772780i \(-0.975377\pi\)
0.942245 + 0.334923i \(0.108710\pi\)
\(332\) 271.710 254.210i 0.818403 0.765693i
\(333\) −133.466 96.9686i −0.400798 0.291197i
\(334\) 99.3224 58.6154i 0.297372 0.175495i
\(335\) −79.5156 + 45.9084i −0.237360 + 0.137040i
\(336\) −28.3655 197.124i −0.0844211 0.586678i
\(337\) 227.924 165.597i 0.676333 0.491385i −0.195806 0.980643i \(-0.562732\pi\)
0.872139 + 0.489258i \(0.162732\pi\)
\(338\) −210.391 91.2749i −0.622458 0.270044i
\(339\) −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
\(344\) −421.348 32.1151i −1.22485 0.0933578i
\(345\) 90.1005 65.4618i 0.261161 0.189744i
\(346\) −517.066 + 236.154i −1.49441 + 0.682526i
\(347\) −242.862 + 140.216i −0.699889 + 0.404081i −0.807306 0.590133i \(-0.799075\pi\)
0.107417 + 0.994214i \(0.465742\pi\)
\(348\) 859.986 + 73.8140i 2.47122 + 0.212109i
\(349\) −156.636 113.803i −0.448814 0.326082i 0.340314 0.940312i \(-0.389467\pi\)
−0.789127 + 0.614230i \(0.789467\pi\)
\(350\) 23.4126 115.563i 0.0668933 0.330180i
\(351\) 14.0873 66.2758i 0.0401349 0.188820i
\(352\) 403.269 61.9651i 1.14565 0.176037i
\(353\) 12.7175 14.1242i 0.0360270 0.0400120i −0.724862 0.688894i \(-0.758097\pi\)
0.760889 + 0.648882i \(0.224763\pi\)
\(354\) 58.6207 + 510.773i 0.165595 + 1.44286i
\(355\) 74.7942 + 7.86119i 0.210688 + 0.0221442i
\(356\) −359.539 + 6.86731i −1.00994 + 0.0192902i
\(357\) 16.0829 49.4981i 0.0450502 0.138650i
\(358\) 322.290 + 284.666i 0.900252 + 0.795157i
\(359\) 198.377 178.619i 0.552582 0.497547i −0.344875 0.938649i \(-0.612079\pi\)
0.897457 + 0.441101i \(0.145412\pi\)
\(360\) 90.3038 + 146.550i 0.250844 + 0.407082i
\(361\) 18.0065 + 171.321i 0.0498796 + 0.474573i
\(362\) −100.590 109.594i −0.277873 0.302745i
\(363\) −75.7035 170.033i −0.208550 0.468410i
\(364\) 78.4121 + 23.8320i 0.215418 + 0.0654726i
\(365\) −237.349 105.675i −0.650272 0.289520i
\(366\) −957.835 91.4341i −2.61703 0.249820i
\(367\) 514.994 + 297.332i 1.40325 + 0.810168i 0.994725 0.102578i \(-0.0327090\pi\)
0.408528 + 0.912746i \(0.366042\pi\)
\(368\) 196.668 + 55.6943i 0.534425 + 0.151343i
\(369\) −283.675 + 60.2970i −0.768767 + 0.163407i
\(370\) −17.4300 + 55.4397i −0.0471080 + 0.149837i
\(371\) 96.0861i 0.258992i
\(372\) 518.996 + 197.420i 1.39515 + 0.530699i
\(373\) −406.698 −1.09034 −0.545172 0.838325i \(-0.683535\pi\)
−0.545172 + 0.838325i \(0.683535\pi\)
\(374\) 101.715 + 31.9788i 0.271966 + 0.0855048i
\(375\) 83.7566 + 394.044i 0.223351 + 1.05078i
\(376\) 130.377 46.5313i 0.346748 0.123754i
\(377\) −177.596 + 307.606i −0.471078 + 0.815931i
\(378\) 4.85606 50.8706i 0.0128467 0.134578i
\(379\) −47.2020 + 106.018i −0.124544 + 0.279730i −0.965047 0.262077i \(-0.915593\pi\)
0.840503 + 0.541806i \(0.182259\pi\)
\(380\) −172.053 52.2926i −0.452771 0.137612i
\(381\) 408.550 181.898i 1.07231 0.477423i
\(382\) 196.754 180.589i 0.515062 0.472747i
\(383\) 229.082 24.0775i 0.598125 0.0628655i 0.199372 0.979924i \(-0.436110\pi\)
0.398753 + 0.917058i \(0.369443\pi\)
\(384\) −197.641 + 538.036i −0.514690 + 1.40113i
\(385\) 46.1660 + 51.2725i 0.119912 + 0.133175i
\(386\) −225.602 + 255.420i −0.584462 + 0.661710i
\(387\) −555.246 180.410i −1.43474 0.466177i
\(388\) 469.171 8.96130i 1.20920 0.0230961i
\(389\) −23.2427 + 221.140i −0.0597499 + 0.568482i 0.923163 + 0.384409i \(0.125595\pi\)
−0.982913 + 0.184073i \(0.941072\pi\)
\(390\) −127.679 + 14.6535i −0.327381 + 0.0375731i
\(391\) 39.6965 + 35.7429i 0.101525 + 0.0914140i
\(392\) −324.809 59.3713i −0.828594 0.151457i
\(393\) −780.077 165.810i −1.98493 0.421910i
\(394\) 105.141 + 21.3011i 0.266855 + 0.0540637i
\(395\) 124.045 170.734i 0.314039 0.432237i
\(396\) 561.628 + 48.2054i 1.41825 + 0.121731i
\(397\) −280.531 485.893i −0.706626 1.22391i −0.966101 0.258163i \(-0.916883\pi\)
0.259475 0.965750i \(-0.416450\pi\)
\(398\) 104.582 + 228.985i 0.262769 + 0.575340i
\(399\) 168.951 + 232.540i 0.423435 + 0.582808i
\(400\) −217.281 + 260.682i −0.543201 + 0.651704i
\(401\) 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
\(406\) −106.617 + 245.756i −0.262604 + 0.605310i
\(407\) 111.859 + 153.961i 0.274839 + 0.378283i
\(408\) −108.401 + 103.378i −0.265688 + 0.253377i
\(409\) 376.592 + 652.277i 0.920764 + 1.59481i 0.798236 + 0.602345i \(0.205767\pi\)
0.122528 + 0.992465i \(0.460900\pi\)
\(410\) 51.9240 + 87.9839i 0.126644 + 0.214595i
\(411\) 220.717 303.790i 0.537023 0.739149i
\(412\) 150.653 140.950i 0.365662 0.342112i
\(413\) −156.077 33.1752i −0.377911 0.0803274i
\(414\) 245.904 + 138.859i 0.593970 + 0.335408i
\(415\) −134.578 121.175i −0.324285 0.291988i
\(416\) −166.015 167.555i −0.399075 0.402775i
\(417\) −29.1314 + 277.167i −0.0698595 + 0.664669i
\(418\) −473.072 + 350.658i −1.13175 + 0.838894i
\(419\) −265.116 86.1415i −0.632736 0.205588i −0.0249492 0.999689i \(-0.507942\pi\)
−0.607787 + 0.794100i \(0.707942\pi\)
\(420\) −94.4071 + 21.9592i −0.224779 + 0.0522838i
\(421\) 192.838 + 214.169i 0.458049 + 0.508714i 0.927284 0.374359i \(-0.122137\pi\)
−0.469235 + 0.883073i \(0.655470\pi\)
\(422\) 170.237 + 764.913i 0.403406 + 1.81259i
\(423\) 190.209 19.9918i 0.449667 0.0472619i
\(424\) −131.357 + 243.358i −0.309803 + 0.573959i
\(425\) −81.0186 + 36.0718i −0.190632 + 0.0848748i
\(426\) 110.052 + 328.013i 0.258337 + 0.769983i
\(427\) 121.462 272.807i 0.284454 0.638893i
\(428\) −431.582 373.924i −1.00837 0.873654i
\(429\) −210.424 + 364.465i −0.490499 + 0.849569i
\(430\) 1.96384 + 205.653i 0.00456707 + 0.478264i
\(431\) −96.4661 453.837i −0.223819 1.05299i −0.936274 0.351269i \(-0.885750\pi\)
0.712455 0.701718i \(-0.247583\pi\)
\(432\) −81.8428 + 122.202i −0.189451 + 0.282875i
\(433\) 206.318 0.476485 0.238243 0.971206i \(-0.423429\pi\)
0.238243 + 0.971206i \(0.423429\pi\)
\(434\) −109.325 + 133.220i −0.251900 + 0.306959i
\(435\) 420.090i 0.965723i
\(436\) −436.452 + 330.017i −1.00104 + 0.756920i
\(437\) −288.564 + 61.3361i −0.660328 + 0.140357i
\(438\) −11.4132 1195.19i −0.0260576 2.72875i
\(439\) −368.310 212.644i −0.838974 0.484382i 0.0179411 0.999839i \(-0.494289\pi\)
−0.856915 + 0.515457i \(0.827622\pi\)
\(440\) −46.8320 192.971i −0.106436 0.438570i
\(441\) −416.750 185.549i −0.945011 0.420746i
\(442\) −19.6070 58.4394i −0.0443597 0.132216i
\(443\) 144.318 + 324.144i 0.325775 + 0.731702i 0.999977 0.00684525i \(-0.00217893\pi\)
−0.674202 + 0.738547i \(0.735512\pi\)
\(444\) −265.309 + 33.0188i −0.597542 + 0.0743667i
\(445\) 18.2944 + 174.059i 0.0411109 + 0.391144i
\(446\) 148.929 + 669.170i 0.333921 + 1.50038i
\(447\) 934.245 841.198i 2.09003 1.88187i
\(448\) −138.801 111.269i −0.309823 0.248369i
\(449\) −198.349 + 610.455i −0.441757 + 1.35959i 0.444245 + 0.895905i \(0.353472\pi\)
−0.886002 + 0.463682i \(0.846528\pi\)
\(450\) −376.666 + 279.198i −0.837035 + 0.620440i
\(451\) 332.715 + 34.9698i 0.737728 + 0.0775383i
\(452\) −140.568 + 254.577i −0.310990 + 0.563224i
\(453\) 650.071 721.977i 1.43504 1.59377i
\(454\) −467.294 263.875i −1.02928 0.581222i
\(455\) 8.29287 39.0149i 0.0182261 0.0857470i
\(456\) −110.004 819.926i −0.241236 1.79808i
\(457\) −258.106 187.525i −0.564784 0.410339i 0.268423 0.963301i \(-0.413498\pi\)
−0.833207 + 0.552962i \(0.813498\pi\)
\(458\) −125.021 211.844i −0.272971 0.462542i
\(459\) −33.2864 + 19.2179i −0.0725195 + 0.0418691i
\(460\) 18.8213 97.6849i 0.0409160 0.212358i
\(461\) 402.528 292.453i 0.873162 0.634389i −0.0582716 0.998301i \(-0.518559\pi\)
0.931434 + 0.363911i \(0.118559\pi\)
\(462\) −126.325 + 291.182i −0.273431 + 0.630264i
\(463\) 344.220 111.844i 0.743456 0.241563i 0.0872927 0.996183i \(-0.472178\pi\)
0.656163 + 0.754619i \(0.272178\pi\)
\(464\) 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 −0.753413 0.657548i \(-0.771594\pi\)
−0.223027 + 0.974812i \(0.571594\pi\)
\(468\) −168.299 279.057i −0.359614 0.596275i
\(469\) 106.058 77.0559i 0.226137 0.164298i
\(470\) −27.9900 61.2849i −0.0595532 0.130393i
\(471\) 227.323 131.245i 0.482639 0.278652i
\(472\) 349.946 + 297.392i 0.741411 + 0.630068i
\(473\) 544.852 + 395.858i 1.15191 + 0.836909i
\(474\) 951.539 + 192.778i 2.00747 + 0.406705i
\(475\) 101.834 479.090i 0.214387 1.00861i
\(476\) −19.7166 42.1015i −0.0414214 0.0884484i
\(477\) −255.658 + 283.937i −0.535971 + 0.595256i
\(478\) −623.997 + 71.6154i −1.30543 + 0.149823i
\(479\) 311.191 + 32.7075i 0.649668 + 0.0682828i 0.423629 0.905836i \(-0.360756\pi\)
0.226038 + 0.974118i \(0.427423\pi\)
\(480\) 269.126 + 73.4449i 0.560679 + 0.153010i
\(481\) 33.9978 104.634i 0.0706814 0.217535i
\(482\) −270.324 + 306.053i −0.560838 + 0.634964i
\(483\) −118.170 + 106.401i −0.244659 + 0.220292i
\(484\) −153.146 64.7094i −0.316416 0.133697i
\(485\) −23.8727 227.134i −0.0492221 0.468317i
\(486\) 506.645 465.021i 1.04248 0.956834i
\(487\) −58.2140 130.751i −0.119536 0.268482i 0.843861 0.536562i \(-0.180277\pi\)
−0.963397 + 0.268080i \(0.913611\pi\)
\(488\) −680.575 + 524.896i −1.39462 + 1.07561i
\(489\) −805.419 358.596i −1.64707 0.733324i
\(490\) −15.2711 + 159.975i −0.0311654 + 0.326479i
\(491\) 182.159 + 105.170i 0.370997 + 0.214195i 0.673894 0.738828i \(-0.264621\pi\)
−0.302897 + 0.953023i \(0.597954\pi\)
\(492\) −268.945 + 385.440i −0.546635 + 0.783415i
\(493\) 197.086 41.8919i 0.399768 0.0849734i
\(494\) 324.758 + 102.102i 0.657404 + 0.206685i
\(495\) 274.346i 0.554235i
\(496\) 459.009 187.954i 0.925422 0.378939i
\(497\) −107.379 −0.216054
\(498\) 249.867 794.756i 0.501742 1.59590i
\(499\) 9.12993 + 42.9530i 0.0182965 + 0.0860781i 0.986349 0.164671i \(-0.0526563\pi\)
−0.968052 + 0.250749i \(0.919323\pi\)
\(500\) 295.105 + 205.913i 0.590211 + 0.411825i
\(501\) 129.111 223.627i 0.257707 0.446362i
\(502\) −213.293 20.3608i −0.424887 0.0405593i
\(503\) −20.5014 + 46.0470i −0.0407583 + 0.0915447i −0.932777 0.360453i \(-0.882622\pi\)
0.892019 + 0.451998i \(0.149289\pi\)
\(504\) −150.101 194.619i −0.297819 0.386149i
\(505\) 56.9642 25.3621i 0.112800 0.0502220i
\(506\) −220.283 240.000i −0.435341 0.474308i
\(507\) −510.676 + 53.6742i −1.00725 + 0.105866i
\(508\) 155.482 367.974i 0.306067 0.724358i
\(509\) 79.7336 + 88.5531i 0.156647 + 0.173975i 0.816360 0.577543i \(-0.195989\pi\)
−0.659712 + 0.751518i \(0.729322\pi\)
\(510\) 54.6410 + 48.2622i 0.107139 + 0.0946318i
\(511\) 352.801 + 114.632i 0.690413 + 0.224329i
\(512\) 199.429 + 471.563i 0.389511 + 0.921022i
\(513\) 22.1886 211.110i 0.0432526 0.411521i
\(514\) −64.8857 565.361i −0.126237 1.09992i
\(515\) −74.6186 67.1869i −0.144891 0.130460i
\(516\) −856.836 + 401.266i −1.66053 + 0.777648i
\(517\) −215.806 45.8709i −0.417419 0.0887252i
\(518\) 16.4760 81.3242i 0.0318069 0.156996i
\(519\) −748.103 + 1029.68i −1.44143 + 1.98396i
\(520\) −74.3396 + 87.4765i −0.142961 + 0.168224i
\(521\) −310.832 538.377i −0.596606 1.03335i −0.993318 0.115409i \(-0.963182\pi\)
0.396712 0.917943i \(-0.370151\pi\)
\(522\) 968.944 442.536i 1.85621 0.847770i
\(523\) 27.2396 + 37.4921i 0.0520834 + 0.0716866i 0.834264 0.551365i \(-0.185893\pi\)
−0.782181 + 0.623051i \(0.785893\pi\)
\(524\) −610.017 + 367.902i −1.16415 + 0.702103i
\(525\) −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
\(530\) 123.475 + 53.5676i 0.232971 + 0.101071i
\(531\) 372.942 + 513.311i 0.702340 + 0.966688i
\(532\) 252.115 + 48.5760i 0.473900 + 0.0913083i
\(533\) −96.7036 167.496i −0.181433 0.314250i
\(534\) −693.414 + 409.220i −1.29853 + 0.766331i
\(535\) −163.357 + 224.842i −0.305341 + 0.420266i
\(536\) −373.956 + 50.1711i −0.697680 + 0.0936029i
\(537\) 941.753 + 200.176i 1.75373 + 0.372767i
\(538\) −341.730 + 605.166i −0.635186 + 1.12484i
\(539\) 391.075 + 352.126i 0.725557 + 0.653294i
\(540\) 62.6636 + 34.6004i 0.116044 + 0.0640748i
\(541\) 70.6467 672.159i 0.130585 1.24244i −0.711342 0.702846i \(-0.751912\pi\)
0.841927 0.539591i \(-0.181421\pi\)
\(542\) 253.836 + 342.450i 0.468332 + 0.631827i
\(543\) −316.771 102.925i −0.583372 0.189549i
\(544\) −7.61923 + 133.585i −0.0140059 + 0.245560i
\(545\) 178.195 + 197.905i 0.326963 + 0.363129i
\(546\) 179.113 39.8630i 0.328046 0.0730092i
\(547\) −652.301 + 68.5596i −1.19251 + 0.125338i −0.679913 0.733293i \(-0.737982\pi\)
−0.512595 + 0.858631i \(0.671316\pi\)
\(548\) −41.4249 332.852i −0.0755929 0.607395i
\(549\) −1084.79 + 482.978i −1.97593 + 0.879741i
\(550\) 512.768 172.039i 0.932305 0.312798i
\(551\) −452.609 + 1016.58i −0.821431 + 1.84496i
\(552\) 444.750 107.936i 0.805706 0.195536i
\(553\) −150.660 + 260.950i −0.272441 + 0.471881i
\(554\) 1047.94 10.0070i 1.89158 0.0180632i
\(555\) 27.0536 + 127.277i 0.0487452 + 0.229328i
\(556\) 150.144 + 198.568i 0.270044 + 0.357137i
\(557\) 966.750 1.73564 0.867819 0.496881i \(-0.165522\pi\)
0.867819 + 0.496881i \(0.165522\pi\)
\(558\) 677.518 102.787i 1.21419 0.184207i
\(559\) 389.345i 0.696503i
\(560\) −48.1788 + 71.9372i −0.0860335 + 0.128459i
\(561\) 233.516 49.6353i 0.416249 0.0884765i
\(562\) 774.280 7.39381i 1.37772 0.0131562i
\(563\) −642.394 370.886i −1.14102 0.658768i −0.194336 0.980935i \(-0.562255\pi\)
−0.946683 + 0.322167i \(0.895589\pi\)
\(564\) 202.961 234.257i 0.359861 0.415350i
\(565\) 129.298 + 57.5672i 0.228846 + 0.101889i
\(566\) 336.509 112.902i 0.594540 0.199474i
\(567\) 65.9249 + 148.070i 0.116270 + 0.261146i
\(568\) 271.960 + 146.795i 0.478803 + 0.258442i
\(569\) −61.7209 587.236i −0.108473 1.03205i −0.904409 0.426668i \(-0.859687\pi\)
0.795936 0.605381i \(-0.206979\pi\)
\(570\) −393.013 + 87.4681i −0.689497 + 0.153453i
\(571\) 508.060 457.459i 0.889773 0.801155i −0.0910926 0.995842i \(-0.529036\pi\)
0.980865 + 0.194687i \(0.0623693\pi\)
\(572\) 85.1665 + 366.148i 0.148892 + 0.640119i
\(573\) 184.782 568.699i 0.322481 0.992495i
\(574\) −86.8618 117.185i −0.151327 0.204156i
\(575\) 269.477 + 28.3232i 0.468656 + 0.0492577i
\(576\) 114.104 + 698.113i 0.198097 + 1.21200i
\(577\) 328.184 364.486i 0.568777 0.631691i −0.388297 0.921534i \(-0.626937\pi\)
0.957074 + 0.289843i \(0.0936033\pi\)
\(578\) 267.014 472.852i 0.461961 0.818083i
\(579\) −158.642 + 746.353i −0.273994 + 1.28904i
\(580\) −256.368 274.016i −0.442013 0.472441i
\(581\) 209.182 + 151.980i 0.360039 + 0.261583i
\(582\) 904.852 534.001i 1.55473 0.917528i
\(583\) 381.699 220.374i 0.654715 0.378000i
\(584\) −736.834 772.634i −1.26170 1.32300i
\(585\) −128.313 + 93.2250i −0.219339 + 0.159359i
\(586\) −149.042 64.6598i −0.254339 0.110341i
\(587\) −51.3250 + 16.6765i −0.0874362 + 0.0284097i −0.352408 0.935846i \(-0.614637\pi\)
0.264972 + 0.964256i \(0.414637\pi\)
\(588\) −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
\(592\) −152.905 + 183.447i −0.258285 + 0.309877i
\(593\) −343.634 + 249.665i −0.579485 + 0.421020i −0.838538 0.544843i \(-0.816589\pi\)
0.259054 + 0.965863i \(0.416589\pi\)
\(594\) 213.219 97.3814i 0.358955 0.163942i
\(595\) −19.5949 + 11.3131i −0.0329326 + 0.0190136i
\(596\) 96.0315 1118.84i 0.161127 1.87724i
\(597\) 455.998 + 331.302i 0.763815 + 0.554944i
\(598\) −37.3954 + 184.581i −0.0625341 + 0.308664i
\(599\) 137.772 648.167i 0.230004 1.08208i −0.699889 0.714251i \(-0.746767\pi\)
0.929893 0.367831i \(-0.119899\pi\)
\(600\) −136.625 + 747.450i −0.227709 + 1.24575i
\(601\) −266.017 + 295.442i −0.442624 + 0.491584i −0.922633 0.385680i \(-0.873967\pi\)
0.480008 + 0.877264i \(0.340634\pi\)
\(602\) −33.4814 291.729i −0.0556169 0.484600i
\(603\) −518.430 54.4891i −0.859750 0.0903634i
\(604\) −16.5723 867.648i −0.0274376 1.43650i
\(605\) −25.0043 + 76.9554i −0.0413295 + 0.127199i
\(606\) 215.003 + 189.903i 0.354790 + 0.313372i
\(607\) −124.255 + 111.880i −0.204703 + 0.184315i −0.765105 0.643905i \(-0.777313\pi\)
0.560402 + 0.828221i \(0.310647\pi\)
\(608\) −572.128 467.688i −0.941000 0.769224i
\(609\) 62.6964 + 596.516i 0.102950 + 0.979501i
\(610\) 282.854 + 308.172i 0.463696 + 0.505200i
\(611\) 51.8784 + 116.521i 0.0849073 + 0.190705i
\(612\) −53.7570 + 176.871i −0.0878383 + 0.289005i
\(613\) −853.826 380.148i −1.39287 0.620144i −0.433202 0.901297i \(-0.642616\pi\)
−0.959663 + 0.281153i \(0.909283\pi\)
\(614\) 228.090 + 21.7732i 0.371482 + 0.0354613i
\(615\) 198.098 + 114.372i 0.322111 + 0.185971i
\(616\) 95.3001 + 267.024i 0.154708 + 0.433480i
\(617\) 901.418 191.602i 1.46097 0.310538i 0.592214 0.805781i \(-0.298254\pi\)
0.868755 + 0.495242i \(0.164921\pi\)
\(618\) 138.542 440.662i 0.224178 0.713046i
\(619\) 958.561i 1.54856i −0.632841 0.774282i \(-0.718111\pi\)
0.632841 0.774282i \(-0.281889\pi\)
\(620\) −110.245 214.756i −0.177815 0.346381i
\(621\) 117.433 0.189103
\(622\) 290.565 + 91.3521i 0.467146 + 0.146868i
\(623\) −51.9550 244.429i −0.0833948 0.392342i
\(624\) −508.138 143.899i −0.814324 0.230608i
\(625\) −177.559 + 307.541i −0.284094 + 0.492065i
\(626\) 55.7331 583.842i 0.0890304 0.932655i
\(627\) −536.270 + 1204.48i −0.855295 + 1.92102i
\(628\) 68.1833 224.337i 0.108572 0.357224i
\(629\) −57.0144 + 25.3845i −0.0906429 + 0.0403568i
\(630\) −88.1259 + 80.8859i −0.139882 + 0.128390i
\(631\) −310.608 + 32.6463i −0.492248 + 0.0517373i −0.347401 0.937717i \(-0.612936\pi\)
−0.144847 + 0.989454i \(0.546269\pi\)
\(632\) 738.315 454.949i 1.16822 0.719857i
\(633\) 1174.03 + 1303.89i 1.85470 + 2.05986i
\(634\) −15.0566 + 17.0466i −0.0237485 + 0.0268873i
\(635\) −184.906 60.0797i −0.291191 0.0946136i
\(636\) 11.8246 + 619.078i 0.0185921 + 0.973394i
\(637\) 31.8006 302.563i 0.0499225 0.474981i
\(638\) −1220.78 + 140.108i −1.91345 + 0.219605i
\(639\) 317.308 + 285.705i 0.496569 + 0.447113i
\(640\) 220.366 116.333i 0.344322 0.181770i
\(641\) 791.733 + 168.288i 1.23515 + 0.262540i 0.778808 0.627263i \(-0.215825\pi\)
0.456346 + 0.889803i \(0.349158\pi\)
\(642\) −1253.10 253.873i −1.95187 0.395441i
\(643\) 41.5388 57.1732i 0.0646015 0.0889163i −0.775494 0.631355i \(-0.782499\pi\)
0.840095 + 0.542439i \(0.182499\pi\)
\(644\) −12.1468 + 141.519i −0.0188615 + 0.219750i
\(645\) 230.241 + 398.789i 0.356963 + 0.618278i
\(646\) −80.2276 175.660i −0.124191 0.271920i
\(647\) −396.694 546.003i −0.613129 0.843899i 0.383702 0.923457i \(-0.374649\pi\)
−0.996830 + 0.0795579i \(0.974649\pi\)
\(648\) 35.4531 465.142i 0.0547115 0.717812i
\(649\) −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 \(0.653812\pi\)
\(654\) −487.598 + 1123.92i −0.745562 + 1.71854i
\(655\) 203.789 + 280.492i 0.311129 + 0.428232i
\(656\) 59.7953 + 415.543i 0.0911513 + 0.633450i
\(657\) −737.533 1277.45i −1.12258 1.94436i
\(658\) 48.8915 + 82.8455i 0.0743033 + 0.125905i
\(659\) −683.346 + 940.545i −1.03694 + 1.42723i −0.137340 + 0.990524i \(0.543855\pi\)
−0.899604 + 0.436707i \(0.856145\pi\)
\(660\) −303.755 324.666i −0.460235 0.491917i
\(661\) −758.545 161.234i −1.14757 0.243924i −0.405404 0.914138i \(-0.632869\pi\)
−0.742168 + 0.670214i \(0.766202\pi\)
\(662\) 151.836 + 85.7399i 0.229359 + 0.129516i
\(663\) −102.565 92.3500i −0.154698 0.139291i
\(664\) −322.032 670.889i −0.484987 1.01037i
\(665\) 13.0619 124.275i 0.0196419 0.186880i
\(666\) −265.068 + 196.477i −0.397999 + 0.295011i
\(667\) −585.477 190.233i −0.877777 0.285207i
\(668\) −52.2562 224.660i −0.0782278 0.336317i
\(669\) 1027.07 + 1140.68i 1.53524 + 1.70505i
\(670\) 39.8930 + 179.248i 0.0595417 + 0.267534i
\(671\) 1362.29 143.182i 2.03024 0.213387i
\(672\) −393.113 64.1241i −0.584989 0.0954227i
\(673\) 279.281 124.344i 0.414979 0.184760i −0.188618 0.982051i \(-0.560401\pi\)
0.603596 + 0.797290i \(0.293734\pi\)
\(674\) −179.228 534.195i −0.265917 0.792574i
\(675\) −79.3011 + 178.113i −0.117483 + 0.263871i
\(676\) −300.347 + 346.660i −0.444301 + 0.512810i
\(677\) −284.189 + 492.230i −0.419777 + 0.727076i −0.995917 0.0902756i \(-0.971225\pi\)
0.576139 + 0.817351i \(0.304559\pi\)
\(678\) 6.21745 + 651.092i 0.00917029 + 0.960313i
\(679\) 67.7972 + 318.961i 0.0998487 + 0.469751i
\(680\) 65.0941 1.86526i 0.0957265 0.00274302i
\(681\) −1201.57 −1.76442
\(682\) −779.949 128.747i −1.14362 0.188779i
\(683\) 192.240i 0.281463i −0.990048 0.140732i \(-0.955055\pi\)
0.990048 0.140732i \(-0.0449455\pi\)
\(684\) −615.760 814.350i −0.900233 1.19057i
\(685\) −159.680 + 33.9410i −0.233109 + 0.0495490i
\(686\) −4.79209 501.828i −0.00698555 0.731527i
\(687\) −476.974 275.381i −0.694286 0.400846i
\(688\) −314.016 + 784.638i −0.456418 + 1.14046i
\(689\) −232.774 103.638i −0.337843 0.150417i
\(690\) −70.8503 211.172i −0.102682 0.306046i
\(691\) −98.4155 221.045i −0.142425 0.319891i 0.828222 0.560400i \(-0.189352\pi\)
−0.970647 + 0.240508i \(0.922686\pi\)
\(692\) 140.407 + 1128.18i 0.202900 + 1.63032i
\(693\) 40.9449 + 389.565i 0.0590835 + 0.562142i
\(694\) 121.844 + 547.470i 0.175567 + 0.788862i
\(695\) 90.0389 81.0714i 0.129552 0.116650i
\(696\) 656.688 1596.51i 0.943517 2.29384i
\(697\) −33.9032 + 104.343i −0.0486417 + 0.149704i
\(698\) −311.084 + 230.586i −0.445679 + 0.330353i
\(699\) 490.984 + 51.6045i 0.702409 + 0.0738262i
\(700\) −206.442 113.989i −0.294918 0.162842i
\(701\) 2.70631 3.00566i 0.00386064 0.00428768i −0.741211 0.671272i \(-0.765748\pi\)
0.745072 + 0.666984i \(0.232415\pi\)
\(702\) −117.999 66.6327i −0.168090 0.0949183i
\(703\) 71.6625 337.146i 0.101938 0.479581i
\(704\) 123.673 806.577i 0.175672 1.14571i
\(705\) −122.042 88.6685i −0.173109 0.125771i
\(706\) −19.3195 32.7364i −0.0273647 0.0463689i
\(707\) −77.1025 + 44.5151i −0.109056 + 0.0629634i
\(708\) 1009.68 + 194.539i 1.42610 + 0.274773i
\(709\) −70.9453 + 51.5448i −0.100064 + 0.0727007i −0.636692 0.771118i \(-0.719698\pi\)
0.536628 + 0.843819i \(0.319698\pi\)
\(710\) 59.8634 137.987i 0.0843146 0.194347i
\(711\) 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
\(716\) 736.446 444.152i 1.02856 0.620324i
\(717\) −1137.73 + 826.609i −1.58679 + 1.15287i
\(718\) −221.798 485.632i −0.308911 0.676368i
\(719\) 805.577 465.100i 1.12041 0.646871i 0.178907 0.983866i \(-0.442744\pi\)
0.941506 + 0.336995i \(0.109411\pi\)
\(720\) 333.774 84.3864i 0.463575 0.117203i
\(721\) 115.984 + 84.2671i 0.160865 + 0.116875i
\(722\) 337.669 + 68.4104i 0.467685 + 0.0947512i
\(723\) −190.090 + 894.305i −0.262919 + 1.23694i
\(724\) −269.435 + 126.180i −0.372148 + 0.174281i
\(725\) 683.897 759.545i 0.943306 1.04765i
\(726\) −369.821 + 42.4439i −0.509395 + 0.0584626i
\(727\) −958.401 100.732i −1.31830 0.138558i −0.580875 0.813993i \(-0.697290\pi\)
−0.737420 + 0.675434i \(0.763956\pi\)
\(728\) 92.5047 135.309i 0.127067 0.185864i
\(729\) 313.644 965.296i 0.430238 1.32414i
\(730\) −343.992 + 389.457i −0.471222 + 0.533503i
\(731\) −164.133 + 147.786i −0.224532 + 0.202169i
\(732\) −749.000 + 1772.63i −1.02322 + 2.42163i
\(733\) 68.2132 + 649.005i 0.0930603 + 0.885409i 0.937084 + 0.349104i \(0.113514\pi\)
−0.844024 + 0.536306i \(0.819819\pi\)
\(734\) 876.203 804.219i 1.19374 1.09567i
\(735\) 146.350 + 328.707i 0.199115 + 0.447220i
\(736\) 224.231 341.821i 0.304661 0.464431i
\(737\) 549.347 + 244.585i 0.745383 + 0.331866i
\(738\) −55.1181 + 577.400i −0.0746858 + 0.782385i
\(739\) 627.641 + 362.368i 0.849311 + 0.490350i 0.860418 0.509589i \(-0.170202\pi\)
−0.0111075 + 0.999938i \(0.503536\pi\)
\(740\) 95.3197 + 66.5102i 0.128810 + 0.0898786i
\(741\) 745.571 158.476i 1.00617 0.213868i
\(742\) −183.325 57.6365i −0.247069 0.0776773i
\(743\) 567.317i 0.763549i 0.924256 + 0.381774i \(0.124687\pi\)
−0.924256 + 0.381774i \(0.875313\pi\)
\(744\) 687.979 871.785i 0.924703 1.17175i
\(745\) −546.534 −0.733602
\(746\) −243.955 + 775.950i −0.327017 + 1.04015i
\(747\) −213.764 1005.68i −0.286163 1.34629i
\(748\) 122.026 174.883i 0.163137 0.233801i
\(749\) 198.407 343.650i 0.264895 0.458812i
\(750\) 802.048 + 76.5629i 1.06940 + 0.102084i
\(751\) −24.8758 + 55.8721i −0.0331236 + 0.0743969i −0.929350 0.369201i \(-0.879631\pi\)
0.896226 + 0.443598i \(0.146298\pi\)
\(752\) −10.5725 276.662i −0.0140592 0.367902i
\(753\) −438.262 + 195.127i −0.582021 + 0.259132i
\(754\) 480.360 + 523.357i 0.637083 + 0.694107i
\(755\) −420.043 + 44.1483i −0.556349 + 0.0584746i
\(756\) −94.1445 39.7794i −0.124530 0.0526182i
\(757\) −773.590 859.159i −1.02192 1.13495i −0.990786 0.135437i \(-0.956756\pi\)
−0.0311302 0.999515i \(-0.509911\pi\)
\(758\) 173.960 + 153.652i 0.229499 + 0.202707i
\(759\) −693.699 225.396i −0.913964 0.296965i
\(760\) −202.975 + 296.897i −0.267073 + 0.390654i
\(761\) 123.165 1171.84i 0.161846 1.53987i −0.548582 0.836097i \(-0.684832\pi\)
0.710428 0.703769i \(-0.248501\pi\)
\(762\) −101.983 888.594i −0.133836 1.16613i
\(763\) −282.568 254.425i −0.370338 0.333454i
\(764\) −226.530 483.717i −0.296506 0.633137i
\(765\) 88.0044 + 18.7059i 0.115038 + 0.0244522i
\(766\) 91.4751 451.515i 0.119419 0.589445i
\(767\) −248.712 + 342.323i −0.324266 + 0.446314i
\(768\) 907.980 + 699.821i 1.18227 + 0.911226i
\(769\) 454.909 + 787.925i 0.591559 + 1.02461i 0.994023 + 0.109174i \(0.0348205\pi\)
−0.402464 + 0.915436i \(0.631846\pi\)
\(770\) 125.517 57.3259i 0.163009 0.0744493i
\(771\) −748.933 1030.82i −0.971379 1.33699i
\(772\) 351.997 + 583.645i 0.455955 + 0.756017i
\(773\) −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
\(778\) 407.976 + 176.994i 0.524391 + 0.227499i
\(779\) −356.153 490.202i −0.457192 0.629271i
\(780\) −48.6293 + 252.392i −0.0623453 + 0.323579i
\(781\) −246.274 426.559i −0.315332 0.546171i
\(782\) 92.0064 54.2979i 0.117655 0.0694346i
\(783\) 260.364 358.360i 0.332521 0.457676i
\(784\) −308.110 + 584.098i −0.392998 + 0.745024i
\(785\) −111.621 23.7259i −0.142193 0.0302240i
\(786\) −784.278 + 1388.87i −0.997809 + 1.76701i
\(787\) −1125.91 1013.77i −1.43064 1.28815i −0.896709 0.442621i \(-0.854049\pi\)
−0.533927 0.845530i \(-0.679284\pi\)
\(788\) 103.709 187.824i 0.131610 0.238355i
\(789\) −91.0474 + 866.258i −0.115396 + 1.09792i
\(790\) −251.340 339.083i −0.318152 0.429219i
\(791\) −192.191 62.4468i −0.242973 0.0789466i
\(792\) 428.861 1042.63i 0.541491 1.31645i
\(793\) −529.884 588.495i −0.668201 0.742113i
\(794\) −1095.32 + 243.773i −1.37950 + 0.307018i
\(795\) 299.706 31.5004i 0.376989 0.0396232i
\(796\) 499.621 62.1800i 0.627664 0.0781155i
\(797\) −27.2883 + 12.1495i −0.0342387 + 0.0152441i −0.423785 0.905763i \(-0.639299\pi\)
0.389546 + 0.921007i \(0.372632\pi\)
\(798\) 545.014 182.858i 0.682975 0.229145i
\(799\) 29.4288 66.0982i 0.0368320 0.0827261i
\(800\) 367.027 + 570.924i 0.458784 + 0.713655i
\(801\) −496.828 + 860.532i −0.620260 + 1.07432i
\(802\) 645.100 6.16023i 0.804364 0.00768109i
\(803\) 353.779 + 1664.40i 0.440572 + 2.07273i
\(804\) −673.847 + 509.520i −0.838118 + 0.633731i
\(805\) 69.1298 0.0858755
\(806\) 204.817 + 408.535i 0.254115 + 0.506867i
\(807\) 1556.08i 1.92823i
\(808\) 256.134 7.33946i 0.316997 0.00908349i
\(809\) −528.027 + 112.236i −0.652691 + 0.138734i −0.522344 0.852735i \(-0.674942\pi\)
−0.130347 + 0.991468i \(0.541609\pi\)
\(810\) −227.029 + 2.16796i −0.280282 + 0.00267649i
\(811\) 412.385 + 238.090i 0.508489 + 0.293576i 0.732212 0.681076i \(-0.238488\pi\)
−0.223723 + 0.974653i \(0.571821\pi\)
\(812\) 404.930 + 350.833i 0.498683 + 0.432060i
\(813\) 871.908 + 388.198i 1.07246 + 0.477489i
\(814\) 360.845 121.067i 0.443299 0.148731i
\(815\) 155.896 + 350.148i 0.191283 + 0.429629i
\(816\) 132.214 + 268.832i 0.162027 + 0.329450i
\(817\) −127.501 1213.09i −0.156060 1.48482i
\(818\) 1470.39 327.247i 1.79755 0.400058i
\(819\) 168.288 151.527i 0.205480 0.185015i
\(820\) 199.013 46.2907i 0.242699 0.0564520i
\(821\) 415.411 1278.50i 0.505981 1.55725i −0.293133 0.956072i \(-0.594698\pi\)
0.799115 0.601179i \(-0.205302\pi\)
\(822\) −447.215 603.338i −0.544057 0.733988i
\(823\) −33.3198 3.50205i −0.0404858 0.00425523i 0.0842639 0.996443i \(-0.473146\pi\)
−0.124750 + 0.992188i \(0.539813\pi\)
\(824\) −178.554 371.983i −0.216692 0.451435i
\(825\) 810.311 899.941i 0.982195 1.09084i
\(826\) −156.918 + 277.884i −0.189973 + 0.336421i
\(827\) −59.1855 + 278.446i −0.0715665 + 0.336694i −0.999335 0.0364623i \(-0.988391\pi\)
0.927769 + 0.373156i \(0.121724\pi\)
\(828\) 412.436 385.873i 0.498111 0.466030i
\(829\) 318.579 + 231.461i 0.384293 + 0.279205i 0.763113 0.646265i \(-0.223670\pi\)
−0.378820 + 0.925470i \(0.623670\pi\)
\(830\) −311.919 + 184.080i −0.375806 + 0.221783i
\(831\) 2032.09 1173.23i 2.44535 1.41182i
\(832\) −419.265 + 216.238i −0.503924 + 0.259902i
\(833\) −139.619 + 101.439i −0.167610 + 0.121776i
\(834\) 511.340 + 221.837i 0.613118 + 0.265992i
\(835\) −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 0.439504 0.898241i \(-0.355154\pi\)
0.883539 + 0.468358i \(0.155154\pi\)
\(840\) −14.7329 + 193.294i −0.0175391 + 0.230112i
\(841\) −1198.21 + 870.554i −1.42475 + 1.03514i
\(842\) 524.291 239.454i 0.622674 0.284387i
\(843\) 1501.43 866.852i 1.78106 1.02829i
\(844\) 1561.52 + 134.027i 1.85014 + 0.158800i
\(845\) 180.600 + 131.214i 0.213728 + 0.155283i
\(846\) 75.9527 374.897i 0.0897786 0.443141i
\(847\) 24.0202 113.006i 0.0283592 0.133420i
\(848\) 385.517 + 396.596i 0.454619 + 0.467683i
\(849\) 531.775 590.596i 0.626355 0.695638i
\(850\) 20.2240 + 176.215i 0.0237929 + 0.207312i
\(851\) 189.636 + 19.9316i 0.222840 + 0.0234214i
\(852\) 691.838 13.2143i 0.812017 0.0155098i
\(853\) −350.261 + 1077.99i −0.410622 + 1.26377i 0.505486 + 0.862835i \(0.331313\pi\)
−0.916108 + 0.400931i \(0.868687\pi\)
\(854\) −447.639 395.382i −0.524167 0.462976i
\(855\) −369.260 + 332.483i −0.431883 + 0.388869i
\(856\) −972.301 + 599.131i −1.13587 + 0.699920i
\(857\) −45.8405 436.143i −0.0534895 0.508919i −0.988163 0.153410i \(-0.950974\pi\)
0.934673 0.355508i \(-0.115692\pi\)
\(858\) 569.152 + 620.096i 0.663347 + 0.722722i
\(859\) 338.879 + 761.135i 0.394504 + 0.886072i 0.996179 + 0.0873305i \(0.0278336\pi\)
−0.601675 + 0.798741i \(0.705500\pi\)
\(860\) 393.550 + 119.613i 0.457616 + 0.139085i
\(861\) −298.364 132.840i −0.346532 0.154286i
\(862\) −923.753 88.1807i −1.07164 0.102298i
\(863\) −788.691 455.351i −0.913894 0.527637i −0.0322122 0.999481i \(-0.510255\pi\)
−0.881682 + 0.471844i \(0.843589\pi\)
\(864\) 184.060 + 229.452i 0.213032 + 0.265570i
\(865\) 541.224 115.041i 0.625692 0.132995i
\(866\) 123.759 393.640i 0.142908 0.454550i
\(867\) 1215.86i 1.40238i
\(868\) 188.597 + 288.494i 0.217277 + 0.332367i
\(869\) −1382.15 −1.59051
\(870\) −801.501 251.988i −0.921265 0.289641i
\(871\) −72.2786 340.044i −0.0829835 0.390407i
\(872\) 367.846 + 1030.68i 0.421842 + 1.18197i
\(873\) 648.322 1122.93i 0.742637 1.28629i
\(874\) −56.0680 + 587.350i −0.0641510 + 0.672026i
\(875\) −101.707 + 228.437i −0.116236 + 0.261071i
\(876\) −2287.19 695.153i −2.61095 0.793553i
\(877\) 324.421 144.441i 0.369921 0.164699i −0.213352 0.976975i \(-0.568438\pi\)
0.583273 + 0.812276i \(0.301772\pi\)
\(878\) −626.637 + 575.156i −0.713709 + 0.655075i
\(879\) −361.767 + 38.0232i −0.411566 + 0.0432573i
\(880\) −396.266 26.4001i −0.450303 0.0300001i
\(881\) −408.209 453.362i −0.463348 0.514600i 0.465507 0.885044i \(-0.345872\pi\)
−0.928855 + 0.370445i \(0.879205\pi\)
\(882\) −603.998 + 683.828i −0.684805 + 0.775315i
\(883\) 993.086 + 322.673i 1.12467 + 0.365428i 0.811549 0.584284i \(-0.198625\pi\)
0.313124 + 0.949712i \(0.398625\pi\)
\(884\) −123.259 + 2.35429i −0.139434 + 0.00266322i
\(885\) 52.3107 497.704i 0.0591082 0.562377i
\(886\) 705.011 80.9132i 0.795724 0.0913242i
\(887\) 501.954 + 451.962i 0.565901 + 0.509540i 0.901682 0.432401i \(-0.142333\pi\)
−0.335780 + 0.941940i \(0.609000\pi\)
\(888\) −96.1459 + 525.996i −0.108272 + 0.592337i
\(889\) 271.528 + 57.7151i 0.305431 + 0.0649214i
\(890\) 343.066 + 69.5039i 0.385468 + 0.0780942i
\(891\) −437.003 + 601.483i −0.490463 + 0.675065i
\(892\) 1366.06 + 117.251i 1.53146 + 0.131448i
\(893\) 199.797 + 346.058i 0.223736 + 0.387523i
\(894\) −1044.54 2287.06i −1.16839 2.55823i
\(895\) −246.026 338.626i −0.274889 0.378353i
\(896\) −295.552 + 198.078i −0.329857 + 0.221069i
\(897\) 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
\(902\) 266.297 613.820i 0.295229 0.680510i
\(903\) −386.453 531.907i −0.427966 0.589045i
\(904\) 401.396 + 420.899i 0.444023 + 0.465596i
\(905\) 72.4001 + 125.401i 0.0800001 + 0.138564i
\(906\) −987.540 1673.36i −1.09000 1.84698i
\(907\) 106.278 146.279i 0.117175 0.161278i −0.746400 0.665497i \(-0.768220\pi\)
0.863576 + 0.504219i \(0.168220\pi\)
\(908\) −783.757 + 733.279i −0.863169 + 0.807576i
\(909\) 346.282 + 73.6045i 0.380948 + 0.0809731i
\(910\) −69.4631 39.2250i −0.0763331 0.0431044i
\(911\) −238.685 214.913i −0.262004 0.235909i 0.527650 0.849462i \(-0.323073\pi\)
−0.789654 + 0.613553i \(0.789740\pi\)
\(912\) −1630.34 281.947i −1.78766 0.309153i
\(913\) −123.974 + 1179.54i −0.135788 + 1.29193i
\(914\) −512.607 + 379.962i −0.560840 + 0.415714i
\(915\) 890.745 + 289.421i 0.973492 + 0.316307i
\(916\) −479.177 + 111.457i −0.523119 + 0.121678i
\(917\) −331.238 367.877i −0.361219 0.401174i
\(918\) 16.6998 + 75.0359i 0.0181915 + 0.0817384i
\(919\) 222.325 23.3673i 0.241920 0.0254268i 0.0172077 0.999852i \(-0.494522\pi\)
0.224713 + 0.974425i \(0.427856\pi\)
\(920\) −175.086 94.5053i −0.190311 0.102723i
\(921\) 468.665 208.663i 0.508865 0.226561i
\(922\) −316.527 943.420i −0.343305 1.02323i
\(923\) −115.818 + 260.132i −0.125480 + 0.281833i
\(924\) 479.779 + 415.682i 0.519241 + 0.449873i
\(925\) −158.290 + 274.166i −0.171124 + 0.296396i
\(926\) −6.91210 723.835i −0.00746447 0.781680i
\(927\) −118.524 557.612i −0.127858 0.601523i
\(928\) −545.959 1442.13i −0.588317 1.55402i
\(929\) 474.252 0.510497 0.255248 0.966875i \(-0.417843\pi\)
0.255248 + 0.966875i \(0.417843\pi\)
\(930\) −451.373 297.325i −0.485348 0.319704i
\(931\) 953.116i 1.02376i
\(932\) 351.751 265.972i 0.377415 0.285377i
\(933\) 667.072 141.790i 0.714975 0.151973i
\(934\) 9.15664 + 958.884i 0.00980369 + 1.02664i
\(935\) −89.8819 51.8933i −0.0961304 0.0555009i
\(936\) −633.373 + 153.713i −0.676681 + 0.164223i
\(937\) −467.413 208.106i −0.498840 0.222098i 0.141864 0.989886i \(-0.454690\pi\)
−0.640703 + 0.767788i \(0.721357\pi\)
\(938\) −83.3988 248.573i −0.0889113 0.265003i
\(939\) −534.116 1199.64i −0.568813 1.27758i
\(940\) −133.717 + 16.6416i −0.142252 + 0.0177039i
\(941\) 55.5276 + 528.309i 0.0590091 + 0.561434i 0.983586 + 0.180439i \(0.0577518\pi\)
−0.924577 + 0.380995i \(0.875581\pi\)
\(942\) −114.048 512.443i −0.121070 0.543994i
\(943\) 249.107 224.297i 0.264164 0.237854i
\(944\) 777.315 489.283i 0.823427 0.518308i
\(945\) −15.3711 + 47.3075i −0.0162657 + 0.0500608i
\(946\) 1082.09 802.085i 1.14386 0.847870i
\(947\) 1528.39 + 160.640i 1.61393 + 0.169631i 0.868058 0.496462i \(-0.165368\pi\)
0.745869 + 0.666093i \(0.232035\pi\)
\(948\) 938.581 1699.83i 0.990064 1.79307i
\(949\) 658.231 731.039i 0.693605 0.770326i
\(950\) −852.985 481.670i −0.897879 0.507021i
\(951\) −10.5877 + 49.8111i −0.0111332 + 0.0523776i
\(952\) −92.1534 + 12.3636i −0.0967998 + 0.0129870i
\(953\) 297.460 + 216.118i 0.312130 + 0.226776i 0.732810 0.680433i \(-0.238208\pi\)
−0.420680 + 0.907209i \(0.638208\pi\)
\(954\) 388.377 + 658.094i 0.407103 + 0.689826i
\(955\) −225.132 + 129.980i −0.235740 + 0.136105i
\(956\) −237.663 + 1233.50i −0.248602 + 1.29027i
\(957\) −2225.84 + 1617.17i −2.32586 + 1.68983i
\(958\) 249.069 574.110i 0.259989 0.599280i
\(959\) 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
\(964\) 421.774 + 699.342i 0.437525 + 0.725459i
\(965\) 268.366 194.979i 0.278099 0.202051i
\(966\) 132.122 + 289.285i 0.136772 + 0.299466i
\(967\) −719.225 + 415.245i −0.743769 + 0.429415i −0.823438 0.567406i \(-0.807947\pi\)
0.0796689 + 0.996821i \(0.474614\pi\)
\(968\) −215.324 + 253.375i −0.222442 + 0.261751i
\(969\) −349.807 254.150i −0.360998 0.262280i
\(970\) −447.675 90.6971i −0.461520 0.0935022i
\(971\) 144.081 677.847i 0.148384 0.698092i −0.839558 0.543270i \(-0.817186\pi\)
0.987942 0.154822i \(-0.0494805\pi\)
\(972\) −583.320 1245.58i −0.600124 1.28146i
\(973\) −115.753 + 128.557i −0.118965 + 0.132124i
\(974\) −284.382 + 32.6382i −0.291974 + 0.0335094i
\(975\) −696.257 73.1795i −0.714109 0.0750559i
\(976\) 593.226 + 1613.34i 0.607813 + 1.65301i
\(977\) 65.5268 201.671i 0.0670694 0.206418i −0.911905 0.410401i \(-0.865389\pi\)
0.978974 + 0.203983i \(0.0653887\pi\)
\(978\) −1167.30 + 1321.58i −1.19356 + 1.35131i
\(979\) 851.827 766.988i 0.870099 0.783440i
\(980\) 296.060 + 125.096i 0.302102 + 0.127649i
\(981\) 158.042 + 1503.67i 0.161103 + 1.53279i
\(982\) 309.923 284.462i 0.315604 0.289676i
\(983\) 770.812 + 1731.27i 0.784143 + 1.76121i 0.635170 + 0.772372i \(0.280930\pi\)
0.148973 + 0.988841i \(0.452403\pi\)
\(984\) 574.068 + 744.330i 0.583402 + 0.756433i
\(985\) −95.3944 42.4723i −0.0968471 0.0431191i
\(986\) 38.2938 401.154i 0.0388375 0.406850i
\(987\) 186.529 + 107.693i 0.188986 + 0.109111i
\(988\) 389.607 558.369i 0.394339 0.565151i
\(989\) 660.053 140.299i 0.667394 0.141859i
\(990\) −523.433 164.565i −0.528721 0.166227i
\(991\) 492.719i 0.497194i 0.968607 + 0.248597i \(0.0799694\pi\)
−0.968607 + 0.248597i \(0.920031\pi\)
\(992\) −83.2692 988.499i −0.0839407 0.996471i
\(993\) 390.421 0.393173
\(994\) −64.4105 + 204.871i −0.0647993 + 0.206108i
\(995\) −50.9464 239.684i −0.0512024 0.240889i
\(996\) −1366.46 953.458i −1.37194 0.957287i
\(997\) 193.403 334.984i 0.193985 0.335992i −0.752582 0.658498i \(-0.771192\pi\)
0.946567 + 0.322506i \(0.104525\pi\)
\(998\) 87.4277 + 8.34577i 0.0876029 + 0.00836250i
\(999\) −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.7.18 yes 240
4.3 odd 2 inner 124.3.n.a.7.7 240
31.9 even 15 inner 124.3.n.a.71.7 yes 240
124.71 odd 30 inner 124.3.n.a.71.18 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.3.n.a.7.7 240 4.3 odd 2 inner
124.3.n.a.7.18 yes 240 1.1 even 1 trivial
124.3.n.a.71.7 yes 240 31.9 even 15 inner
124.3.n.a.71.18 yes 240 124.71 odd 30 inner