Properties

Label 78.3.f.b.73.4
Level $78$
Weight $3$
Character 78.73
Analytic conductor $2.125$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [78,3,Mod(31,78)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(78, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("78.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.564373557504.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 86x^{6} + 2523x^{4} - 28394x^{2} + 113569 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 73.4
Root \(5.82017 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.73
Dual form 78.3.f.b.31.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(4.95414 + 4.95414i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.89463 + 2.89463i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(4.95414 + 4.95414i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-2.89463 + 2.89463i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -9.90829i q^{10} +(14.8823 - 14.8823i) q^{11} +3.46410i q^{12} +(-6.40459 + 11.3129i) q^{13} +5.78927 q^{14} +(8.58083 + 8.58083i) q^{15} -4.00000 q^{16} -10.7175i q^{17} +(-3.00000 - 3.00000i) q^{18} +(-13.7311 - 13.7311i) q^{19} +(-9.90829 + 9.90829i) q^{20} +(-5.01365 + 5.01365i) q^{21} -29.7647 q^{22} +24.6929i q^{23} +(3.46410 - 3.46410i) q^{24} +24.0871i q^{25} +(17.7175 - 4.90829i) q^{26} +5.19615 q^{27} +(-5.78927 - 5.78927i) q^{28} -50.5859 q^{29} -17.1617i q^{30} +(-13.0137 - 13.0137i) q^{31} +(4.00000 + 4.00000i) q^{32} +(25.7770 - 25.7770i) q^{33} +(-10.7175 + 10.7175i) q^{34} -28.6809 q^{35} +6.00000i q^{36} +(15.6656 - 15.6656i) q^{37} +27.4622i q^{38} +(-11.0931 + 19.5945i) q^{39} +19.8166 q^{40} +(-6.00136 - 6.00136i) q^{41} +10.0273 q^{42} -10.3450i q^{43} +(29.7647 + 29.7647i) q^{44} +(14.8624 + 14.8624i) q^{45} +(24.6929 - 24.6929i) q^{46} +(49.4437 - 49.4437i) q^{47} -6.92820 q^{48} +32.2422i q^{49} +(24.0871 - 24.0871i) q^{50} -18.5632i q^{51} +(-22.6258 - 12.8092i) q^{52} +4.69934 q^{53} +(-5.19615 - 5.19615i) q^{54} +147.459 q^{55} +11.5785i q^{56} +(-23.7830 - 23.7830i) q^{57} +(50.5859 + 50.5859i) q^{58} +(40.3844 - 40.3844i) q^{59} +(-17.1617 + 17.1617i) q^{60} -88.3293 q^{61} +26.0273i q^{62} +(-8.68390 + 8.68390i) q^{63} -8.00000i q^{64} +(-87.7749 + 24.3163i) q^{65} -51.5540 q^{66} +(-18.7237 - 18.7237i) q^{67} +21.4349 q^{68} +42.7693i q^{69} +(28.6809 + 28.6809i) q^{70} +(-75.9296 - 75.9296i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-14.2029 + 14.2029i) q^{73} -31.3312 q^{74} +41.7200i q^{75} +(27.4622 - 27.4622i) q^{76} +86.1579i q^{77} +(30.6876 - 8.50140i) q^{78} +18.7698 q^{79} +(-19.8166 - 19.8166i) q^{80} +9.00000 q^{81} +12.0027i q^{82} +(53.7860 + 53.7860i) q^{83} +(-10.0273 - 10.0273i) q^{84} +(53.0959 - 53.0959i) q^{85} +(-10.3450 + 10.3450i) q^{86} -87.6174 q^{87} -59.5294i q^{88} +(-20.1329 + 20.1329i) q^{89} -29.7249i q^{90} +(-14.2077 - 51.2856i) q^{91} -49.3858 q^{92} +(-22.5403 - 22.5403i) q^{93} -98.8874 q^{94} -136.052i q^{95} +(6.92820 + 6.92820i) q^{96} +(89.2469 + 89.2469i) q^{97} +(32.2422 - 32.2422i) q^{98} +(44.6470 - 44.6470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 4 q^{7} + 16 q^{8} + 24 q^{9} + 24 q^{11} - 36 q^{13} - 8 q^{14} - 12 q^{15} - 32 q^{16} - 24 q^{18} + 52 q^{19} + 12 q^{21} - 48 q^{22} + 32 q^{26} + 8 q^{28} - 168 q^{29} - 52 q^{31} + 32 q^{32} + 84 q^{33} + 24 q^{34} - 16 q^{37} - 48 q^{39} + 72 q^{41} - 24 q^{42} + 48 q^{44} - 48 q^{46} - 72 q^{47} + 160 q^{50} + 8 q^{52} + 144 q^{53} + 264 q^{55} - 60 q^{57} + 168 q^{58} - 48 q^{59} + 24 q^{60} - 72 q^{61} + 12 q^{63} + 48 q^{65} - 168 q^{66} - 116 q^{67} - 48 q^{68} - 432 q^{71} + 48 q^{72} - 128 q^{73} + 32 q^{74} - 104 q^{76} + 72 q^{78} + 240 q^{79} + 72 q^{81} + 144 q^{83} + 24 q^{84} - 48 q^{85} - 24 q^{86} + 192 q^{87} - 168 q^{89} - 20 q^{91} + 96 q^{92} + 12 q^{93} + 144 q^{94} + 224 q^{97} - 344 q^{98} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.73205 0.577350
\(4\) 2.00000i 0.500000i
\(5\) 4.95414 + 4.95414i 0.990829 + 0.990829i 0.999958 0.00912980i \(-0.00290615\pi\)
−0.00912980 + 0.999958i \(0.502906\pi\)
\(6\) −1.73205 1.73205i −0.288675 0.288675i
\(7\) −2.89463 + 2.89463i −0.413519 + 0.413519i −0.882963 0.469443i \(-0.844455\pi\)
0.469443 + 0.882963i \(0.344455\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 9.90829i 0.990829i
\(11\) 14.8823 14.8823i 1.35294 1.35294i 0.470587 0.882354i \(-0.344042\pi\)
0.882354 0.470587i \(-0.155958\pi\)
\(12\) 3.46410i 0.288675i
\(13\) −6.40459 + 11.3129i −0.492661 + 0.870221i
\(14\) 5.78927 0.413519
\(15\) 8.58083 + 8.58083i 0.572055 + 0.572055i
\(16\) −4.00000 −0.250000
\(17\) 10.7175i 0.630439i −0.949019 0.315220i \(-0.897922\pi\)
0.949019 0.315220i \(-0.102078\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) −13.7311 13.7311i −0.722691 0.722691i 0.246462 0.969152i \(-0.420732\pi\)
−0.969152 + 0.246462i \(0.920732\pi\)
\(20\) −9.90829 + 9.90829i −0.495414 + 0.495414i
\(21\) −5.01365 + 5.01365i −0.238745 + 0.238745i
\(22\) −29.7647 −1.35294
\(23\) 24.6929i 1.07360i 0.843708 + 0.536802i \(0.180368\pi\)
−0.843708 + 0.536802i \(0.819632\pi\)
\(24\) 3.46410 3.46410i 0.144338 0.144338i
\(25\) 24.0871i 0.963482i
\(26\) 17.7175 4.90829i 0.681441 0.188780i
\(27\) 5.19615 0.192450
\(28\) −5.78927 5.78927i −0.206760 0.206760i
\(29\) −50.5859 −1.74434 −0.872171 0.489201i \(-0.837288\pi\)
−0.872171 + 0.489201i \(0.837288\pi\)
\(30\) 17.1617i 0.572055i
\(31\) −13.0137 13.0137i −0.419795 0.419795i 0.465338 0.885133i \(-0.345933\pi\)
−0.885133 + 0.465338i \(0.845933\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 25.7770 25.7770i 0.781121 0.781121i
\(34\) −10.7175 + 10.7175i −0.315220 + 0.315220i
\(35\) −28.6809 −0.819453
\(36\) 6.00000i 0.166667i
\(37\) 15.6656 15.6656i 0.423394 0.423394i −0.462976 0.886371i \(-0.653219\pi\)
0.886371 + 0.462976i \(0.153219\pi\)
\(38\) 27.4622i 0.722691i
\(39\) −11.0931 + 19.5945i −0.284438 + 0.502423i
\(40\) 19.8166 0.495414
\(41\) −6.00136 6.00136i −0.146375 0.146375i 0.630122 0.776496i \(-0.283005\pi\)
−0.776496 + 0.630122i \(0.783005\pi\)
\(42\) 10.0273 0.238745
\(43\) 10.3450i 0.240582i −0.992739 0.120291i \(-0.961617\pi\)
0.992739 0.120291i \(-0.0383827\pi\)
\(44\) 29.7647 + 29.7647i 0.676470 + 0.676470i
\(45\) 14.8624 + 14.8624i 0.330276 + 0.330276i
\(46\) 24.6929 24.6929i 0.536802 0.536802i
\(47\) 49.4437 49.4437i 1.05199 1.05199i 0.0534213 0.998572i \(-0.482987\pi\)
0.998572 0.0534213i \(-0.0170126\pi\)
\(48\) −6.92820 −0.144338
\(49\) 32.2422i 0.658004i
\(50\) 24.0871 24.0871i 0.481741 0.481741i
\(51\) 18.5632i 0.363984i
\(52\) −22.6258 12.8092i −0.435111 0.246330i
\(53\) 4.69934 0.0886668 0.0443334 0.999017i \(-0.485884\pi\)
0.0443334 + 0.999017i \(0.485884\pi\)
\(54\) −5.19615 5.19615i −0.0962250 0.0962250i
\(55\) 147.459 2.68106
\(56\) 11.5785i 0.206760i
\(57\) −23.7830 23.7830i −0.417246 0.417246i
\(58\) 50.5859 + 50.5859i 0.872171 + 0.872171i
\(59\) 40.3844 40.3844i 0.684482 0.684482i −0.276525 0.961007i \(-0.589183\pi\)
0.961007 + 0.276525i \(0.0891828\pi\)
\(60\) −17.1617 + 17.1617i −0.286028 + 0.286028i
\(61\) −88.3293 −1.44802 −0.724010 0.689789i \(-0.757703\pi\)
−0.724010 + 0.689789i \(0.757703\pi\)
\(62\) 26.0273i 0.419795i
\(63\) −8.68390 + 8.68390i −0.137840 + 0.137840i
\(64\) 8.00000i 0.125000i
\(65\) −87.7749 + 24.3163i −1.35038 + 0.374098i
\(66\) −51.5540 −0.781121
\(67\) −18.7237 18.7237i −0.279459 0.279459i 0.553434 0.832893i \(-0.313317\pi\)
−0.832893 + 0.553434i \(0.813317\pi\)
\(68\) 21.4349 0.315220
\(69\) 42.7693i 0.619846i
\(70\) 28.6809 + 28.6809i 0.409726 + 0.409726i
\(71\) −75.9296 75.9296i −1.06943 1.06943i −0.997403 0.0720279i \(-0.977053\pi\)
−0.0720279 0.997403i \(-0.522947\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) −14.2029 + 14.2029i −0.194560 + 0.194560i −0.797663 0.603103i \(-0.793931\pi\)
0.603103 + 0.797663i \(0.293931\pi\)
\(74\) −31.3312 −0.423394
\(75\) 41.7200i 0.556267i
\(76\) 27.4622 27.4622i 0.361345 0.361345i
\(77\) 86.1579i 1.11893i
\(78\) 30.6876 8.50140i 0.393430 0.108992i
\(79\) 18.7698 0.237593 0.118796 0.992919i \(-0.462096\pi\)
0.118796 + 0.992919i \(0.462096\pi\)
\(80\) −19.8166 19.8166i −0.247707 0.247707i
\(81\) 9.00000 0.111111
\(82\) 12.0027i 0.146375i
\(83\) 53.7860 + 53.7860i 0.648024 + 0.648024i 0.952515 0.304491i \(-0.0984865\pi\)
−0.304491 + 0.952515i \(0.598486\pi\)
\(84\) −10.0273 10.0273i −0.119373 0.119373i
\(85\) 53.0959 53.0959i 0.624657 0.624657i
\(86\) −10.3450 + 10.3450i −0.120291 + 0.120291i
\(87\) −87.6174 −1.00710
\(88\) 59.5294i 0.676470i
\(89\) −20.1329 + 20.1329i −0.226213 + 0.226213i −0.811108 0.584896i \(-0.801135\pi\)
0.584896 + 0.811108i \(0.301135\pi\)
\(90\) 29.7249i 0.330276i
\(91\) −14.2077 51.2856i −0.156128 0.563578i
\(92\) −49.3858 −0.536802
\(93\) −22.5403 22.5403i −0.242369 0.242369i
\(94\) −98.8874 −1.05199
\(95\) 136.052i 1.43212i
\(96\) 6.92820 + 6.92820i 0.0721688 + 0.0721688i
\(97\) 89.2469 + 89.2469i 0.920071 + 0.920071i 0.997034 0.0769633i \(-0.0245224\pi\)
−0.0769633 + 0.997034i \(0.524522\pi\)
\(98\) 32.2422 32.2422i 0.329002 0.329002i
\(99\) 44.6470 44.6470i 0.450980 0.450980i
\(100\) −48.1741 −0.481741
\(101\) 69.0811i 0.683971i 0.939705 + 0.341986i \(0.111099\pi\)
−0.939705 + 0.341986i \(0.888901\pi\)
\(102\) −18.5632 + 18.5632i −0.181992 + 0.181992i
\(103\) 97.2640i 0.944311i 0.881515 + 0.472156i \(0.156524\pi\)
−0.881515 + 0.472156i \(0.843476\pi\)
\(104\) 9.81657 + 35.4349i 0.0943901 + 0.340721i
\(105\) −49.6767 −0.473111
\(106\) −4.69934 4.69934i −0.0443334 0.0443334i
\(107\) −37.7342 −0.352656 −0.176328 0.984331i \(-0.556422\pi\)
−0.176328 + 0.984331i \(0.556422\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 100.492 + 100.492i 0.921947 + 0.921947i 0.997167 0.0752195i \(-0.0239657\pi\)
−0.0752195 + 0.997167i \(0.523966\pi\)
\(110\) −147.459 147.459i −1.34053 1.34053i
\(111\) 27.1336 27.1336i 0.244447 0.244447i
\(112\) 11.5785 11.5785i 0.103380 0.103380i
\(113\) 60.2534 0.533216 0.266608 0.963805i \(-0.414097\pi\)
0.266608 + 0.963805i \(0.414097\pi\)
\(114\) 47.5660i 0.417246i
\(115\) −122.332 + 122.332i −1.06376 + 1.06376i
\(116\) 101.172i 0.872171i
\(117\) −19.2138 + 33.9386i −0.164220 + 0.290074i
\(118\) −80.7689 −0.684482
\(119\) 31.0231 + 31.0231i 0.260699 + 0.260699i
\(120\) 34.3233 0.286028
\(121\) 321.968i 2.66090i
\(122\) 88.3293 + 88.3293i 0.724010 + 0.724010i
\(123\) −10.3947 10.3947i −0.0845095 0.0845095i
\(124\) 26.0273 26.0273i 0.209898 0.209898i
\(125\) 4.52285 4.52285i 0.0361828 0.0361828i
\(126\) 17.3678 0.137840
\(127\) 40.6683i 0.320223i 0.987099 + 0.160111i \(0.0511854\pi\)
−0.987099 + 0.160111i \(0.948815\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 17.9181i 0.138900i
\(130\) 112.091 + 63.4585i 0.862240 + 0.488143i
\(131\) 214.111 1.63444 0.817218 0.576328i \(-0.195515\pi\)
0.817218 + 0.576328i \(0.195515\pi\)
\(132\) 51.5540 + 51.5540i 0.390560 + 0.390560i
\(133\) 79.4931 0.597693
\(134\) 37.4475i 0.279459i
\(135\) 25.7425 + 25.7425i 0.190685 + 0.190685i
\(136\) −21.4349 21.4349i −0.157610 0.157610i
\(137\) −118.462 + 118.462i −0.864685 + 0.864685i −0.991878 0.127193i \(-0.959403\pi\)
0.127193 + 0.991878i \(0.459403\pi\)
\(138\) 42.7693 42.7693i 0.309923 0.309923i
\(139\) −54.6810 −0.393388 −0.196694 0.980465i \(-0.563021\pi\)
−0.196694 + 0.980465i \(0.563021\pi\)
\(140\) 57.3617i 0.409726i
\(141\) 85.6390 85.6390i 0.607369 0.607369i
\(142\) 151.859i 1.06943i
\(143\) 73.0468 + 263.678i 0.510817 + 1.84390i
\(144\) −12.0000 −0.0833333
\(145\) −250.610 250.610i −1.72834 1.72834i
\(146\) 28.4057 0.194560
\(147\) 55.8451i 0.379899i
\(148\) 31.3312 + 31.3312i 0.211697 + 0.211697i
\(149\) 123.029 + 123.029i 0.825699 + 0.825699i 0.986919 0.161220i \(-0.0515428\pi\)
−0.161220 + 0.986919i \(0.551543\pi\)
\(150\) 41.7200 41.7200i 0.278133 0.278133i
\(151\) −29.7840 + 29.7840i −0.197245 + 0.197245i −0.798818 0.601573i \(-0.794541\pi\)
0.601573 + 0.798818i \(0.294541\pi\)
\(152\) −54.9245 −0.361345
\(153\) 32.1524i 0.210146i
\(154\) 86.1579 86.1579i 0.559467 0.559467i
\(155\) 128.943i 0.831890i
\(156\) −39.1890 22.1862i −0.251211 0.142219i
\(157\) 171.846 1.09456 0.547281 0.836949i \(-0.315663\pi\)
0.547281 + 0.836949i \(0.315663\pi\)
\(158\) −18.7698 18.7698i −0.118796 0.118796i
\(159\) 8.13950 0.0511918
\(160\) 39.6331i 0.247707i
\(161\) −71.4769 71.4769i −0.443956 0.443956i
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) −165.153 + 165.153i −1.01321 + 1.01321i −0.0132972 + 0.999912i \(0.504233\pi\)
−0.999912 + 0.0132972i \(0.995767\pi\)
\(164\) 12.0027 12.0027i 0.0731874 0.0731874i
\(165\) 255.406 1.54791
\(166\) 107.572i 0.648024i
\(167\) 65.6217 65.6217i 0.392944 0.392944i −0.482791 0.875735i \(-0.660377\pi\)
0.875735 + 0.482791i \(0.160377\pi\)
\(168\) 20.0546i 0.119373i
\(169\) −86.9624 144.909i −0.514570 0.857448i
\(170\) −106.192 −0.624657
\(171\) −41.1934 41.1934i −0.240897 0.240897i
\(172\) 20.6900 0.120291
\(173\) 216.560i 1.25179i −0.779906 0.625897i \(-0.784733\pi\)
0.779906 0.625897i \(-0.215267\pi\)
\(174\) 87.6174 + 87.6174i 0.503548 + 0.503548i
\(175\) −69.7232 69.7232i −0.398418 0.398418i
\(176\) −59.5294 + 59.5294i −0.338235 + 0.338235i
\(177\) 69.9479 69.9479i 0.395186 0.395186i
\(178\) 40.2658 0.226213
\(179\) 22.1128i 0.123535i 0.998091 + 0.0617676i \(0.0196738\pi\)
−0.998091 + 0.0617676i \(0.980326\pi\)
\(180\) −29.7249 + 29.7249i −0.165138 + 0.165138i
\(181\) 41.5239i 0.229414i 0.993399 + 0.114707i \(0.0365929\pi\)
−0.993399 + 0.114707i \(0.963407\pi\)
\(182\) −37.0779 + 65.4933i −0.203725 + 0.359853i
\(183\) −152.991 −0.836015
\(184\) 49.3858 + 49.3858i 0.268401 + 0.268401i
\(185\) 155.219 0.839022
\(186\) 45.0806i 0.242369i
\(187\) −159.501 159.501i −0.852947 0.852947i
\(188\) 98.8874 + 98.8874i 0.525997 + 0.525997i
\(189\) −15.0410 + 15.0410i −0.0795818 + 0.0795818i
\(190\) −136.052 + 136.052i −0.716062 + 0.716062i
\(191\) −221.663 −1.16054 −0.580269 0.814425i \(-0.697053\pi\)
−0.580269 + 0.814425i \(0.697053\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −255.579 + 255.579i −1.32424 + 1.32424i −0.413937 + 0.910305i \(0.635847\pi\)
−0.910305 + 0.413937i \(0.864153\pi\)
\(194\) 178.494i 0.920071i
\(195\) −152.031 + 42.1171i −0.779644 + 0.215985i
\(196\) −64.4844 −0.329002
\(197\) 138.728 + 138.728i 0.704204 + 0.704204i 0.965310 0.261106i \(-0.0840873\pi\)
−0.261106 + 0.965310i \(0.584087\pi\)
\(198\) −89.2941 −0.450980
\(199\) 258.963i 1.30132i 0.759369 + 0.650660i \(0.225508\pi\)
−0.759369 + 0.650660i \(0.774492\pi\)
\(200\) 48.1741 + 48.1741i 0.240871 + 0.240871i
\(201\) −32.4305 32.4305i −0.161346 0.161346i
\(202\) 69.0811 69.0811i 0.341986 0.341986i
\(203\) 146.428 146.428i 0.721319 0.721319i
\(204\) 37.1264 0.181992
\(205\) 59.4632i 0.290065i
\(206\) 97.2640 97.2640i 0.472156 0.472156i
\(207\) 74.0787i 0.357868i
\(208\) 25.6184 45.2515i 0.123165 0.217555i
\(209\) −408.703 −1.95551
\(210\) 49.6767 + 49.6767i 0.236556 + 0.236556i
\(211\) −220.454 −1.04480 −0.522402 0.852699i \(-0.674964\pi\)
−0.522402 + 0.852699i \(0.674964\pi\)
\(212\) 9.39868i 0.0443334i
\(213\) −131.514 131.514i −0.617436 0.617436i
\(214\) 37.7342 + 37.7342i 0.176328 + 0.176328i
\(215\) 51.2507 51.2507i 0.238375 0.238375i
\(216\) 10.3923 10.3923i 0.0481125 0.0481125i
\(217\) 75.3395 0.347187
\(218\) 200.985i 0.921947i
\(219\) −24.6001 + 24.6001i −0.112329 + 0.112329i
\(220\) 294.917i 1.34053i
\(221\) 121.245 + 68.6410i 0.548622 + 0.310593i
\(222\) −54.2672 −0.244447
\(223\) −163.765 163.765i −0.734370 0.734370i 0.237112 0.971482i \(-0.423799\pi\)
−0.971482 + 0.237112i \(0.923799\pi\)
\(224\) −23.1571 −0.103380
\(225\) 72.2612i 0.321161i
\(226\) −60.2534 60.2534i −0.266608 0.266608i
\(227\) 113.077 + 113.077i 0.498136 + 0.498136i 0.910857 0.412721i \(-0.135422\pi\)
−0.412721 + 0.910857i \(0.635422\pi\)
\(228\) 47.5660 47.5660i 0.208623 0.208623i
\(229\) 34.8308 34.8308i 0.152100 0.152100i −0.626955 0.779055i \(-0.715699\pi\)
0.779055 + 0.626955i \(0.215699\pi\)
\(230\) 244.664 1.06376
\(231\) 149.230i 0.646016i
\(232\) −101.172 + 101.172i −0.436086 + 0.436086i
\(233\) 222.050i 0.953004i −0.879173 0.476502i \(-0.841905\pi\)
0.879173 0.476502i \(-0.158095\pi\)
\(234\) 53.1524 14.7249i 0.227147 0.0629267i
\(235\) 489.902 2.08469
\(236\) 80.7689 + 80.7689i 0.342241 + 0.342241i
\(237\) 32.5103 0.137174
\(238\) 62.0463i 0.260699i
\(239\) −269.828 269.828i −1.12899 1.12899i −0.990342 0.138644i \(-0.955725\pi\)
−0.138644 0.990342i \(-0.544275\pi\)
\(240\) −34.3233 34.3233i −0.143014 0.143014i
\(241\) 281.175 281.175i 1.16670 1.16670i 0.183721 0.982978i \(-0.441186\pi\)
0.982978 0.183721i \(-0.0588142\pi\)
\(242\) −321.968 + 321.968i −1.33045 + 1.33045i
\(243\) 15.5885 0.0641500
\(244\) 176.659i 0.724010i
\(245\) −159.732 + 159.732i −0.651969 + 0.651969i
\(246\) 20.7893i 0.0845095i
\(247\) 243.281 67.3963i 0.984942 0.272859i
\(248\) −52.0546 −0.209898
\(249\) 93.1600 + 93.1600i 0.374137 + 0.374137i
\(250\) −9.04569 −0.0361828
\(251\) 172.399i 0.686847i 0.939181 + 0.343423i \(0.111587\pi\)
−0.939181 + 0.343423i \(0.888413\pi\)
\(252\) −17.3678 17.3678i −0.0689198 0.0689198i
\(253\) 367.488 + 367.488i 1.45252 + 1.45252i
\(254\) 40.6683 40.6683i 0.160111 0.160111i
\(255\) 91.9648 91.9648i 0.360646 0.360646i
\(256\) 16.0000 0.0625000
\(257\) 136.658i 0.531743i 0.964008 + 0.265871i \(0.0856597\pi\)
−0.964008 + 0.265871i \(0.914340\pi\)
\(258\) −17.9181 + 17.9181i −0.0694500 + 0.0694500i
\(259\) 90.6923i 0.350163i
\(260\) −48.6327 175.550i −0.187049 0.675191i
\(261\) −151.758 −0.581447
\(262\) −214.111 214.111i −0.817218 0.817218i
\(263\) −242.846 −0.923369 −0.461684 0.887044i \(-0.652755\pi\)
−0.461684 + 0.887044i \(0.652755\pi\)
\(264\) 103.108i 0.390560i
\(265\) 23.2812 + 23.2812i 0.0878536 + 0.0878536i
\(266\) −79.4931 79.4931i −0.298846 0.298846i
\(267\) −34.8712 + 34.8712i −0.130604 + 0.130604i
\(268\) 37.4475 37.4475i 0.139729 0.139729i
\(269\) 266.841 0.991975 0.495988 0.868330i \(-0.334806\pi\)
0.495988 + 0.868330i \(0.334806\pi\)
\(270\) 51.4850i 0.190685i
\(271\) 353.211 353.211i 1.30336 1.30336i 0.377247 0.926113i \(-0.376871\pi\)
0.926113 0.377247i \(-0.123129\pi\)
\(272\) 42.8699i 0.157610i
\(273\) −24.6084 88.8292i −0.0901408 0.325382i
\(274\) 236.924 0.864685
\(275\) 358.472 + 358.472i 1.30353 + 1.30353i
\(276\) −85.5387 −0.309923
\(277\) 318.494i 1.14980i 0.818225 + 0.574898i \(0.194958\pi\)
−0.818225 + 0.574898i \(0.805042\pi\)
\(278\) 54.6810 + 54.6810i 0.196694 + 0.196694i
\(279\) −39.0410 39.0410i −0.139932 0.139932i
\(280\) −57.3617 + 57.3617i −0.204863 + 0.204863i
\(281\) 62.1237 62.1237i 0.221081 0.221081i −0.587873 0.808954i \(-0.700034\pi\)
0.808954 + 0.587873i \(0.200034\pi\)
\(282\) −171.278 −0.607369
\(283\) 99.5260i 0.351682i −0.984419 0.175841i \(-0.943736\pi\)
0.984419 0.175841i \(-0.0562645\pi\)
\(284\) 151.859 151.859i 0.534715 0.534715i
\(285\) 235.649i 0.826838i
\(286\) 190.631 336.724i 0.666541 1.17736i
\(287\) 34.7435 0.121057
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 174.136 0.602546
\(290\) 501.220i 1.72834i
\(291\) 154.580 + 154.580i 0.531203 + 0.531203i
\(292\) −28.4057 28.4057i −0.0972799 0.0972799i
\(293\) −10.4011 + 10.4011i −0.0354987 + 0.0354987i −0.724633 0.689135i \(-0.757991\pi\)
0.689135 + 0.724633i \(0.257991\pi\)
\(294\) 55.8451 55.8451i 0.189949 0.189949i
\(295\) 400.140 1.35641
\(296\) 62.6624i 0.211697i
\(297\) 77.3309 77.3309i 0.260374 0.260374i
\(298\) 246.058i 0.825699i
\(299\) −279.348 158.148i −0.934273 0.528923i
\(300\) −83.4400 −0.278133
\(301\) 29.9450 + 29.9450i 0.0994851 + 0.0994851i
\(302\) 59.5680 0.197245
\(303\) 119.652i 0.394891i
\(304\) 54.9245 + 54.9245i 0.180673 + 0.180673i
\(305\) −437.596 437.596i −1.43474 1.43474i
\(306\) −32.1524 + 32.1524i −0.105073 + 0.105073i
\(307\) −308.228 + 308.228i −1.00400 + 1.00400i −0.00400658 + 0.999992i \(0.501275\pi\)
−0.999992 + 0.00400658i \(0.998725\pi\)
\(308\) −172.316 −0.559467
\(309\) 168.466i 0.545198i
\(310\) −128.943 + 128.943i −0.415945 + 0.415945i
\(311\) 51.6238i 0.165993i −0.996550 0.0829965i \(-0.973551\pi\)
0.996550 0.0829965i \(-0.0264490\pi\)
\(312\) 17.0028 + 61.3751i 0.0544961 + 0.196715i
\(313\) 188.224 0.601354 0.300677 0.953726i \(-0.402787\pi\)
0.300677 + 0.953726i \(0.402787\pi\)
\(314\) −171.846 171.846i −0.547281 0.547281i
\(315\) −86.0426 −0.273151
\(316\) 37.5397i 0.118796i
\(317\) −154.717 154.717i −0.488067 0.488067i 0.419629 0.907696i \(-0.362160\pi\)
−0.907696 + 0.419629i \(0.862160\pi\)
\(318\) −8.13950 8.13950i −0.0255959 0.0255959i
\(319\) −752.837 + 752.837i −2.35999 + 2.35999i
\(320\) 39.6331 39.6331i 0.123854 0.123854i
\(321\) −65.3575 −0.203606
\(322\) 142.954i 0.443956i
\(323\) −147.163 + 147.163i −0.455613 + 0.455613i
\(324\) 18.0000i 0.0555556i
\(325\) −272.494 154.268i −0.838443 0.474670i
\(326\) 330.306 1.01321
\(327\) 174.058 + 174.058i 0.532287 + 0.532287i
\(328\) −24.0055 −0.0731874
\(329\) 286.243i 0.870039i
\(330\) −255.406 255.406i −0.773957 0.773957i
\(331\) 112.730 + 112.730i 0.340575 + 0.340575i 0.856584 0.516008i \(-0.172583\pi\)
−0.516008 + 0.856584i \(0.672583\pi\)
\(332\) −107.572 + 107.572i −0.324012 + 0.324012i
\(333\) 46.9968 46.9968i 0.141131 0.141131i
\(334\) −131.243 −0.392944
\(335\) 185.520i 0.553791i
\(336\) 20.0546 20.0546i 0.0596863 0.0596863i
\(337\) 322.005i 0.955504i −0.878495 0.477752i \(-0.841452\pi\)
0.878495 0.477752i \(-0.158548\pi\)
\(338\) −57.9463 + 231.871i −0.171439 + 0.686009i
\(339\) 104.362 0.307853
\(340\) 106.192 + 106.192i 0.312329 + 0.312329i
\(341\) −387.347 −1.13592
\(342\) 82.3867i 0.240897i
\(343\) −235.166 235.166i −0.685616 0.685616i
\(344\) −20.6900 20.6900i −0.0601454 0.0601454i
\(345\) −211.885 + 211.885i −0.614161 + 0.614161i
\(346\) −216.560 + 216.560i −0.625897 + 0.625897i
\(347\) 181.180 0.522133 0.261066 0.965321i \(-0.415926\pi\)
0.261066 + 0.965321i \(0.415926\pi\)
\(348\) 175.235i 0.503548i
\(349\) 57.1882 57.1882i 0.163863 0.163863i −0.620413 0.784276i \(-0.713035\pi\)
0.784276 + 0.620413i \(0.213035\pi\)
\(350\) 139.446i 0.398418i
\(351\) −33.2792 + 58.7834i −0.0948126 + 0.167474i
\(352\) 119.059 0.338235
\(353\) 187.552 + 187.552i 0.531309 + 0.531309i 0.920962 0.389653i \(-0.127405\pi\)
−0.389653 + 0.920962i \(0.627405\pi\)
\(354\) −139.896 −0.395186
\(355\) 752.332i 2.11924i
\(356\) −40.2658 40.2658i −0.113106 0.113106i
\(357\) 53.7337 + 53.7337i 0.150514 + 0.150514i
\(358\) 22.1128 22.1128i 0.0617676 0.0617676i
\(359\) 139.842 139.842i 0.389532 0.389532i −0.484989 0.874520i \(-0.661176\pi\)
0.874520 + 0.484989i \(0.161176\pi\)
\(360\) 59.4497 0.165138
\(361\) 16.0874i 0.0445635i
\(362\) 41.5239 41.5239i 0.114707 0.114707i
\(363\) 557.666i 1.53627i
\(364\) 102.571 28.4154i 0.281789 0.0780642i
\(365\) −140.726 −0.385551
\(366\) 152.991 + 152.991i 0.418008 + 0.418008i
\(367\) 54.5159 0.148545 0.0742724 0.997238i \(-0.476337\pi\)
0.0742724 + 0.997238i \(0.476337\pi\)
\(368\) 98.7716i 0.268401i
\(369\) −18.0041 18.0041i −0.0487916 0.0487916i
\(370\) −155.219 155.219i −0.419511 0.419511i
\(371\) −13.6029 + 13.6029i −0.0366654 + 0.0366654i
\(372\) 45.0806 45.0806i 0.121184 0.121184i
\(373\) −236.635 −0.634410 −0.317205 0.948357i \(-0.602744\pi\)
−0.317205 + 0.948357i \(0.602744\pi\)
\(374\) 319.002i 0.852947i
\(375\) 7.83380 7.83380i 0.0208901 0.0208901i
\(376\) 197.775i 0.525997i
\(377\) 323.982 572.272i 0.859369 1.51796i
\(378\) 30.0819 0.0795818
\(379\) 81.9661 + 81.9661i 0.216269 + 0.216269i 0.806924 0.590655i \(-0.201131\pi\)
−0.590655 + 0.806924i \(0.701131\pi\)
\(380\) 272.104 0.716062
\(381\) 70.4396i 0.184881i
\(382\) 221.663 + 221.663i 0.580269 + 0.580269i
\(383\) −314.234 314.234i −0.820453 0.820453i 0.165720 0.986173i \(-0.447005\pi\)
−0.986173 + 0.165720i \(0.947005\pi\)
\(384\) −13.8564 + 13.8564i −0.0360844 + 0.0360844i
\(385\) −426.838 + 426.838i −1.10867 + 1.10867i
\(386\) 511.158 1.32424
\(387\) 31.0350i 0.0801939i
\(388\) −178.494 + 178.494i −0.460035 + 0.460035i
\(389\) 328.370i 0.844138i 0.906564 + 0.422069i \(0.138696\pi\)
−0.906564 + 0.422069i \(0.861304\pi\)
\(390\) 194.148 + 109.913i 0.497815 + 0.281829i
\(391\) 264.645 0.676842
\(392\) 64.4844 + 64.4844i 0.164501 + 0.164501i
\(393\) 370.852 0.943643
\(394\) 277.456i 0.704204i
\(395\) 92.9885 + 92.9885i 0.235414 + 0.235414i
\(396\) 89.2941 + 89.2941i 0.225490 + 0.225490i
\(397\) −48.4976 + 48.4976i −0.122160 + 0.122160i −0.765544 0.643384i \(-0.777530\pi\)
0.643384 + 0.765544i \(0.277530\pi\)
\(398\) 258.963 258.963i 0.650660 0.650660i
\(399\) 137.686 0.345078
\(400\) 96.3482i 0.240871i
\(401\) −176.776 + 176.776i −0.440839 + 0.440839i −0.892294 0.451455i \(-0.850905\pi\)
0.451455 + 0.892294i \(0.350905\pi\)
\(402\) 64.8609i 0.161346i
\(403\) 230.569 63.8747i 0.572131 0.158498i
\(404\) −138.162 −0.341986
\(405\) 44.5873 + 44.5873i 0.110092 + 0.110092i
\(406\) −292.855 −0.721319
\(407\) 466.281i 1.14565i
\(408\) −37.1264 37.1264i −0.0909961 0.0909961i
\(409\) −137.725 137.725i −0.336735 0.336735i 0.518402 0.855137i \(-0.326527\pi\)
−0.855137 + 0.518402i \(0.826527\pi\)
\(410\) −59.4632 + 59.4632i −0.145032 + 0.145032i
\(411\) −205.182 + 205.182i −0.499226 + 0.499226i
\(412\) −194.528 −0.472156
\(413\) 233.796i 0.566093i
\(414\) 74.0787 74.0787i 0.178934 0.178934i
\(415\) 532.927i 1.28416i
\(416\) −70.8699 + 19.6331i −0.170360 + 0.0471951i
\(417\) −94.7103 −0.227123
\(418\) 408.703 + 408.703i 0.977757 + 0.977757i
\(419\) −54.8057 −0.130801 −0.0654006 0.997859i \(-0.520833\pi\)
−0.0654006 + 0.997859i \(0.520833\pi\)
\(420\) 99.3534i 0.236556i
\(421\) −399.548 399.548i −0.949046 0.949046i 0.0497174 0.998763i \(-0.484168\pi\)
−0.998763 + 0.0497174i \(0.984168\pi\)
\(422\) 220.454 + 220.454i 0.522402 + 0.522402i
\(423\) 148.331 148.331i 0.350664 0.350664i
\(424\) 9.39868 9.39868i 0.0221667 0.0221667i
\(425\) 258.152 0.607417
\(426\) 263.028i 0.617436i
\(427\) 255.681 255.681i 0.598784 0.598784i
\(428\) 75.4683i 0.176328i
\(429\) 126.521 + 456.703i 0.294920 + 1.06458i
\(430\) −102.501 −0.238375
\(431\) 266.968 + 266.968i 0.619416 + 0.619416i 0.945382 0.325965i \(-0.105689\pi\)
−0.325965 + 0.945382i \(0.605689\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 783.673i 1.80987i 0.425551 + 0.904934i \(0.360080\pi\)
−0.425551 + 0.904934i \(0.639920\pi\)
\(434\) −75.3395 75.3395i −0.173593 0.173593i
\(435\) −434.069 434.069i −0.997860 0.997860i
\(436\) −200.985 + 200.985i −0.460974 + 0.460974i
\(437\) 339.061 339.061i 0.775884 0.775884i
\(438\) 49.2001 0.112329
\(439\) 411.297i 0.936895i −0.883491 0.468447i \(-0.844814\pi\)
0.883491 0.468447i \(-0.155186\pi\)
\(440\) 294.917 294.917i 0.670266 0.670266i
\(441\) 96.7266i 0.219335i
\(442\) −52.6044 189.886i −0.119014 0.429607i
\(443\) 166.429 0.375686 0.187843 0.982199i \(-0.439850\pi\)
0.187843 + 0.982199i \(0.439850\pi\)
\(444\) 54.2672 + 54.2672i 0.122223 + 0.122223i
\(445\) −199.483 −0.448276
\(446\) 327.529i 0.734370i
\(447\) 213.093 + 213.093i 0.476717 + 0.476717i
\(448\) 23.1571 + 23.1571i 0.0516899 + 0.0516899i
\(449\) 280.017 280.017i 0.623645 0.623645i −0.322817 0.946462i \(-0.604630\pi\)
0.946462 + 0.322817i \(0.104630\pi\)
\(450\) 72.2612 72.2612i 0.160580 0.160580i
\(451\) −178.629 −0.396073
\(452\) 120.507i 0.266608i
\(453\) −51.5874 + 51.5874i −0.113879 + 0.113879i
\(454\) 226.154i 0.498136i
\(455\) 183.689 324.463i 0.403712 0.713105i
\(456\) −95.1320 −0.208623
\(457\) −392.456 392.456i −0.858766 0.858766i 0.132427 0.991193i \(-0.457723\pi\)
−0.991193 + 0.132427i \(0.957723\pi\)
\(458\) −69.6617 −0.152100
\(459\) 55.6896i 0.121328i
\(460\) −244.664 244.664i −0.531879 0.531879i
\(461\) 474.185 + 474.185i 1.02860 + 1.02860i 0.999579 + 0.0290214i \(0.00923909\pi\)
0.0290214 + 0.999579i \(0.490761\pi\)
\(462\) 149.230 149.230i 0.323008 0.323008i
\(463\) −218.266 + 218.266i −0.471418 + 0.471418i −0.902373 0.430955i \(-0.858177\pi\)
0.430955 + 0.902373i \(0.358177\pi\)
\(464\) 202.344 0.436086
\(465\) 223.336i 0.480292i
\(466\) −222.050 + 222.050i −0.476502 + 0.476502i
\(467\) 170.592i 0.365293i −0.983179 0.182646i \(-0.941534\pi\)
0.983179 0.182646i \(-0.0584664\pi\)
\(468\) −67.8773 38.4276i −0.145037 0.0821102i
\(469\) 108.397 0.231123
\(470\) −489.902 489.902i −1.04235 1.04235i
\(471\) 297.646 0.631945
\(472\) 161.538i 0.342241i
\(473\) −153.958 153.958i −0.325493 0.325493i
\(474\) −32.5103 32.5103i −0.0685872 0.0685872i
\(475\) 330.742 330.742i 0.696300 0.696300i
\(476\) −62.0463 + 62.0463i −0.130349 + 0.130349i
\(477\) 14.0980 0.0295556
\(478\) 539.656i 1.12899i
\(479\) −40.5687 + 40.5687i −0.0846946 + 0.0846946i −0.748185 0.663490i \(-0.769074\pi\)
0.663490 + 0.748185i \(0.269074\pi\)
\(480\) 68.6466i 0.143014i
\(481\) 76.8912 + 277.555i 0.159857 + 0.577037i
\(482\) −562.349 −1.16670
\(483\) −123.802 123.802i −0.256318 0.256318i
\(484\) 643.937 1.33045
\(485\) 884.283i 1.82326i
\(486\) −15.5885 15.5885i −0.0320750 0.0320750i
\(487\) −112.692 112.692i −0.231399 0.231399i 0.581877 0.813277i \(-0.302318\pi\)
−0.813277 + 0.581877i \(0.802318\pi\)
\(488\) −176.659 + 176.659i −0.362005 + 0.362005i
\(489\) −286.053 + 286.053i −0.584976 + 0.584976i
\(490\) 319.465 0.651969
\(491\) 400.234i 0.815140i 0.913174 + 0.407570i \(0.133624\pi\)
−0.913174 + 0.407570i \(0.866376\pi\)
\(492\) 20.7893 20.7893i 0.0422547 0.0422547i
\(493\) 542.153i 1.09970i
\(494\) −310.677 175.884i −0.628901 0.356041i
\(495\) 442.376 0.893688
\(496\) 52.0546 + 52.0546i 0.104949 + 0.104949i
\(497\) 439.577 0.884460
\(498\) 186.320i 0.374137i
\(499\) 395.751 + 395.751i 0.793087 + 0.793087i 0.981995 0.188908i \(-0.0604947\pi\)
−0.188908 + 0.981995i \(0.560495\pi\)
\(500\) 9.04569 + 9.04569i 0.0180914 + 0.0180914i
\(501\) 113.660 113.660i 0.226866 0.226866i
\(502\) 172.399 172.399i 0.343423 0.343423i
\(503\) −186.068 −0.369917 −0.184958 0.982746i \(-0.559215\pi\)
−0.184958 + 0.982746i \(0.559215\pi\)
\(504\) 34.7356i 0.0689198i
\(505\) −342.238 + 342.238i −0.677698 + 0.677698i
\(506\) 734.976i 1.45252i
\(507\) −150.623 250.989i −0.297087 0.495048i
\(508\) −81.3366 −0.160111
\(509\) −713.760 713.760i −1.40228 1.40228i −0.792808 0.609472i \(-0.791382\pi\)
−0.609472 0.792808i \(-0.708618\pi\)
\(510\) −183.930 −0.360646
\(511\) 82.2241i 0.160908i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −71.3490 71.3490i −0.139082 0.139082i
\(514\) 136.658 136.658i 0.265871 0.265871i
\(515\) −481.860 + 481.860i −0.935650 + 0.935650i
\(516\) 35.8362 0.0694500
\(517\) 1471.68i 2.84657i
\(518\) 90.6923 90.6923i 0.175082 0.175082i
\(519\) 375.094i 0.722724i
\(520\) −126.917 + 224.182i −0.244071 + 0.431120i
\(521\) −949.290 −1.82205 −0.911027 0.412347i \(-0.864709\pi\)
−0.911027 + 0.412347i \(0.864709\pi\)
\(522\) 151.758 + 151.758i 0.290724 + 0.290724i
\(523\) 253.311 0.484342 0.242171 0.970234i \(-0.422140\pi\)
0.242171 + 0.970234i \(0.422140\pi\)
\(524\) 428.222i 0.817218i
\(525\) −120.764 120.764i −0.230027 0.230027i
\(526\) 242.846 + 242.846i 0.461684 + 0.461684i
\(527\) −139.473 + 139.473i −0.264655 + 0.264655i
\(528\) −103.108 + 103.108i −0.195280 + 0.195280i
\(529\) −80.7391 −0.152626
\(530\) 46.5624i 0.0878536i
\(531\) 121.153 121.153i 0.228161 0.228161i
\(532\) 158.986i 0.298846i
\(533\) 106.329 29.4564i 0.199492 0.0552653i
\(534\) 69.7425 0.130604
\(535\) −186.940 186.940i −0.349421 0.349421i
\(536\) −74.8949 −0.139729
\(537\) 38.3005i 0.0713231i
\(538\) −266.841 266.841i −0.495988 0.495988i
\(539\) 479.840 + 479.840i 0.890240 + 0.890240i
\(540\) −51.4850 + 51.4850i −0.0953425 + 0.0953425i
\(541\) 305.522 305.522i 0.564735 0.564735i −0.365914 0.930649i \(-0.619243\pi\)
0.930649 + 0.365914i \(0.119243\pi\)
\(542\) −706.421 −1.30336
\(543\) 71.9215i 0.132452i
\(544\) 42.8699 42.8699i 0.0788049 0.0788049i
\(545\) 995.706i 1.82698i
\(546\) −64.2208 + 113.438i −0.117620 + 0.207761i
\(547\) −550.333 −1.00609 −0.503047 0.864259i \(-0.667788\pi\)
−0.503047 + 0.864259i \(0.667788\pi\)
\(548\) −236.924 236.924i −0.432342 0.432342i
\(549\) −264.988 −0.482674
\(550\) 716.944i 1.30353i
\(551\) 694.601 + 694.601i 1.26062 + 1.26062i
\(552\) 85.5387 + 85.5387i 0.154961 + 0.154961i
\(553\) −54.3318 + 54.3318i −0.0982492 + 0.0982492i
\(554\) 318.494 318.494i 0.574898 0.574898i
\(555\) 268.847 0.484410
\(556\) 109.362i 0.196694i
\(557\) −8.16464 + 8.16464i −0.0146582 + 0.0146582i −0.714398 0.699740i \(-0.753299\pi\)
0.699740 + 0.714398i \(0.253299\pi\)
\(558\) 78.0819i 0.139932i
\(559\) 117.032 + 66.2556i 0.209359 + 0.118525i
\(560\) 114.723 0.204863
\(561\) −276.264 276.264i −0.492449 0.492449i
\(562\) −124.247 −0.221081
\(563\) 613.374i 1.08947i −0.838607 0.544737i \(-0.816629\pi\)
0.838607 0.544737i \(-0.183371\pi\)
\(564\) 171.278 + 171.278i 0.303684 + 0.303684i
\(565\) 298.504 + 298.504i 0.528326 + 0.528326i
\(566\) −99.5260 + 99.5260i −0.175841 + 0.175841i
\(567\) −26.0517 + 26.0517i −0.0459466 + 0.0459466i
\(568\) −303.718 −0.534715
\(569\) 292.821i 0.514624i 0.966328 + 0.257312i \(0.0828367\pi\)
−0.966328 + 0.257312i \(0.917163\pi\)
\(570\) −235.649 + 235.649i −0.413419 + 0.413419i
\(571\) 208.583i 0.365295i −0.983179 0.182647i \(-0.941533\pi\)
0.983179 0.182647i \(-0.0584666\pi\)
\(572\) −527.355 + 146.094i −0.921949 + 0.255408i
\(573\) −383.931 −0.670037
\(574\) −34.7435 34.7435i −0.0605287 0.0605287i
\(575\) −594.779 −1.03440
\(576\) 24.0000i 0.0416667i
\(577\) 495.420 + 495.420i 0.858614 + 0.858614i 0.991175 0.132561i \(-0.0423201\pi\)
−0.132561 + 0.991175i \(0.542320\pi\)
\(578\) −174.136 174.136i −0.301273 0.301273i
\(579\) −442.676 + 442.676i −0.764552 + 0.764552i
\(580\) 501.220 501.220i 0.864172 0.864172i
\(581\) −311.381 −0.535940
\(582\) 309.160i 0.531203i
\(583\) 69.9372 69.9372i 0.119961 0.119961i
\(584\) 56.8114i 0.0972799i
\(585\) −263.325 + 72.9490i −0.450128 + 0.124699i
\(586\) 20.8022 0.0354987
\(587\) 242.505 + 242.505i 0.413126 + 0.413126i 0.882826 0.469700i \(-0.155638\pi\)
−0.469700 + 0.882826i \(0.655638\pi\)
\(588\) −111.690 −0.189949
\(589\) 357.384i 0.606764i
\(590\) −400.140 400.140i −0.678204 0.678204i
\(591\) 240.284 + 240.284i 0.406572 + 0.406572i
\(592\) −62.6624 + 62.6624i −0.105849 + 0.105849i
\(593\) 661.970 661.970i 1.11631 1.11631i 0.124029 0.992279i \(-0.460418\pi\)
0.992279 0.124029i \(-0.0395816\pi\)
\(594\) −154.662 −0.260374
\(595\) 307.386i 0.516615i
\(596\) −246.058 + 246.058i −0.412849 + 0.412849i
\(597\) 448.537i 0.751318i
\(598\) 121.200 + 437.496i 0.202675 + 0.731598i
\(599\) −592.427 −0.989027 −0.494514 0.869170i \(-0.664654\pi\)
−0.494514 + 0.869170i \(0.664654\pi\)
\(600\) 83.4400 + 83.4400i 0.139067 + 0.139067i
\(601\) 3.03593 0.00505147 0.00252573 0.999997i \(-0.499196\pi\)
0.00252573 + 0.999997i \(0.499196\pi\)
\(602\) 59.8900i 0.0994851i
\(603\) −56.1712 56.1712i −0.0931529 0.0931529i
\(604\) −59.5680 59.5680i −0.0986225 0.0986225i
\(605\) 1595.08 1595.08i 2.63649 2.63649i
\(606\) 119.652 119.652i 0.197446 0.197446i
\(607\) 365.518 0.602171 0.301085 0.953597i \(-0.402651\pi\)
0.301085 + 0.953597i \(0.402651\pi\)
\(608\) 109.849i 0.180673i
\(609\) 253.620 253.620i 0.416454 0.416454i
\(610\) 875.191i 1.43474i
\(611\) 242.684 + 876.017i 0.397191 + 1.43374i
\(612\) 64.3048 0.105073
\(613\) 787.305 + 787.305i 1.28435 + 1.28435i 0.938168 + 0.346180i \(0.112521\pi\)
0.346180 + 0.938168i \(0.387479\pi\)
\(614\) 616.455 1.00400
\(615\) 102.993i 0.167469i
\(616\) 172.316 + 172.316i 0.279733 + 0.279733i
\(617\) 181.253 + 181.253i 0.293765 + 0.293765i 0.838566 0.544801i \(-0.183395\pi\)
−0.544801 + 0.838566i \(0.683395\pi\)
\(618\) 168.466 168.466i 0.272599 0.272599i
\(619\) 475.455 475.455i 0.768102 0.768102i −0.209671 0.977772i \(-0.567239\pi\)
0.977772 + 0.209671i \(0.0672391\pi\)
\(620\) 257.886 0.415945
\(621\) 128.308i 0.206615i
\(622\) −51.6238 + 51.6238i −0.0829965 + 0.0829965i
\(623\) 116.555i 0.187086i
\(624\) 44.3723 78.3779i 0.0711095 0.125606i
\(625\) 646.990 1.03518
\(626\) −188.224 188.224i −0.300677 0.300677i
\(627\) −707.894 −1.12902
\(628\) 343.692i 0.547281i
\(629\) −167.895 167.895i −0.266924 0.266924i
\(630\) 86.0426 + 86.0426i 0.136575 + 0.136575i
\(631\) 220.841 220.841i 0.349985 0.349985i −0.510119 0.860104i \(-0.670399\pi\)
0.860104 + 0.510119i \(0.170399\pi\)
\(632\) 37.5397 37.5397i 0.0593982 0.0593982i
\(633\) −381.837 −0.603218
\(634\) 309.435i 0.488067i
\(635\) −201.477 + 201.477i −0.317286 + 0.317286i
\(636\) 16.2790i 0.0255959i
\(637\) −364.752 206.498i −0.572609 0.324173i
\(638\) 1505.67 2.35999
\(639\) −227.789 227.789i −0.356477 0.356477i
\(640\) −79.2663 −0.123854
\(641\) 1061.61i 1.65618i −0.560593 0.828091i \(-0.689427\pi\)
0.560593 0.828091i \(-0.310573\pi\)
\(642\) 65.3575 + 65.3575i 0.101803 + 0.101803i
\(643\) −492.440 492.440i −0.765847 0.765847i 0.211526 0.977372i \(-0.432157\pi\)
−0.977372 + 0.211526i \(0.932157\pi\)
\(644\) 142.954 142.954i 0.221978 0.221978i
\(645\) 88.7688 88.7688i 0.137626 0.137626i
\(646\) 294.326 0.455613
\(647\) 1042.77i 1.61170i −0.592119 0.805850i \(-0.701709\pi\)
0.592119 0.805850i \(-0.298291\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1202.03i 1.85213i
\(650\) 118.226 + 426.762i 0.181886 + 0.656556i
\(651\) 130.492 0.200448
\(652\) −330.306 330.306i −0.506604 0.506604i
\(653\) −188.757 −0.289061 −0.144531 0.989500i \(-0.546167\pi\)
−0.144531 + 0.989500i \(0.546167\pi\)
\(654\) 348.115i 0.532287i
\(655\) 1060.74 + 1060.74i 1.61945 + 1.61945i
\(656\) 24.0055 + 24.0055i 0.0365937 + 0.0365937i
\(657\) −42.6086 + 42.6086i −0.0648532 + 0.0648532i
\(658\) 286.243 286.243i 0.435019 0.435019i
\(659\) −134.577 −0.204214 −0.102107 0.994773i \(-0.532558\pi\)
−0.102107 + 0.994773i \(0.532558\pi\)
\(660\) 510.811i 0.773957i
\(661\) 110.259 110.259i 0.166807 0.166807i −0.618768 0.785574i \(-0.712368\pi\)
0.785574 + 0.618768i \(0.212368\pi\)
\(662\) 225.461i 0.340575i
\(663\) 210.003 + 118.890i 0.316747 + 0.179321i
\(664\) 215.144 0.324012
\(665\) 393.820 + 393.820i 0.592211 + 0.592211i
\(666\) −93.9935 −0.141131
\(667\) 1249.11i 1.87273i
\(668\) 131.243 + 131.243i 0.196472 + 0.196472i
\(669\) −283.648 283.648i −0.423989 0.423989i
\(670\) −185.520 + 185.520i −0.276896 + 0.276896i
\(671\) −1314.55 + 1314.55i −1.95909 + 1.95909i
\(672\) −40.1092 −0.0596863
\(673\) 1027.47i 1.52670i 0.645984 + 0.763351i \(0.276447\pi\)
−0.645984 + 0.763351i \(0.723553\pi\)
\(674\) −322.005 + 322.005i −0.477752 + 0.477752i
\(675\) 125.160i 0.185422i
\(676\) 289.817 173.925i 0.428724 0.257285i
\(677\) 254.223 0.375514 0.187757 0.982216i \(-0.439878\pi\)
0.187757 + 0.982216i \(0.439878\pi\)
\(678\) −104.362 104.362i −0.153926 0.153926i
\(679\) −516.674 −0.760933
\(680\) 212.383i 0.312329i
\(681\) 195.855 + 195.855i 0.287599 + 0.287599i
\(682\) 387.347 + 387.347i 0.567958 + 0.567958i
\(683\) −179.840 + 179.840i −0.263309 + 0.263309i −0.826397 0.563088i \(-0.809613\pi\)
0.563088 + 0.826397i \(0.309613\pi\)
\(684\) 82.3867 82.3867i 0.120448 0.120448i
\(685\) −1173.75 −1.71351
\(686\) 470.333i 0.685616i
\(687\) 60.3288 60.3288i 0.0878148 0.0878148i
\(688\) 41.3801i 0.0601454i
\(689\) −30.0974 + 53.1631i −0.0436827 + 0.0771597i
\(690\) 423.771 0.614161
\(691\) −552.911 552.911i −0.800160 0.800160i 0.182960 0.983120i \(-0.441432\pi\)
−0.983120 + 0.182960i \(0.941432\pi\)
\(692\) 433.121 0.625897
\(693\) 258.474i 0.372978i
\(694\) −181.180 181.180i −0.261066 0.261066i
\(695\) −270.897 270.897i −0.389780 0.389780i
\(696\) −175.235 + 175.235i −0.251774 + 0.251774i
\(697\) −64.3194 + 64.3194i −0.0922804 + 0.0922804i
\(698\) −114.376 −0.163863
\(699\) 384.602i 0.550217i
\(700\) 139.446 139.446i 0.199209 0.199209i
\(701\) 307.529i 0.438701i 0.975646 + 0.219350i \(0.0703938\pi\)
−0.975646 + 0.219350i \(0.929606\pi\)
\(702\) 92.0627 25.5042i 0.131143 0.0363308i
\(703\) −430.212 −0.611966
\(704\) −119.059 119.059i −0.169118 0.169118i
\(705\) 848.535 1.20360
\(706\) 375.104i 0.531309i
\(707\) −199.964 199.964i −0.282835 0.282835i
\(708\) 139.896 + 139.896i 0.197593 + 0.197593i
\(709\) 126.877 126.877i 0.178952 0.178952i −0.611947 0.790899i \(-0.709613\pi\)
0.790899 + 0.611947i \(0.209613\pi\)
\(710\) −752.332 + 752.332i −1.05962 + 1.05962i
\(711\) 56.3095 0.0791976
\(712\) 80.5317i 0.113106i
\(713\) 321.345 321.345i 0.450694 0.450694i
\(714\) 107.467i 0.150514i
\(715\) −944.412 + 1668.18i −1.32086 + 2.33312i
\(716\) −44.2256 −0.0617676
\(717\) −467.355 467.355i −0.651821 0.651821i
\(718\) −279.684 −0.389532
\(719\) 132.467i 0.184238i 0.995748 + 0.0921191i \(0.0293640\pi\)
−0.995748 + 0.0921191i \(0.970636\pi\)
\(720\) −59.4497 59.4497i −0.0825690 0.0825690i
\(721\) −281.544 281.544i −0.390491 0.390491i
\(722\) 16.0874 16.0874i 0.0222817 0.0222817i
\(723\) 487.009 487.009i 0.673594 0.673594i
\(724\) −83.0479 −0.114707
\(725\) 1218.47i 1.68064i
\(726\) −557.666 + 557.666i −0.768135 + 0.768135i
\(727\) 445.841i 0.613261i −0.951829 0.306630i \(-0.900798\pi\)
0.951829 0.306630i \(-0.0992016\pi\)
\(728\) −130.987 74.1558i −0.179927 0.101862i
\(729\) 27.0000 0.0370370
\(730\) 140.726 + 140.726i 0.192775 + 0.192775i
\(731\) −110.872 −0.151672
\(732\) 305.982i 0.418008i
\(733\) 213.665 + 213.665i 0.291494 + 0.291494i 0.837670 0.546177i \(-0.183917\pi\)
−0.546177 + 0.837670i \(0.683917\pi\)
\(734\) −54.5159 54.5159i −0.0742724 0.0742724i
\(735\) −276.665 + 276.665i −0.376415 + 0.376415i
\(736\) −98.7716 + 98.7716i −0.134201 + 0.134201i
\(737\) −557.306 −0.756182
\(738\) 36.0082i 0.0487916i
\(739\) 831.408 831.408i 1.12505 1.12505i 0.134074 0.990971i \(-0.457194\pi\)
0.990971 0.134074i \(-0.0428059\pi\)
\(740\) 310.438i 0.419511i
\(741\) 421.375 116.734i 0.568657 0.157535i
\(742\) 27.2057 0.0366654
\(743\) 198.919 + 198.919i 0.267724 + 0.267724i 0.828182 0.560459i \(-0.189375\pi\)
−0.560459 + 0.828182i \(0.689375\pi\)
\(744\) −90.1612 −0.121184
\(745\) 1219.01i 1.63625i
\(746\) 236.635 + 236.635i 0.317205 + 0.317205i
\(747\) 161.358 + 161.358i 0.216008 + 0.216008i
\(748\) 319.002 319.002i 0.426474 0.426474i
\(749\) 109.227 109.227i 0.145830 0.145830i
\(750\) −15.6676 −0.0208901
\(751\) 479.541i 0.638537i 0.947664 + 0.319268i \(0.103437\pi\)
−0.947664 + 0.319268i \(0.896563\pi\)
\(752\) −197.775 + 197.775i −0.262998 + 0.262998i
\(753\) 298.603i 0.396551i
\(754\) −896.254 + 248.290i −1.18867 + 0.329297i
\(755\) −295.108 −0.390872
\(756\) −30.0819 30.0819i −0.0397909 0.0397909i
\(757\) 154.927 0.204660 0.102330 0.994751i \(-0.467370\pi\)
0.102330 + 0.994751i \(0.467370\pi\)
\(758\) 163.932i 0.216269i
\(759\) 636.508 + 636.508i 0.838614 + 0.838614i
\(760\) −272.104 272.104i −0.358031 0.358031i
\(761\) −220.102 + 220.102i −0.289228 + 0.289228i −0.836775 0.547547i \(-0.815562\pi\)
0.547547 + 0.836775i \(0.315562\pi\)
\(762\) 70.4396 70.4396i 0.0924404 0.0924404i
\(763\) −581.777 −0.762486
\(764\) 443.326i 0.580269i
\(765\) 159.288 159.288i 0.208219 0.208219i
\(766\) 628.467i 0.820453i
\(767\) 198.218 + 715.510i 0.258433 + 0.932868i
\(768\) 27.7128 0.0360844
\(769\) −658.837 658.837i −0.856745 0.856745i 0.134208 0.990953i \(-0.457151\pi\)
−0.990953 + 0.134208i \(0.957151\pi\)
\(770\) 853.677 1.10867
\(771\) 236.698i 0.307002i
\(772\) −511.158 511.158i −0.662121 0.662121i
\(773\) −415.757 415.757i −0.537849 0.537849i 0.385048 0.922897i \(-0.374185\pi\)
−0.922897 + 0.385048i \(0.874185\pi\)
\(774\) −31.0350 + 31.0350i −0.0400970 + 0.0400970i
\(775\) 313.461 313.461i 0.404465 0.404465i
\(776\) 356.987 0.460035
\(777\) 157.084i 0.202167i
\(778\) 328.370 328.370i 0.422069 0.422069i
\(779\) 164.811i 0.211567i
\(780\) −84.2343 304.061i −0.107993 0.389822i
\(781\) −2260.02 −2.89375
\(782\) −264.645 264.645i −0.338421 0.338421i
\(783\) −262.852 −0.335699
\(784\) 128.969i 0.164501i
\(785\) 851.350 + 851.350i 1.08452 + 1.08452i
\(786\) −370.852 370.852i −0.471821 0.471821i
\(787\) −550.553 + 550.553i −0.699559 + 0.699559i −0.964315 0.264756i \(-0.914708\pi\)
0.264756 + 0.964315i \(0.414708\pi\)
\(788\) −277.456 + 277.456i −0.352102 + 0.352102i
\(789\) −420.621 −0.533107
\(790\) 185.977i 0.235414i
\(791\) −174.412 + 174.412i −0.220495 + 0.220495i
\(792\) 178.588i 0.225490i
\(793\) 565.713 999.258i 0.713383 1.26010i
\(794\) 96.9952 0.122160
\(795\) 40.3242 + 40.3242i 0.0507223 + 0.0507223i
\(796\) −517.926 −0.650660
\(797\) 542.210i 0.680314i −0.940369 0.340157i \(-0.889520\pi\)
0.940369 0.340157i \(-0.110480\pi\)
\(798\) −137.686 137.686i −0.172539 0.172539i
\(799\) −529.911 529.911i −0.663218 0.663218i
\(800\) −96.3482 + 96.3482i −0.120435 + 0.120435i
\(801\) −60.3987 + 60.3987i −0.0754042 + 0.0754042i
\(802\) 353.553 0.440839
\(803\) 422.744i 0.526455i
\(804\) 64.8609 64.8609i 0.0806728 0.0806728i
\(805\) 708.213i 0.879768i
\(806\) −294.444 166.694i −0.365315 0.206817i
\(807\) 462.183 0.572717
\(808\) 138.162 + 138.162i 0.170993 + 0.170993i
\(809\) 1593.57 1.96980 0.984900 0.173122i \(-0.0553855\pi\)
0.984900 + 0.173122i \(0.0553855\pi\)
\(810\) 89.1746i 0.110092i
\(811\) 220.059 + 220.059i 0.271342 + 0.271342i 0.829640 0.558298i \(-0.188545\pi\)
−0.558298 + 0.829640i \(0.688545\pi\)
\(812\) 292.855 + 292.855i 0.360659 + 0.360659i
\(813\) 611.779 611.779i 0.752495 0.752495i
\(814\) −466.281 + 466.281i −0.572827 + 0.572827i
\(815\) −1636.38 −2.00783
\(816\) 74.2528i 0.0909961i
\(817\) −142.049 + 142.049i −0.173866 + 0.173866i
\(818\) 275.450i 0.336735i
\(819\) −42.6231 153.857i −0.0520428 0.187859i
\(820\) 118.926 0.145032
\(821\) −218.126 218.126i −0.265684 0.265684i 0.561675 0.827358i \(-0.310157\pi\)
−0.827358 + 0.561675i \(0.810157\pi\)
\(822\) 410.364 0.499226
\(823\) 513.628i 0.624092i 0.950067 + 0.312046i \(0.101014\pi\)
−0.950067 + 0.312046i \(0.898986\pi\)
\(824\) 194.528 + 194.528i 0.236078 + 0.236078i
\(825\) 620.892 + 620.892i 0.752596 + 0.752596i
\(826\) 233.796 233.796i 0.283046 0.283046i
\(827\) 380.987 380.987i 0.460686 0.460686i −0.438195 0.898880i \(-0.644382\pi\)
0.898880 + 0.438195i \(0.144382\pi\)
\(828\) −148.157 −0.178934
\(829\) 1083.19i 1.30662i 0.757089 + 0.653312i \(0.226621\pi\)
−0.757089 + 0.653312i \(0.773379\pi\)
\(830\) 532.927 532.927i 0.642080 0.642080i
\(831\) 551.647i 0.663835i
\(832\) 90.5030 + 51.2367i 0.108778 + 0.0615826i
\(833\) 345.555 0.414832
\(834\) 94.7103 + 94.7103i 0.113561 + 0.113561i
\(835\) 650.198 0.778680
\(836\) 817.405i 0.977757i
\(837\) −67.6209 67.6209i −0.0807896 0.0807896i
\(838\) 54.8057 + 54.8057i 0.0654006 + 0.0654006i
\(839\) 564.487 564.487i 0.672810 0.672810i −0.285553 0.958363i \(-0.592177\pi\)
0.958363 + 0.285553i \(0.0921773\pi\)
\(840\) −99.3534 + 99.3534i −0.118278 + 0.118278i
\(841\) 1717.94 2.04273
\(842\) 799.097i 0.949046i
\(843\) 107.601 107.601i 0.127641 0.127641i
\(844\) 440.907i 0.522402i
\(845\) 287.074 1148.72i 0.339733 1.35944i
\(846\) −296.662 −0.350664
\(847\) 931.981 + 931.981i 1.10033 + 1.10033i
\(848\) −18.7974 −0.0221667
\(849\) 172.384i 0.203044i
\(850\) −258.152 258.152i −0.303709 0.303709i
\(851\) 386.829 + 386.829i 0.454558 + 0.454558i
\(852\) 263.028 263.028i 0.308718 0.308718i
\(853\) −78.1611 + 78.1611i −0.0916309 + 0.0916309i −0.751436 0.659806i \(-0.770639\pi\)
0.659806 + 0.751436i \(0.270639\pi\)
\(854\) −511.362 −0.598784
\(855\) 408.156i 0.477375i
\(856\) −75.4683 + 75.4683i −0.0881639 + 0.0881639i
\(857\) 640.540i 0.747422i 0.927545 + 0.373711i \(0.121915\pi\)
−0.927545 + 0.373711i \(0.878085\pi\)
\(858\) 330.182 583.224i 0.384828 0.679748i
\(859\) −631.942 −0.735671 −0.367836 0.929891i \(-0.619901\pi\)
−0.367836 + 0.929891i \(0.619901\pi\)
\(860\) 102.501 + 102.501i 0.119188 + 0.119188i
\(861\) 60.1775 0.0698926
\(862\) 533.937i 0.619416i
\(863\) −838.507 838.507i −0.971619 0.971619i 0.0279890 0.999608i \(-0.491090\pi\)
−0.999608 + 0.0279890i \(0.991090\pi\)
\(864\) 20.7846 + 20.7846i 0.0240563 + 0.0240563i
\(865\) 1072.87 1072.87i 1.24031 1.24031i
\(866\) 783.673 783.673i 0.904934 0.904934i
\(867\) 301.612 0.347880
\(868\) 150.679i 0.173593i
\(869\) 279.339 279.339i 0.321449 0.321449i
\(870\) 868.138i 0.997860i
\(871\) 331.737 91.9014i 0.380869 0.105513i
\(872\) 401.969 0.460974
\(873\) 267.741 + 267.741i 0.306690 + 0.306690i
\(874\) −678.122 −0.775884
\(875\) 26.1840i 0.0299245i
\(876\) −49.2001 49.2001i −0.0561645 0.0561645i
\(877\) 70.3069 + 70.3069i 0.0801675 + 0.0801675i 0.746054 0.665886i \(-0.231946\pi\)
−0.665886 + 0.746054i \(0.731946\pi\)
\(878\) −411.297 + 411.297i −0.468447 + 0.468447i
\(879\) −18.0153 + 18.0153i −0.0204952 + 0.0204952i
\(880\) −589.834 −0.670266
\(881\) 824.918i 0.936343i 0.883638 + 0.468171i \(0.155087\pi\)
−0.883638 + 0.468171i \(0.844913\pi\)
\(882\) 96.7266 96.7266i 0.109667 0.109667i
\(883\) 1624.86i 1.84016i 0.391726 + 0.920082i \(0.371878\pi\)
−0.391726 + 0.920082i \(0.628122\pi\)
\(884\) −137.282 + 242.491i −0.155296 + 0.274311i
\(885\) 693.064 0.783123
\(886\) −166.429 166.429i −0.187843 0.187843i
\(887\) −494.247 −0.557212 −0.278606 0.960406i \(-0.589872\pi\)
−0.278606 + 0.960406i \(0.589872\pi\)
\(888\) 108.534i 0.122223i
\(889\) −117.720 117.720i −0.132418 0.132418i
\(890\) 199.483 + 199.483i 0.224138 + 0.224138i
\(891\) 133.941 133.941i 0.150327 0.150327i
\(892\) 327.529 327.529i 0.367185 0.367185i
\(893\) −1357.83 −1.52053
\(894\) 426.185i 0.476717i
\(895\) −109.550 + 109.550i −0.122402 + 0.122402i
\(896\) 46.3141i 0.0516899i
\(897\) −483.844 273.920i −0.539403 0.305374i
\(898\) −560.033 −0.623645
\(899\) 658.308 + 658.308i 0.732266 + 0.732266i
\(900\) −144.522 −0.160580
\(901\) 50.3650i 0.0558990i
\(902\) 178.629 + 178.629i 0.198036 + 0.198036i
\(903\) 51.8663 + 51.8663i 0.0574378 + 0.0574378i
\(904\) 120.507 120.507i 0.133304 0.133304i
\(905\) −205.715 + 205.715i −0.227310 + 0.227310i
\(906\) 103.175 0.113879
\(907\) 553.094i 0.609806i 0.952383 + 0.304903i \(0.0986240\pi\)
−0.952383 + 0.304903i \(0.901376\pi\)
\(908\) −226.154 + 226.154i −0.249068 + 0.249068i
\(909\) 207.243i 0.227990i
\(910\) −508.152 + 140.774i −0.558409 + 0.154696i
\(911\) 991.642 1.08852 0.544260 0.838917i \(-0.316810\pi\)
0.544260 + 0.838917i \(0.316810\pi\)
\(912\) 95.1320 + 95.1320i 0.104311 + 0.104311i
\(913\) 1600.92 1.75348
\(914\) 784.912i 0.858766i
\(915\) −757.938 757.938i −0.828348 0.828348i
\(916\) 69.6617 + 69.6617i 0.0760499 + 0.0760499i
\(917\) −619.773 + 619.773i −0.675871 + 0.675871i
\(918\) −55.6896 + 55.6896i −0.0606641 + 0.0606641i
\(919\) 91.7872 0.0998773 0.0499386 0.998752i \(-0.484097\pi\)
0.0499386 + 0.998752i \(0.484097\pi\)
\(920\) 489.328i 0.531879i
\(921\) −533.866 + 533.866i −0.579659 + 0.579659i
\(922\) 948.369i 1.02860i
\(923\) 1345.28 372.684i 1.45751 0.403775i
\(924\) −298.460 −0.323008
\(925\) 377.338 + 377.338i 0.407933 + 0.407933i
\(926\) 436.533 0.471418
\(927\) 291.792i 0.314770i
\(928\) −202.344 202.344i −0.218043 0.218043i
\(929\) 343.654 + 343.654i 0.369919 + 0.369919i 0.867447 0.497529i \(-0.165759\pi\)
−0.497529 + 0.867447i \(0.665759\pi\)
\(930\) −223.336 + 223.336i −0.240146 + 0.240146i
\(931\) 442.722 442.722i 0.475533 0.475533i
\(932\) 444.100 0.476502
\(933\) 89.4151i 0.0958361i
\(934\) −170.592 + 170.592i −0.182646 + 0.182646i
\(935\) 1580.38i 1.69025i
\(936\) 29.4497 + 106.305i 0.0314634 + 0.113574i
\(937\) −1140.31 −1.21698 −0.608488 0.793563i \(-0.708223\pi\)
−0.608488 + 0.793563i \(0.708223\pi\)
\(938\) −108.397 108.397i −0.115562 0.115562i
\(939\) 326.013 0.347192
\(940\) 979.804i 1.04235i
\(941\) −221.565 221.565i −0.235457 0.235457i 0.579509 0.814966i \(-0.303244\pi\)
−0.814966 + 0.579509i \(0.803244\pi\)
\(942\) −297.646 297.646i −0.315973 0.315973i
\(943\) 148.191 148.191i 0.157149 0.157149i
\(944\) −161.538 + 161.538i −0.171120 + 0.171120i
\(945\) −149.030 −0.157704
\(946\) 307.916i 0.325493i
\(947\) 169.150 169.150i 0.178617 0.178617i −0.612136 0.790753i \(-0.709689\pi\)
0.790753 + 0.612136i \(0.209689\pi\)
\(948\) 65.0206i 0.0685872i
\(949\) −69.7117 251.639i −0.0734580 0.265162i
\(950\) −661.485 −0.696300
\(951\) −267.978 267.978i −0.281786 0.281786i
\(952\) 124.093 0.130349
\(953\) 580.946i 0.609598i 0.952417 + 0.304799i \(0.0985892\pi\)
−0.952417 + 0.304799i \(0.901411\pi\)
\(954\) −14.0980 14.0980i −0.0147778 0.0147778i
\(955\) −1098.15 1098.15i −1.14989 1.14989i
\(956\) 539.656 539.656i 0.564493 0.564493i
\(957\) −1303.95 + 1303.95i −1.36254 + 1.36254i
\(958\) 81.1374 0.0846946
\(959\) 685.807i 0.715127i
\(960\) 68.6466 68.6466i 0.0715069 0.0715069i
\(961\) 622.290i 0.647544i
\(962\) 200.663 354.446i 0.208590 0.368447i
\(963\) −113.203 −0.117552
\(964\) 562.349 + 562.349i 0.583350 + 0.583350i
\(965\) −2532.35 −2.62419
\(966\) 247.603i 0.256318i
\(967\) 191.274 + 191.274i 0.197802 + 0.197802i 0.799057 0.601255i \(-0.205332\pi\)
−0.601255 + 0.799057i \(0.705332\pi\)
\(968\) −643.937 643.937i −0.665224 0.665224i
\(969\) −254.894 + 254.894i −0.263048 + 0.263048i
\(970\) 884.283 884.283i 0.911632 0.911632i
\(971\) 1344.57 1.38473 0.692364 0.721549i \(-0.256569\pi\)
0.692364 + 0.721549i \(0.256569\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 158.281 158.281i 0.162674 0.162674i
\(974\) 225.383i 0.231399i
\(975\) −471.973 267.200i −0.484075 0.274051i
\(976\) 353.317 0.362005
\(977\) −1006.88 1006.88i −1.03058 1.03058i −0.999517 0.0310628i \(-0.990111\pi\)
−0.0310628 0.999517i \(-0.509889\pi\)
\(978\) 572.107 0.584976
\(979\) 599.250i 0.612104i
\(980\) −319.465 319.465i −0.325985 0.325985i
\(981\) 301.477 + 301.477i 0.307316 + 0.307316i
\(982\) 400.234 400.234i 0.407570 0.407570i
\(983\) 541.766 541.766i 0.551135 0.551135i −0.375633 0.926768i \(-0.622575\pi\)
0.926768 + 0.375633i \(0.122575\pi\)
\(984\) −41.5787 −0.0422547
\(985\) 1374.56i 1.39549i
\(986\) 542.153 542.153i 0.549851 0.549851i
\(987\) 495.787i 0.502317i
\(988\) 134.793 + 486.561i 0.136430 + 0.492471i
\(989\) 255.448 0.258290
\(990\) −442.376 442.376i −0.446844 0.446844i
\(991\) −976.262 −0.985128 −0.492564 0.870276i \(-0.663940\pi\)
−0.492564 + 0.870276i \(0.663940\pi\)
\(992\) 104.109i 0.104949i
\(993\) 195.255 + 195.255i 0.196631 + 0.196631i
\(994\) −439.577 439.577i −0.442230 0.442230i
\(995\) −1282.94 + 1282.94i −1.28939 + 1.28939i
\(996\) −186.320 + 186.320i −0.187068 + 0.187068i
\(997\) 859.899 0.862487 0.431243 0.902236i \(-0.358075\pi\)
0.431243 + 0.902236i \(0.358075\pi\)
\(998\) 791.501i 0.793087i
\(999\) 81.4008 81.4008i 0.0814823 0.0814823i
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 78.3.f.b.73.4 yes 8
3.2 odd 2 234.3.i.e.73.1 8
4.3 odd 2 624.3.ba.c.385.2 8
13.5 odd 4 inner 78.3.f.b.31.4 8
13.8 odd 4 1014.3.f.i.577.3 8
13.12 even 2 1014.3.f.i.775.3 8
39.5 even 4 234.3.i.e.109.1 8
52.31 even 4 624.3.ba.c.577.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.f.b.31.4 8 13.5 odd 4 inner
78.3.f.b.73.4 yes 8 1.1 even 1 trivial
234.3.i.e.73.1 8 3.2 odd 2
234.3.i.e.109.1 8 39.5 even 4
624.3.ba.c.385.2 8 4.3 odd 2
624.3.ba.c.577.2 8 52.31 even 4
1014.3.f.i.577.3 8 13.8 odd 4
1014.3.f.i.775.3 8 13.12 even 2