Properties

Label 230.3.f.a.93.4
Level $230$
Weight $3$
Character 230.93
Analytic conductor $6.267$
Analytic rank $0$
Dimension $20$
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] = [230,3,Mod(47,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.47");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 52 x^{17} + 1020 x^{16} - 1316 x^{15} + 1352 x^{14} - 18724 x^{13} + 250686 x^{12} - 439644 x^{11} + 460536 x^{10} - 1833716 x^{9} + 16970128 x^{8} + \cdots + 88804 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 93.4
Root \(-0.454110 - 0.454110i\) of defining polynomial
Character \(\chi\) \(=\) 230.93
Dual form 230.3.f.a.47.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-0.454110 - 0.454110i) q^{3} -2.00000i q^{4} +(4.61282 + 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 + 8.21299i) q^{7} +(2.00000 + 2.00000i) q^{8} -8.58757i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-0.454110 - 0.454110i) q^{3} -2.00000i q^{4} +(4.61282 + 1.92922i) q^{5} +0.908220 q^{6} +(-8.21299 + 8.21299i) q^{7} +(2.00000 + 2.00000i) q^{8} -8.58757i q^{9} +(-6.54204 + 2.68360i) q^{10} -1.80844 q^{11} +(-0.908220 + 0.908220i) q^{12} +(12.1431 + 12.1431i) q^{13} -16.4260i q^{14} +(-1.21865 - 2.97081i) q^{15} -4.00000 q^{16} +(-13.2264 + 13.2264i) q^{17} +(8.58757 + 8.58757i) q^{18} +13.8065i q^{19} +(3.85844 - 9.22564i) q^{20} +7.45921 q^{21} +(1.80844 - 1.80844i) q^{22} +(-3.39116 - 3.39116i) q^{23} -1.81644i q^{24} +(17.5562 + 17.7983i) q^{25} -24.2862 q^{26} +(-7.98669 + 7.98669i) q^{27} +(16.4260 + 16.4260i) q^{28} +47.4104i q^{29} +(4.18945 + 1.75216i) q^{30} -56.5594 q^{31} +(4.00000 - 4.00000i) q^{32} +(0.821229 + 0.821229i) q^{33} -26.4528i q^{34} +(-53.7297 + 22.0404i) q^{35} -17.1751 q^{36} +(3.64057 - 3.64057i) q^{37} +(-13.8065 - 13.8065i) q^{38} -11.0286i q^{39} +(5.36720 + 13.0841i) q^{40} -8.30147 q^{41} +(-7.45921 + 7.45921i) q^{42} +(17.7220 + 17.7220i) q^{43} +3.61687i q^{44} +(16.5673 - 39.6129i) q^{45} +6.78233 q^{46} +(8.93900 - 8.93900i) q^{47} +(1.81644 + 1.81644i) q^{48} -85.9066i q^{49} +(-35.3545 - 0.242091i) q^{50} +12.0125 q^{51} +(24.2862 - 24.2862i) q^{52} +(24.9637 + 24.9637i) q^{53} -15.9734i q^{54} +(-8.34199 - 3.48888i) q^{55} -32.8520 q^{56} +(6.26965 - 6.26965i) q^{57} +(-47.4104 - 47.4104i) q^{58} -6.35948i q^{59} +(-5.94161 + 2.43730i) q^{60} +98.9683 q^{61} +(56.5594 - 56.5594i) q^{62} +(70.5297 + 70.5297i) q^{63} +8.00000i q^{64} +(32.5872 + 79.4406i) q^{65} -1.64246 q^{66} +(-16.0688 + 16.0688i) q^{67} +(26.4528 + 26.4528i) q^{68} +3.07992i q^{69} +(31.6894 - 75.7701i) q^{70} +110.405 q^{71} +(17.1751 - 17.1751i) q^{72} +(-72.6670 - 72.6670i) q^{73} +7.28114i q^{74} +(0.109936 - 16.0548i) q^{75} +27.6129 q^{76} +(14.8527 - 14.8527i) q^{77} +(11.0286 + 11.0286i) q^{78} -81.2609i q^{79} +(-18.4513 - 7.71689i) q^{80} -70.0344 q^{81} +(8.30147 - 8.30147i) q^{82} +(70.5250 + 70.5250i) q^{83} -14.9184i q^{84} +(-86.5276 + 35.4943i) q^{85} -35.4441 q^{86} +(21.5295 - 21.5295i) q^{87} +(-3.61687 - 3.61687i) q^{88} -131.148i q^{89} +(23.0456 + 56.1802i) q^{90} -199.462 q^{91} +(-6.78233 + 6.78233i) q^{92} +(25.6842 + 25.6842i) q^{93} +17.8780i q^{94} +(-26.6357 + 63.6867i) q^{95} -3.63288 q^{96} +(79.5123 - 79.5123i) q^{97} +(85.9066 + 85.9066i) q^{98} +15.5301i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 20 q^{2} + 4 q^{5} + 8 q^{7} + 40 q^{8} + 4 q^{10} + 56 q^{11} - 4 q^{13} - 48 q^{15} - 80 q^{16} - 72 q^{17} - 28 q^{18} - 16 q^{20} + 8 q^{21} - 56 q^{22} + 36 q^{25} + 8 q^{26} + 156 q^{27} - 16 q^{28} + 84 q^{30} - 212 q^{31} + 80 q^{32} - 100 q^{33} + 56 q^{36} + 72 q^{37} + 88 q^{38} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 120 q^{43} - 32 q^{45} + 8 q^{47} - 28 q^{50} + 64 q^{51} - 8 q^{52} - 244 q^{53} + 68 q^{55} + 32 q^{56} - 384 q^{57} - 188 q^{58} - 72 q^{60} + 328 q^{61} + 212 q^{62} + 172 q^{63} + 20 q^{65} + 200 q^{66} + 56 q^{67} + 144 q^{68} - 28 q^{70} - 92 q^{71} - 56 q^{72} + 144 q^{73} - 124 q^{75} - 176 q^{76} + 292 q^{77} - 208 q^{78} - 16 q^{80} - 84 q^{81} + 12 q^{82} - 72 q^{83} - 20 q^{85} - 240 q^{86} - 208 q^{87} + 112 q^{88} - 56 q^{90} - 192 q^{91} + 256 q^{93} - 96 q^{95} - 276 q^{97} + 104 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.500000 + 0.500000i
\(3\) −0.454110 0.454110i −0.151370 0.151370i 0.627360 0.778730i \(-0.284136\pi\)
−0.778730 + 0.627360i \(0.784136\pi\)
\(4\) 2.00000i 0.500000i
\(5\) 4.61282 + 1.92922i 0.922564 + 0.385844i
\(6\) 0.908220 0.151370
\(7\) −8.21299 + 8.21299i −1.17328 + 1.17328i −0.191863 + 0.981422i \(0.561453\pi\)
−0.981422 + 0.191863i \(0.938547\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 8.58757i 0.954174i
\(10\) −6.54204 + 2.68360i −0.654204 + 0.268360i
\(11\) −1.80844 −0.164403 −0.0822017 0.996616i \(-0.526195\pi\)
−0.0822017 + 0.996616i \(0.526195\pi\)
\(12\) −0.908220 + 0.908220i −0.0756850 + 0.0756850i
\(13\) 12.1431 + 12.1431i 0.934084 + 0.934084i 0.997958 0.0638744i \(-0.0203457\pi\)
−0.0638744 + 0.997958i \(0.520346\pi\)
\(14\) 16.4260i 1.17328i
\(15\) −1.21865 2.97081i −0.0812432 0.198054i
\(16\) −4.00000 −0.250000
\(17\) −13.2264 + 13.2264i −0.778023 + 0.778023i −0.979494 0.201471i \(-0.935428\pi\)
0.201471 + 0.979494i \(0.435428\pi\)
\(18\) 8.58757 + 8.58757i 0.477087 + 0.477087i
\(19\) 13.8065i 0.726656i 0.931661 + 0.363328i \(0.118360\pi\)
−0.931661 + 0.363328i \(0.881640\pi\)
\(20\) 3.85844 9.22564i 0.192922 0.461282i
\(21\) 7.45921 0.355200
\(22\) 1.80844 1.80844i 0.0822017 0.0822017i
\(23\) −3.39116 3.39116i −0.147442 0.147442i
\(24\) 1.81644i 0.0756850i
\(25\) 17.5562 + 17.7983i 0.702248 + 0.711932i
\(26\) −24.2862 −0.934084
\(27\) −7.98669 + 7.98669i −0.295803 + 0.295803i
\(28\) 16.4260 + 16.4260i 0.586642 + 0.586642i
\(29\) 47.4104i 1.63484i 0.576042 + 0.817420i \(0.304597\pi\)
−0.576042 + 0.817420i \(0.695403\pi\)
\(30\) 4.18945 + 1.75216i 0.139648 + 0.0584052i
\(31\) −56.5594 −1.82450 −0.912248 0.409637i \(-0.865655\pi\)
−0.912248 + 0.409637i \(0.865655\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) 0.821229 + 0.821229i 0.0248857 + 0.0248857i
\(34\) 26.4528i 0.778023i
\(35\) −53.7297 + 22.0404i −1.53514 + 0.629725i
\(36\) −17.1751 −0.477087
\(37\) 3.64057 3.64057i 0.0983938 0.0983938i −0.656196 0.754590i \(-0.727836\pi\)
0.754590 + 0.656196i \(0.227836\pi\)
\(38\) −13.8065 13.8065i −0.363328 0.363328i
\(39\) 11.0286i 0.282784i
\(40\) 5.36720 + 13.0841i 0.134180 + 0.327102i
\(41\) −8.30147 −0.202475 −0.101237 0.994862i \(-0.532280\pi\)
−0.101237 + 0.994862i \(0.532280\pi\)
\(42\) −7.45921 + 7.45921i −0.177600 + 0.177600i
\(43\) 17.7220 + 17.7220i 0.412140 + 0.412140i 0.882484 0.470343i \(-0.155870\pi\)
−0.470343 + 0.882484i \(0.655870\pi\)
\(44\) 3.61687i 0.0822017i
\(45\) 16.5673 39.6129i 0.368163 0.880287i
\(46\) 6.78233 0.147442
\(47\) 8.93900 8.93900i 0.190191 0.190191i −0.605587 0.795779i \(-0.707062\pi\)
0.795779 + 0.605587i \(0.207062\pi\)
\(48\) 1.81644 + 1.81644i 0.0378425 + 0.0378425i
\(49\) 85.9066i 1.75320i
\(50\) −35.3545 0.242091i −0.707090 0.00484182i
\(51\) 12.0125 0.235539
\(52\) 24.2862 24.2862i 0.467042 0.467042i
\(53\) 24.9637 + 24.9637i 0.471014 + 0.471014i 0.902243 0.431229i \(-0.141920\pi\)
−0.431229 + 0.902243i \(0.641920\pi\)
\(54\) 15.9734i 0.295803i
\(55\) −8.34199 3.48888i −0.151673 0.0634341i
\(56\) −32.8520 −0.586642
\(57\) 6.26965 6.26965i 0.109994 0.109994i
\(58\) −47.4104 47.4104i −0.817420 0.817420i
\(59\) 6.35948i 0.107788i −0.998547 0.0538939i \(-0.982837\pi\)
0.998547 0.0538939i \(-0.0171633\pi\)
\(60\) −5.94161 + 2.43730i −0.0990269 + 0.0406216i
\(61\) 98.9683 1.62243 0.811215 0.584748i \(-0.198806\pi\)
0.811215 + 0.584748i \(0.198806\pi\)
\(62\) 56.5594 56.5594i 0.912248 0.912248i
\(63\) 70.5297 + 70.5297i 1.11952 + 1.11952i
\(64\) 8.00000i 0.125000i
\(65\) 32.5872 + 79.4406i 0.501341 + 1.22216i
\(66\) −1.64246 −0.0248857
\(67\) −16.0688 + 16.0688i −0.239833 + 0.239833i −0.816781 0.576948i \(-0.804244\pi\)
0.576948 + 0.816781i \(0.304244\pi\)
\(68\) 26.4528 + 26.4528i 0.389012 + 0.389012i
\(69\) 3.07992i 0.0446366i
\(70\) 31.6894 75.7701i 0.452705 1.08243i
\(71\) 110.405 1.55500 0.777499 0.628884i \(-0.216488\pi\)
0.777499 + 0.628884i \(0.216488\pi\)
\(72\) 17.1751 17.1751i 0.238544 0.238544i
\(73\) −72.6670 72.6670i −0.995438 0.995438i 0.00455142 0.999990i \(-0.498551\pi\)
−0.999990 + 0.00455142i \(0.998551\pi\)
\(74\) 7.28114i 0.0983938i
\(75\) 0.109936 16.0548i 0.00146581 0.214064i
\(76\) 27.6129 0.363328
\(77\) 14.8527 14.8527i 0.192892 0.192892i
\(78\) 11.0286 + 11.0286i 0.141392 + 0.141392i
\(79\) 81.2609i 1.02862i −0.857605 0.514310i \(-0.828048\pi\)
0.857605 0.514310i \(-0.171952\pi\)
\(80\) −18.4513 7.71689i −0.230641 0.0964611i
\(81\) −70.0344 −0.864623
\(82\) 8.30147 8.30147i 0.101237 0.101237i
\(83\) 70.5250 + 70.5250i 0.849699 + 0.849699i 0.990095 0.140396i \(-0.0448376\pi\)
−0.140396 + 0.990095i \(0.544838\pi\)
\(84\) 14.9184i 0.177600i
\(85\) −86.5276 + 35.4943i −1.01797 + 0.417580i
\(86\) −35.4441 −0.412140
\(87\) 21.5295 21.5295i 0.247466 0.247466i
\(88\) −3.61687 3.61687i −0.0411008 0.0411008i
\(89\) 131.148i 1.47358i −0.676124 0.736788i \(-0.736342\pi\)
0.676124 0.736788i \(-0.263658\pi\)
\(90\) 23.0456 + 56.1802i 0.256062 + 0.624225i
\(91\) −199.462 −2.19189
\(92\) −6.78233 + 6.78233i −0.0737210 + 0.0737210i
\(93\) 25.6842 + 25.6842i 0.276174 + 0.276174i
\(94\) 17.8780i 0.190191i
\(95\) −26.6357 + 63.6867i −0.280376 + 0.670387i
\(96\) −3.63288 −0.0378425
\(97\) 79.5123 79.5123i 0.819715 0.819715i −0.166352 0.986066i \(-0.553199\pi\)
0.986066 + 0.166352i \(0.0531987\pi\)
\(98\) 85.9066 + 85.9066i 0.876598 + 0.876598i
\(99\) 15.5301i 0.156869i
\(100\) 35.5966 35.1124i 0.355966 0.351124i
\(101\) 106.466 1.05412 0.527060 0.849828i \(-0.323294\pi\)
0.527060 + 0.849828i \(0.323294\pi\)
\(102\) −12.0125 + 12.0125i −0.117769 + 0.117769i
\(103\) −4.25928 4.25928i −0.0413523 0.0413523i 0.686128 0.727481i \(-0.259309\pi\)
−0.727481 + 0.686128i \(0.759309\pi\)
\(104\) 48.5723i 0.467042i
\(105\) 34.4080 + 14.3905i 0.327695 + 0.137052i
\(106\) −49.9274 −0.471014
\(107\) −22.3097 + 22.3097i −0.208502 + 0.208502i −0.803631 0.595129i \(-0.797101\pi\)
0.595129 + 0.803631i \(0.297101\pi\)
\(108\) 15.9734 + 15.9734i 0.147902 + 0.147902i
\(109\) 151.792i 1.39258i −0.717759 0.696292i \(-0.754832\pi\)
0.717759 0.696292i \(-0.245168\pi\)
\(110\) 11.8309 4.85312i 0.107553 0.0441193i
\(111\) −3.30644 −0.0297877
\(112\) 32.8520 32.8520i 0.293321 0.293321i
\(113\) 35.4658 + 35.4658i 0.313857 + 0.313857i 0.846402 0.532545i \(-0.178764\pi\)
−0.532545 + 0.846402i \(0.678764\pi\)
\(114\) 12.5393i 0.109994i
\(115\) −9.10052 22.1851i −0.0791350 0.192914i
\(116\) 94.8207 0.817420
\(117\) 104.280 104.280i 0.891278 0.891278i
\(118\) 6.35948 + 6.35948i 0.0538939 + 0.0538939i
\(119\) 217.257i 1.82569i
\(120\) 3.50431 8.37891i 0.0292026 0.0698242i
\(121\) −117.730 −0.972972
\(122\) −98.9683 + 98.9683i −0.811215 + 0.811215i
\(123\) 3.76978 + 3.76978i 0.0306486 + 0.0306486i
\(124\) 113.119i 0.912248i
\(125\) 46.6468 + 115.970i 0.373174 + 0.927761i
\(126\) −141.059 −1.11952
\(127\) −0.468171 + 0.468171i −0.00368639 + 0.00368639i −0.708948 0.705261i \(-0.750830\pi\)
0.705261 + 0.708948i \(0.250830\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 16.0955i 0.124771i
\(130\) −112.028 46.8534i −0.861752 0.360411i
\(131\) −57.9083 −0.442048 −0.221024 0.975268i \(-0.570940\pi\)
−0.221024 + 0.975268i \(0.570940\pi\)
\(132\) 1.64246 1.64246i 0.0124429 0.0124429i
\(133\) −113.392 113.392i −0.852575 0.852575i
\(134\) 32.1376i 0.239833i
\(135\) −52.2493 + 21.4331i −0.387032 + 0.158763i
\(136\) −52.9056 −0.389012
\(137\) −90.9859 + 90.9859i −0.664131 + 0.664131i −0.956351 0.292220i \(-0.905606\pi\)
0.292220 + 0.956351i \(0.405606\pi\)
\(138\) −3.07992 3.07992i −0.0223183 0.0223183i
\(139\) 15.9583i 0.114808i −0.998351 0.0574041i \(-0.981718\pi\)
0.998351 0.0574041i \(-0.0182824\pi\)
\(140\) 44.0808 + 107.459i 0.314863 + 0.767568i
\(141\) −8.11858 −0.0575785
\(142\) −110.405 + 110.405i −0.777499 + 0.777499i
\(143\) −21.9600 21.9600i −0.153566 0.153566i
\(144\) 34.3503i 0.238544i
\(145\) −91.4651 + 218.695i −0.630794 + 1.50824i
\(146\) 145.334 0.995438
\(147\) −39.0110 + 39.0110i −0.265381 + 0.265381i
\(148\) −7.28114 7.28114i −0.0491969 0.0491969i
\(149\) 273.895i 1.83822i 0.394003 + 0.919109i \(0.371090\pi\)
−0.394003 + 0.919109i \(0.628910\pi\)
\(150\) 15.9449 + 16.1648i 0.106299 + 0.107765i
\(151\) −67.1415 −0.444646 −0.222323 0.974973i \(-0.571364\pi\)
−0.222323 + 0.974973i \(0.571364\pi\)
\(152\) −27.6129 + 27.6129i −0.181664 + 0.181664i
\(153\) 113.583 + 113.583i 0.742370 + 0.742370i
\(154\) 29.7054i 0.192892i
\(155\) −260.898 109.116i −1.68322 0.703972i
\(156\) −22.0572 −0.141392
\(157\) 20.7386 20.7386i 0.132093 0.132093i −0.637969 0.770062i \(-0.720225\pi\)
0.770062 + 0.637969i \(0.220225\pi\)
\(158\) 81.2609 + 81.2609i 0.514310 + 0.514310i
\(159\) 22.6725i 0.142595i
\(160\) 26.1682 10.7344i 0.163551 0.0670900i
\(161\) 55.7032 0.345983
\(162\) 70.0344 70.0344i 0.432311 0.432311i
\(163\) −5.13555 5.13555i −0.0315064 0.0315064i 0.691178 0.722685i \(-0.257092\pi\)
−0.722685 + 0.691178i \(0.757092\pi\)
\(164\) 16.6029i 0.101237i
\(165\) 2.20385 + 5.37252i 0.0133567 + 0.0325607i
\(166\) −141.050 −0.849699
\(167\) −4.29668 + 4.29668i −0.0257286 + 0.0257286i −0.719854 0.694125i \(-0.755791\pi\)
0.694125 + 0.719854i \(0.255791\pi\)
\(168\) 14.9184 + 14.9184i 0.0888001 + 0.0888001i
\(169\) 125.909i 0.745024i
\(170\) 51.0333 122.022i 0.300196 0.717776i
\(171\) 118.564 0.693357
\(172\) 35.4441 35.4441i 0.206070 0.206070i
\(173\) −59.7225 59.7225i −0.345217 0.345217i 0.513107 0.858324i \(-0.328494\pi\)
−0.858324 + 0.513107i \(0.828494\pi\)
\(174\) 43.0590i 0.247466i
\(175\) −290.366 1.98829i −1.65924 0.0113617i
\(176\) 7.23375 0.0411008
\(177\) −2.88790 + 2.88790i −0.0163158 + 0.0163158i
\(178\) 131.148 + 131.148i 0.736788 + 0.736788i
\(179\) 186.219i 1.04033i 0.854065 + 0.520166i \(0.174130\pi\)
−0.854065 + 0.520166i \(0.825870\pi\)
\(180\) −79.2258 33.1346i −0.440143 0.184081i
\(181\) 243.615 1.34594 0.672970 0.739670i \(-0.265018\pi\)
0.672970 + 0.739670i \(0.265018\pi\)
\(182\) 199.462 199.462i 1.09595 1.09595i
\(183\) −44.9425 44.9425i −0.245587 0.245587i
\(184\) 13.5647i 0.0737210i
\(185\) 23.8168 9.76983i 0.128739 0.0528099i
\(186\) −51.3684 −0.276174
\(187\) 23.9191 23.9191i 0.127910 0.127910i
\(188\) −17.8780 17.8780i −0.0950957 0.0950957i
\(189\) 131.189i 0.694123i
\(190\) −37.0510 90.3225i −0.195005 0.475381i
\(191\) 325.057 1.70187 0.850935 0.525271i \(-0.176036\pi\)
0.850935 + 0.525271i \(0.176036\pi\)
\(192\) 3.63288 3.63288i 0.0189212 0.0189212i
\(193\) 189.666 + 189.666i 0.982725 + 0.982725i 0.999853 0.0171285i \(-0.00545243\pi\)
−0.0171285 + 0.999853i \(0.505452\pi\)
\(194\) 159.025i 0.819715i
\(195\) 21.2766 50.8729i 0.109111 0.260887i
\(196\) −171.813 −0.876598
\(197\) 29.6698 29.6698i 0.150608 0.150608i −0.627781 0.778390i \(-0.716037\pi\)
0.778390 + 0.627781i \(0.216037\pi\)
\(198\) −15.5301 15.5301i −0.0784347 0.0784347i
\(199\) 71.7477i 0.360541i 0.983617 + 0.180271i \(0.0576974\pi\)
−0.983617 + 0.180271i \(0.942303\pi\)
\(200\) −0.484182 + 70.7090i −0.00242091 + 0.353545i
\(201\) 14.5940 0.0726071
\(202\) −106.466 + 106.466i −0.527060 + 0.527060i
\(203\) −389.381 389.381i −1.91813 1.91813i
\(204\) 24.0250i 0.117769i
\(205\) −38.2932 16.0154i −0.186796 0.0781238i
\(206\) 8.51856 0.0413523
\(207\) −29.1219 + 29.1219i −0.140685 + 0.140685i
\(208\) −48.5723 48.5723i −0.233521 0.233521i
\(209\) 24.9681i 0.119465i
\(210\) −48.7984 + 20.0175i −0.232373 + 0.0953215i
\(211\) 193.990 0.919385 0.459693 0.888078i \(-0.347960\pi\)
0.459693 + 0.888078i \(0.347960\pi\)
\(212\) 49.9274 49.9274i 0.235507 0.235507i
\(213\) −50.1360 50.1360i −0.235380 0.235380i
\(214\) 44.6194i 0.208502i
\(215\) 47.5588 + 115.938i 0.221204 + 0.539248i
\(216\) −31.9468 −0.147902
\(217\) 464.522 464.522i 2.14065 2.14065i
\(218\) 151.792 + 151.792i 0.696292 + 0.696292i
\(219\) 65.9976i 0.301359i
\(220\) −6.97775 + 16.6840i −0.0317171 + 0.0758363i
\(221\) −321.219 −1.45348
\(222\) 3.30644 3.30644i 0.0148939 0.0148939i
\(223\) −141.481 141.481i −0.634445 0.634445i 0.314735 0.949180i \(-0.398084\pi\)
−0.949180 + 0.314735i \(0.898084\pi\)
\(224\) 65.7040i 0.293321i
\(225\) 152.844 150.765i 0.679307 0.670067i
\(226\) −70.9316 −0.313857
\(227\) −299.127 + 299.127i −1.31774 + 1.31774i −0.402179 + 0.915561i \(0.631747\pi\)
−0.915561 + 0.402179i \(0.868253\pi\)
\(228\) −12.5393 12.5393i −0.0549970 0.0549970i
\(229\) 30.5265i 0.133304i 0.997776 + 0.0666518i \(0.0212317\pi\)
−0.997776 + 0.0666518i \(0.978768\pi\)
\(230\) 31.2857 + 13.0846i 0.136025 + 0.0568896i
\(231\) −13.4895 −0.0583961
\(232\) −94.8207 + 94.8207i −0.408710 + 0.408710i
\(233\) −52.7346 52.7346i −0.226329 0.226329i 0.584828 0.811157i \(-0.301162\pi\)
−0.811157 + 0.584828i \(0.801162\pi\)
\(234\) 208.559i 0.891278i
\(235\) 58.4793 23.9887i 0.248848 0.102079i
\(236\) −12.7190 −0.0538939
\(237\) −36.9014 + 36.9014i −0.155702 + 0.155702i
\(238\) 217.257 + 217.257i 0.912843 + 0.912843i
\(239\) 128.388i 0.537190i −0.963253 0.268595i \(-0.913441\pi\)
0.963253 0.268595i \(-0.0865593\pi\)
\(240\) 4.87459 + 11.8832i 0.0203108 + 0.0495134i
\(241\) 148.698 0.617006 0.308503 0.951223i \(-0.400172\pi\)
0.308503 + 0.951223i \(0.400172\pi\)
\(242\) 117.730 117.730i 0.486486 0.486486i
\(243\) 103.684 + 103.684i 0.426681 + 0.426681i
\(244\) 197.937i 0.811215i
\(245\) 165.733 396.271i 0.676460 1.61743i
\(246\) −7.53956 −0.0306486
\(247\) −167.653 + 167.653i −0.678757 + 0.678757i
\(248\) −113.119 113.119i −0.456124 0.456124i
\(249\) 64.0522i 0.257238i
\(250\) −162.617 69.3234i −0.650468 0.277294i
\(251\) 410.299 1.63466 0.817329 0.576172i \(-0.195454\pi\)
0.817329 + 0.576172i \(0.195454\pi\)
\(252\) 141.059 141.059i 0.559759 0.559759i
\(253\) 6.13271 + 6.13271i 0.0242400 + 0.0242400i
\(254\) 0.936342i 0.00368639i
\(255\) 55.4114 + 23.1747i 0.217300 + 0.0908813i
\(256\) 16.0000 0.0625000
\(257\) −222.112 + 222.112i −0.864250 + 0.864250i −0.991829 0.127578i \(-0.959280\pi\)
0.127578 + 0.991829i \(0.459280\pi\)
\(258\) 16.0955 + 16.0955i 0.0623857 + 0.0623857i
\(259\) 59.8000i 0.230888i
\(260\) 158.881 65.1743i 0.611081 0.250670i
\(261\) 407.140 1.55992
\(262\) 57.9083 57.9083i 0.221024 0.221024i
\(263\) 191.483 + 191.483i 0.728071 + 0.728071i 0.970235 0.242165i \(-0.0778574\pi\)
−0.242165 + 0.970235i \(0.577857\pi\)
\(264\) 3.28492i 0.0124429i
\(265\) 66.9926 + 163.314i 0.252802 + 0.616278i
\(266\) 226.785 0.852575
\(267\) −59.5557 + 59.5557i −0.223055 + 0.223055i
\(268\) 32.1376 + 32.1376i 0.119917 + 0.119917i
\(269\) 448.520i 1.66736i −0.552249 0.833679i \(-0.686230\pi\)
0.552249 0.833679i \(-0.313770\pi\)
\(270\) 30.8162 73.6823i 0.114134 0.272897i
\(271\) −355.709 −1.31258 −0.656289 0.754509i \(-0.727875\pi\)
−0.656289 + 0.754509i \(0.727875\pi\)
\(272\) 52.9056 52.9056i 0.194506 0.194506i
\(273\) 90.5778 + 90.5778i 0.331787 + 0.331787i
\(274\) 181.972i 0.664131i
\(275\) −31.7493 32.1871i −0.115452 0.117044i
\(276\) 6.15985 0.0223183
\(277\) −74.7381 + 74.7381i −0.269813 + 0.269813i −0.829025 0.559212i \(-0.811104\pi\)
0.559212 + 0.829025i \(0.311104\pi\)
\(278\) 15.9583 + 15.9583i 0.0574041 + 0.0574041i
\(279\) 485.708i 1.74089i
\(280\) −151.540 63.3787i −0.541215 0.226353i
\(281\) −29.5344 −0.105105 −0.0525523 0.998618i \(-0.516736\pi\)
−0.0525523 + 0.998618i \(0.516736\pi\)
\(282\) 8.11858 8.11858i 0.0287893 0.0287893i
\(283\) −337.330 337.330i −1.19198 1.19198i −0.976511 0.215466i \(-0.930873\pi\)
−0.215466 0.976511i \(-0.569127\pi\)
\(284\) 220.810i 0.777499i
\(285\) 41.0163 16.8252i 0.143917 0.0590359i
\(286\) 43.9200 0.153566
\(287\) 68.1800 68.1800i 0.237561 0.237561i
\(288\) −34.3503 34.3503i −0.119272 0.119272i
\(289\) 60.8752i 0.210641i
\(290\) −127.230 310.161i −0.438725 1.06952i
\(291\) −72.2147 −0.248160
\(292\) −145.334 + 145.334i −0.497719 + 0.497719i
\(293\) −0.725430 0.725430i −0.00247587 0.00247587i 0.705868 0.708344i \(-0.250557\pi\)
−0.708344 + 0.705868i \(0.750557\pi\)
\(294\) 78.0220i 0.265381i
\(295\) 12.2688 29.3351i 0.0415893 0.0994412i
\(296\) 14.5623 0.0491969
\(297\) 14.4434 14.4434i 0.0486311 0.0486311i
\(298\) −273.895 273.895i −0.919109 0.919109i
\(299\) 82.3584i 0.275446i
\(300\) −32.1097 0.219872i −0.107032 0.000732907i
\(301\) −291.102 −0.967116
\(302\) 67.1415 67.1415i 0.222323 0.222323i
\(303\) −48.3473 48.3473i −0.159562 0.159562i
\(304\) 55.2259i 0.181664i
\(305\) 456.523 + 190.932i 1.49680 + 0.626006i
\(306\) −227.165 −0.742370
\(307\) 312.017 312.017i 1.01634 1.01634i 0.0164770 0.999864i \(-0.494755\pi\)
0.999864 0.0164770i \(-0.00524503\pi\)
\(308\) −29.7054 29.7054i −0.0964460 0.0964460i
\(309\) 3.86836i 0.0125190i
\(310\) 370.014 151.783i 1.19359 0.489622i
\(311\) −442.383 −1.42245 −0.711227 0.702962i \(-0.751860\pi\)
−0.711227 + 0.702962i \(0.751860\pi\)
\(312\) 22.0572 22.0572i 0.0706961 0.0706961i
\(313\) −345.560 345.560i −1.10403 1.10403i −0.993920 0.110107i \(-0.964881\pi\)
−0.110107 0.993920i \(-0.535119\pi\)
\(314\) 41.4772i 0.132093i
\(315\) 189.273 + 461.408i 0.600867 + 1.46479i
\(316\) −162.522 −0.514310
\(317\) −446.526 + 446.526i −1.40860 + 1.40860i −0.641363 + 0.767238i \(0.721631\pi\)
−0.767238 + 0.641363i \(0.778369\pi\)
\(318\) 22.6725 + 22.6725i 0.0712973 + 0.0712973i
\(319\) 85.7387i 0.268773i
\(320\) −15.4338 + 36.9026i −0.0482305 + 0.115320i
\(321\) 20.2621 0.0631219
\(322\) −55.7032 + 55.7032i −0.172991 + 0.172991i
\(323\) −182.610 182.610i −0.565355 0.565355i
\(324\) 140.069i 0.432311i
\(325\) −2.93973 + 429.313i −0.00904533 + 1.32096i
\(326\) 10.2711 0.0315064
\(327\) −68.9301 + 68.9301i −0.210795 + 0.210795i
\(328\) −16.6029 16.6029i −0.0506187 0.0506187i
\(329\) 146.832i 0.446297i
\(330\) −7.57637 3.16867i −0.0229587 0.00960202i
\(331\) 541.509 1.63598 0.817989 0.575234i \(-0.195089\pi\)
0.817989 + 0.575234i \(0.195089\pi\)
\(332\) 141.050 141.050i 0.424850 0.424850i
\(333\) −31.2637 31.2637i −0.0938848 0.0938848i
\(334\) 8.59336i 0.0257286i
\(335\) −105.123 + 43.1223i −0.313800 + 0.128723i
\(336\) −29.8368 −0.0888001
\(337\) 50.2998 50.2998i 0.149258 0.149258i −0.628529 0.777786i \(-0.716343\pi\)
0.777786 + 0.628529i \(0.216343\pi\)
\(338\) −125.909 125.909i −0.372512 0.372512i
\(339\) 32.2107i 0.0950169i
\(340\) 70.9887 + 173.055i 0.208790 + 0.508986i
\(341\) 102.284 0.299953
\(342\) −118.564 + 118.564i −0.346678 + 0.346678i
\(343\) 303.113 + 303.113i 0.883712 + 0.883712i
\(344\) 70.8881i 0.206070i
\(345\) −5.94185 + 14.2071i −0.0172228 + 0.0411801i
\(346\) 119.445 0.345217
\(347\) 286.439 286.439i 0.825472 0.825472i −0.161414 0.986887i \(-0.551606\pi\)
0.986887 + 0.161414i \(0.0516056\pi\)
\(348\) −43.0590 43.0590i −0.123733 0.123733i
\(349\) 240.906i 0.690275i −0.938552 0.345137i \(-0.887832\pi\)
0.938552 0.345137i \(-0.112168\pi\)
\(350\) 292.355 288.378i 0.835299 0.823937i
\(351\) −193.966 −0.552610
\(352\) −7.23375 + 7.23375i −0.0205504 + 0.0205504i
\(353\) 189.988 + 189.988i 0.538209 + 0.538209i 0.923003 0.384794i \(-0.125727\pi\)
−0.384794 + 0.923003i \(0.625727\pi\)
\(354\) 5.77581i 0.0163158i
\(355\) 509.278 + 212.995i 1.43459 + 0.599987i
\(356\) −262.297 −0.736788
\(357\) −98.6584 + 98.6584i −0.276354 + 0.276354i
\(358\) −186.219 186.219i −0.520166 0.520166i
\(359\) 467.461i 1.30212i 0.759026 + 0.651060i \(0.225676\pi\)
−0.759026 + 0.651060i \(0.774324\pi\)
\(360\) 112.360 46.0912i 0.312112 0.128031i
\(361\) 170.382 0.471971
\(362\) −243.615 + 243.615i −0.672970 + 0.672970i
\(363\) 53.4622 + 53.4622i 0.147279 + 0.147279i
\(364\) 398.924i 1.09595i
\(365\) −195.009 475.390i −0.534271 1.30244i
\(366\) 89.8850 0.245587
\(367\) 396.041 396.041i 1.07913 1.07913i 0.0825436 0.996587i \(-0.473696\pi\)
0.996587 0.0825436i \(-0.0263044\pi\)
\(368\) 13.5647 + 13.5647i 0.0368605 + 0.0368605i
\(369\) 71.2895i 0.193196i
\(370\) −14.0469 + 33.5866i −0.0379647 + 0.0907746i
\(371\) −410.054 −1.10527
\(372\) 51.3684 51.3684i 0.138087 0.138087i
\(373\) −61.2680 61.2680i −0.164257 0.164257i 0.620192 0.784450i \(-0.287055\pi\)
−0.784450 + 0.620192i \(0.787055\pi\)
\(374\) 47.8382i 0.127910i
\(375\) 31.4804 73.8460i 0.0839479 0.196923i
\(376\) 35.7560 0.0950957
\(377\) −575.708 + 575.708i −1.52708 + 1.52708i
\(378\) 131.189 + 131.189i 0.347062 + 0.347062i
\(379\) 2.27599i 0.00600525i 0.999995 + 0.00300262i \(0.000955767\pi\)
−0.999995 + 0.00300262i \(0.999044\pi\)
\(380\) 127.373 + 53.2715i 0.335193 + 0.140188i
\(381\) 0.425202 0.00111602
\(382\) −325.057 + 325.057i −0.850935 + 0.850935i
\(383\) 455.092 + 455.092i 1.18823 + 1.18823i 0.977557 + 0.210673i \(0.0675655\pi\)
0.210673 + 0.977557i \(0.432435\pi\)
\(384\) 7.26576i 0.0189212i
\(385\) 97.1669 39.8586i 0.252381 0.103529i
\(386\) −379.332 −0.982725
\(387\) 152.189 152.189i 0.393254 0.393254i
\(388\) −159.025 159.025i −0.409857 0.409857i
\(389\) 94.4517i 0.242806i 0.992603 + 0.121403i \(0.0387394\pi\)
−0.992603 + 0.121403i \(0.961261\pi\)
\(390\) 29.5963 + 72.1495i 0.0758880 + 0.184999i
\(391\) 89.7058 0.229427
\(392\) 171.813 171.813i 0.438299 0.438299i
\(393\) 26.2967 + 26.2967i 0.0669128 + 0.0669128i
\(394\) 59.3397i 0.150608i
\(395\) 156.770 374.842i 0.396887 0.948967i
\(396\) 31.0602 0.0784347
\(397\) −166.649 + 166.649i −0.419771 + 0.419771i −0.885125 0.465354i \(-0.845927\pi\)
0.465354 + 0.885125i \(0.345927\pi\)
\(398\) −71.7477 71.7477i −0.180271 0.180271i
\(399\) 102.985i 0.258108i
\(400\) −70.2248 71.1932i −0.175562 0.177983i
\(401\) −56.3098 −0.140424 −0.0702118 0.997532i \(-0.522368\pi\)
−0.0702118 + 0.997532i \(0.522368\pi\)
\(402\) −14.5940 + 14.5940i −0.0363035 + 0.0363035i
\(403\) −686.806 686.806i −1.70423 1.70423i
\(404\) 212.932i 0.527060i
\(405\) −323.056 135.112i −0.797670 0.333610i
\(406\) 778.762 1.91813
\(407\) −6.58374 + 6.58374i −0.0161763 + 0.0161763i
\(408\) 24.0250 + 24.0250i 0.0588847 + 0.0588847i
\(409\) 617.869i 1.51068i 0.655331 + 0.755342i \(0.272529\pi\)
−0.655331 + 0.755342i \(0.727471\pi\)
\(410\) 54.3086 22.2778i 0.132460 0.0543361i
\(411\) 82.6352 0.201059
\(412\) −8.51856 + 8.51856i −0.0206761 + 0.0206761i
\(413\) 52.2304 + 52.2304i 0.126466 + 0.126466i
\(414\) 58.2437i 0.140685i
\(415\) 189.261 + 461.378i 0.456050 + 1.11175i
\(416\) 97.1447 0.233521
\(417\) −7.24684 + 7.24684i −0.0173785 + 0.0173785i
\(418\) 24.9681 + 24.9681i 0.0597324 + 0.0597324i
\(419\) 327.397i 0.781377i 0.920523 + 0.390688i \(0.127763\pi\)
−0.920523 + 0.390688i \(0.872237\pi\)
\(420\) 28.7809 68.8159i 0.0685260 0.163847i
\(421\) 271.135 0.644026 0.322013 0.946735i \(-0.395641\pi\)
0.322013 + 0.946735i \(0.395641\pi\)
\(422\) −193.990 + 193.990i −0.459693 + 0.459693i
\(423\) −76.7642 76.7642i −0.181476 0.181476i
\(424\) 99.8549i 0.235507i
\(425\) −467.613 3.20199i −1.10027 0.00753410i
\(426\) 100.272 0.235380
\(427\) −812.826 + 812.826i −1.90357 + 1.90357i
\(428\) 44.6194 + 44.6194i 0.104251 + 0.104251i
\(429\) 19.9445i 0.0464907i
\(430\) −163.497 68.3795i −0.380226 0.159022i
\(431\) 148.281 0.344039 0.172019 0.985094i \(-0.444971\pi\)
0.172019 + 0.985094i \(0.444971\pi\)
\(432\) 31.9468 31.9468i 0.0739508 0.0739508i
\(433\) 437.637 + 437.637i 1.01071 + 1.01071i 0.999942 + 0.0107659i \(0.00342697\pi\)
0.0107659 + 0.999942i \(0.496573\pi\)
\(434\) 929.044i 2.14065i
\(435\) 140.847 57.7766i 0.323786 0.132820i
\(436\) −303.583 −0.696292
\(437\) 46.8200 46.8200i 0.107140 0.107140i
\(438\) −65.9976 65.9976i −0.150679 0.150679i
\(439\) 387.950i 0.883712i −0.897086 0.441856i \(-0.854320\pi\)
0.897086 0.441856i \(-0.145680\pi\)
\(440\) −9.70624 23.6617i −0.0220596 0.0537767i
\(441\) −737.728 −1.67285
\(442\) 321.219 321.219i 0.726739 0.726739i
\(443\) 33.5070 + 33.5070i 0.0756366 + 0.0756366i 0.743913 0.668276i \(-0.232968\pi\)
−0.668276 + 0.743913i \(0.732968\pi\)
\(444\) 6.61288i 0.0148939i
\(445\) 253.014 604.963i 0.568571 1.35947i
\(446\) 282.962 0.634445
\(447\) 124.378 124.378i 0.278251 0.278251i
\(448\) −65.7040 65.7040i −0.146661 0.146661i
\(449\) 90.3725i 0.201275i −0.994923 0.100638i \(-0.967912\pi\)
0.994923 0.100638i \(-0.0320883\pi\)
\(450\) −2.07897 + 303.609i −0.00461994 + 0.674687i
\(451\) 15.0127 0.0332876
\(452\) 70.9316 70.9316i 0.156928 0.156928i
\(453\) 30.4896 + 30.4896i 0.0673060 + 0.0673060i
\(454\) 598.254i 1.31774i
\(455\) −920.083 384.807i −2.02216 0.845729i
\(456\) 25.0786 0.0549970
\(457\) −432.641 + 432.641i −0.946698 + 0.946698i −0.998650 0.0519513i \(-0.983456\pi\)
0.0519513 + 0.998650i \(0.483456\pi\)
\(458\) −30.5265 30.5265i −0.0666518 0.0666518i
\(459\) 211.270i 0.460284i
\(460\) −44.3703 + 18.2010i −0.0964571 + 0.0395675i
\(461\) 477.708 1.03624 0.518121 0.855307i \(-0.326632\pi\)
0.518121 + 0.855307i \(0.326632\pi\)
\(462\) 13.4895 13.4895i 0.0291981 0.0291981i
\(463\) −509.566 509.566i −1.10058 1.10058i −0.994341 0.106234i \(-0.966121\pi\)
−0.106234 0.994341i \(-0.533879\pi\)
\(464\) 189.641i 0.408710i
\(465\) 68.9260 + 168.027i 0.148228 + 0.361348i
\(466\) 105.469 0.226329
\(467\) 508.548 508.548i 1.08897 1.08897i 0.0933331 0.995635i \(-0.470248\pi\)
0.995635 0.0933331i \(-0.0297522\pi\)
\(468\) −208.559 208.559i −0.445639 0.445639i
\(469\) 263.946i 0.562785i
\(470\) −34.4906 + 82.4680i −0.0733843 + 0.175464i
\(471\) −18.8352 −0.0399898
\(472\) 12.7190 12.7190i 0.0269470 0.0269470i
\(473\) −32.0492 32.0492i −0.0677573 0.0677573i
\(474\) 73.8028i 0.155702i
\(475\) −245.732 + 242.389i −0.517330 + 0.510293i
\(476\) −434.513 −0.912843
\(477\) 214.378 214.378i 0.449429 0.449429i
\(478\) 128.388 + 128.388i 0.268595 + 0.268595i
\(479\) 213.247i 0.445192i −0.974911 0.222596i \(-0.928547\pi\)
0.974911 0.222596i \(-0.0714531\pi\)
\(480\) −16.7578 7.00863i −0.0349121 0.0146013i
\(481\) 88.4155 0.183816
\(482\) −148.698 + 148.698i −0.308503 + 0.308503i
\(483\) −25.2954 25.2954i −0.0523714 0.0523714i
\(484\) 235.459i 0.486486i
\(485\) 520.173 213.379i 1.07252 0.439957i
\(486\) −207.367 −0.426681
\(487\) −444.728 + 444.728i −0.913198 + 0.913198i −0.996523 0.0833241i \(-0.973446\pi\)
0.0833241 + 0.996523i \(0.473446\pi\)
\(488\) 197.937 + 197.937i 0.405608 + 0.405608i
\(489\) 4.66421i 0.00953826i
\(490\) 230.539 + 562.004i 0.470487 + 1.14695i
\(491\) 488.473 0.994854 0.497427 0.867506i \(-0.334278\pi\)
0.497427 + 0.867506i \(0.334278\pi\)
\(492\) 7.53956 7.53956i 0.0153243 0.0153243i
\(493\) −627.068 627.068i −1.27194 1.27194i
\(494\) 335.306i 0.678757i
\(495\) −29.9610 + 71.6374i −0.0605272 + 0.144722i
\(496\) 226.238 0.456124
\(497\) −906.755 + 906.755i −1.82446 + 1.82446i
\(498\) 64.0522 + 64.0522i 0.128619 + 0.128619i
\(499\) 727.731i 1.45838i 0.684312 + 0.729189i \(0.260103\pi\)
−0.684312 + 0.729189i \(0.739897\pi\)
\(500\) 231.940 93.2935i 0.463881 0.186587i
\(501\) 3.90233 0.00778909
\(502\) −410.299 + 410.299i −0.817329 + 0.817329i
\(503\) 146.384 + 146.384i 0.291021 + 0.291021i 0.837484 0.546463i \(-0.184026\pi\)
−0.546463 + 0.837484i \(0.684026\pi\)
\(504\) 282.119i 0.559759i
\(505\) 491.109 + 205.397i 0.972493 + 0.406726i
\(506\) −12.2654 −0.0242400
\(507\) 57.1766 57.1766i 0.112774 0.112774i
\(508\) 0.936342 + 0.936342i 0.00184319 + 0.00184319i
\(509\) 629.870i 1.23747i −0.785601 0.618733i \(-0.787646\pi\)
0.785601 0.618733i \(-0.212354\pi\)
\(510\) −78.5861 + 32.2367i −0.154090 + 0.0632091i
\(511\) 1193.63 2.33587
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −110.268 110.268i −0.214947 0.214947i
\(514\) 444.225i 0.864250i
\(515\) −11.4302 27.8644i −0.0221946 0.0541056i
\(516\) −32.1910 −0.0623857
\(517\) −16.1656 + 16.1656i −0.0312681 + 0.0312681i
\(518\) −59.8000 59.8000i −0.115444 0.115444i
\(519\) 54.2412i 0.104511i
\(520\) −93.7068 + 224.055i −0.180205 + 0.430876i
\(521\) −299.772 −0.575379 −0.287690 0.957724i \(-0.592887\pi\)
−0.287690 + 0.957724i \(0.592887\pi\)
\(522\) −407.140 + 407.140i −0.779961 + 0.779961i
\(523\) 189.039 + 189.039i 0.361451 + 0.361451i 0.864347 0.502896i \(-0.167732\pi\)
−0.502896 + 0.864347i \(0.667732\pi\)
\(524\) 115.817i 0.221024i
\(525\) 130.955 + 132.761i 0.249439 + 0.252878i
\(526\) −382.965 −0.728071
\(527\) 748.077 748.077i 1.41950 1.41950i
\(528\) −3.28492 3.28492i −0.00622143 0.00622143i
\(529\) 23.0000i 0.0434783i
\(530\) −230.306 96.3211i −0.434540 0.181738i
\(531\) −54.6125 −0.102848
\(532\) −226.785 + 226.785i −0.426287 + 0.426287i
\(533\) −100.806 100.806i −0.189129 0.189129i
\(534\) 119.111i 0.223055i
\(535\) −145.951 + 59.8703i −0.272806 + 0.111907i
\(536\) −64.2753 −0.119917
\(537\) 84.5641 84.5641i 0.157475 0.157475i
\(538\) 448.520 + 448.520i 0.833679 + 0.833679i
\(539\) 155.357i 0.288231i
\(540\) 42.8661 + 104.499i 0.0793817 + 0.193516i
\(541\) −428.185 −0.791470 −0.395735 0.918365i \(-0.629510\pi\)
−0.395735 + 0.918365i \(0.629510\pi\)
\(542\) 355.709 355.709i 0.656289 0.656289i
\(543\) −110.628 110.628i −0.203735 0.203735i
\(544\) 105.811i 0.194506i
\(545\) 292.840 700.187i 0.537320 1.28475i
\(546\) −181.156 −0.331787
\(547\) 402.240 402.240i 0.735356 0.735356i −0.236319 0.971676i \(-0.575941\pi\)
0.971676 + 0.236319i \(0.0759411\pi\)
\(548\) 181.972 + 181.972i 0.332065 + 0.332065i
\(549\) 849.897i 1.54808i
\(550\) 63.9364 + 0.437807i 0.116248 + 0.000796012i
\(551\) −654.570 −1.18797
\(552\) −6.15985 + 6.15985i −0.0111591 + 0.0111591i
\(553\) 667.395 + 667.395i 1.20686 + 1.20686i
\(554\) 149.476i 0.269813i
\(555\) −15.2520 6.37885i −0.0274811 0.0114934i
\(556\) −31.9167 −0.0574041
\(557\) −133.006 + 133.006i −0.238789 + 0.238789i −0.816349 0.577560i \(-0.804005\pi\)
0.577560 + 0.816349i \(0.304005\pi\)
\(558\) −485.708 485.708i −0.870444 0.870444i
\(559\) 430.400i 0.769947i
\(560\) 214.919 88.1615i 0.383784 0.157431i
\(561\) −21.7238 −0.0387234
\(562\) 29.5344 29.5344i 0.0525523 0.0525523i
\(563\) −490.785 490.785i −0.871733 0.871733i 0.120929 0.992661i \(-0.461413\pi\)
−0.992661 + 0.120929i \(0.961413\pi\)
\(564\) 16.2372i 0.0287893i
\(565\) 95.1760 + 232.019i 0.168453 + 0.410653i
\(566\) 674.659 1.19198
\(567\) 575.192 575.192i 1.01445 1.01445i
\(568\) 220.810 + 220.810i 0.388750 + 0.388750i
\(569\) 258.800i 0.454834i 0.973798 + 0.227417i \(0.0730280\pi\)
−0.973798 + 0.227417i \(0.926972\pi\)
\(570\) −24.1911 + 57.8416i −0.0424405 + 0.101476i
\(571\) −122.892 −0.215223 −0.107612 0.994193i \(-0.534320\pi\)
−0.107612 + 0.994193i \(0.534320\pi\)
\(572\) −43.9200 + 43.9200i −0.0767832 + 0.0767832i
\(573\) −147.612 147.612i −0.257612 0.257612i
\(574\) 136.360i 0.237561i
\(575\) 0.820971 119.893i 0.00142778 0.208510i
\(576\) 68.7005 0.119272
\(577\) −86.1991 + 86.1991i −0.149392 + 0.149392i −0.777846 0.628454i \(-0.783688\pi\)
0.628454 + 0.777846i \(0.283688\pi\)
\(578\) 60.8752 + 60.8752i 0.105320 + 0.105320i
\(579\) 172.258i 0.297510i
\(580\) 437.391 + 182.930i 0.754122 + 0.315397i
\(581\) −1158.44 −1.99388
\(582\) 72.2147 72.2147i 0.124080 0.124080i
\(583\) −45.1453 45.1453i −0.0774362 0.0774362i
\(584\) 290.668i 0.497719i
\(585\) 682.201 279.844i 1.16616 0.478367i
\(586\) 1.45086 0.00247587
\(587\) 41.7886 41.7886i 0.0711901 0.0711901i −0.670615 0.741805i \(-0.733970\pi\)
0.741805 + 0.670615i \(0.233970\pi\)
\(588\) 78.0220 + 78.0220i 0.132691 + 0.132691i
\(589\) 780.885i 1.32578i
\(590\) 17.0663 + 41.6040i 0.0289259 + 0.0705152i
\(591\) −26.9467 −0.0455952
\(592\) −14.5623 + 14.5623i −0.0245985 + 0.0245985i
\(593\) 0.797812 + 0.797812i 0.00134538 + 0.00134538i 0.707779 0.706434i \(-0.249697\pi\)
−0.706434 + 0.707779i \(0.749697\pi\)
\(594\) 28.8869i 0.0486311i
\(595\) 419.136 1002.17i 0.704431 1.68431i
\(596\) 547.789 0.919109
\(597\) 32.5814 32.5814i 0.0545752 0.0545752i
\(598\) 82.3584 + 82.3584i 0.137723 + 0.137723i
\(599\) 547.221i 0.913558i −0.889580 0.456779i \(-0.849003\pi\)
0.889580 0.456779i \(-0.150997\pi\)
\(600\) 32.3295 31.8898i 0.0538826 0.0531497i
\(601\) −798.410 −1.32847 −0.664235 0.747524i \(-0.731243\pi\)
−0.664235 + 0.747524i \(0.731243\pi\)
\(602\) 291.102 291.102i 0.483558 0.483558i
\(603\) 137.992 + 137.992i 0.228843 + 0.228843i
\(604\) 134.283i 0.222323i
\(605\) −543.065 227.126i −0.897628 0.375416i
\(606\) 96.6947 0.159562
\(607\) 431.327 431.327i 0.710588 0.710588i −0.256070 0.966658i \(-0.582428\pi\)
0.966658 + 0.256070i \(0.0824279\pi\)
\(608\) 55.2259 + 55.2259i 0.0908320 + 0.0908320i
\(609\) 353.644i 0.580696i
\(610\) −647.454 + 265.591i −1.06140 + 0.435395i
\(611\) 217.094 0.355309
\(612\) 227.165 227.165i 0.371185 0.371185i
\(613\) −538.393 538.393i −0.878293 0.878293i 0.115065 0.993358i \(-0.463292\pi\)
−0.993358 + 0.115065i \(0.963292\pi\)
\(614\) 624.034i 1.01634i
\(615\) 10.1166 + 24.6621i 0.0164497 + 0.0401009i
\(616\) 59.4107 0.0964460
\(617\) 535.160 535.160i 0.867358 0.867358i −0.124821 0.992179i \(-0.539836\pi\)
0.992179 + 0.124821i \(0.0398358\pi\)
\(618\) −3.86836 3.86836i −0.00625949 0.00625949i
\(619\) 103.368i 0.166991i 0.996508 + 0.0834957i \(0.0266085\pi\)
−0.996508 + 0.0834957i \(0.973392\pi\)
\(620\) −218.231 + 521.797i −0.351986 + 0.841608i
\(621\) 54.1684 0.0872276
\(622\) 442.383 442.383i 0.711227 0.711227i
\(623\) 1077.12 + 1077.12i 1.72892 + 1.72892i
\(624\) 44.1144i 0.0706961i
\(625\) −8.55901 + 624.941i −0.0136944 + 0.999906i
\(626\) 691.121 1.10403
\(627\) −11.3383 + 11.3383i −0.0180834 + 0.0180834i
\(628\) −41.4772 41.4772i −0.0660465 0.0660465i
\(629\) 96.3033i 0.153105i
\(630\) −650.681 272.135i −1.03283 0.431960i
\(631\) 914.802 1.44977 0.724883 0.688872i \(-0.241894\pi\)
0.724883 + 0.688872i \(0.241894\pi\)
\(632\) 162.522 162.522i 0.257155 0.257155i
\(633\) −88.0929 88.0929i −0.139167 0.139167i
\(634\) 893.053i 1.40860i
\(635\) −3.06279 + 1.25638i −0.00482330 + 0.00197856i
\(636\) −45.3451 −0.0712973
\(637\) 1043.17 1043.17i 1.63763 1.63763i
\(638\) 85.7387 + 85.7387i 0.134387 + 0.134387i
\(639\) 948.110i 1.48374i
\(640\) −21.4688 52.3363i −0.0335450 0.0817755i
\(641\) 629.609 0.982230 0.491115 0.871095i \(-0.336590\pi\)
0.491115 + 0.871095i \(0.336590\pi\)
\(642\) −20.2621 + 20.2621i −0.0315610 + 0.0315610i
\(643\) 469.588 + 469.588i 0.730307 + 0.730307i 0.970681 0.240373i \(-0.0772698\pi\)
−0.240373 + 0.970681i \(0.577270\pi\)
\(644\) 111.406i 0.172991i
\(645\) 31.0518 74.2457i 0.0481423 0.115110i
\(646\) 365.220 0.565355
\(647\) −102.877 + 102.877i −0.159007 + 0.159007i −0.782126 0.623120i \(-0.785865\pi\)
0.623120 + 0.782126i \(0.285865\pi\)
\(648\) −140.069 140.069i −0.216156 0.216156i
\(649\) 11.5007i 0.0177207i
\(650\) −426.373 432.253i −0.655959 0.665004i
\(651\) −421.888 −0.648062
\(652\) −10.2711 + 10.2711i −0.0157532 + 0.0157532i
\(653\) 108.889 + 108.889i 0.166752 + 0.166752i 0.785550 0.618798i \(-0.212380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(654\) 137.860i 0.210795i
\(655\) −267.120 111.718i −0.407817 0.170562i
\(656\) 33.2059 0.0506187
\(657\) −624.033 + 624.033i −0.949822 + 0.949822i
\(658\) −146.832 146.832i −0.223149 0.223149i
\(659\) 534.158i 0.810558i 0.914193 + 0.405279i \(0.132826\pi\)
−0.914193 + 0.405279i \(0.867174\pi\)
\(660\) 10.7450 4.40770i 0.0162804 0.00667833i
\(661\) −596.050 −0.901740 −0.450870 0.892590i \(-0.648886\pi\)
−0.450870 + 0.892590i \(0.648886\pi\)
\(662\) −541.509 + 541.509i −0.817989 + 0.817989i
\(663\) 145.869 + 145.869i 0.220013 + 0.220013i
\(664\) 282.100i 0.424850i
\(665\) −304.300 741.818i −0.457594 1.11552i
\(666\) 62.5273 0.0938848
\(667\) 160.776 160.776i 0.241044 0.241044i
\(668\) 8.59336 + 8.59336i 0.0128643 + 0.0128643i
\(669\) 128.496i 0.192072i
\(670\) 62.0006 148.245i 0.0925382 0.221261i
\(671\) −178.978 −0.266733
\(672\) 29.8368 29.8368i 0.0444000 0.0444000i
\(673\) 159.122 + 159.122i 0.236437 + 0.236437i 0.815373 0.578936i \(-0.196532\pi\)
−0.578936 + 0.815373i \(0.696532\pi\)
\(674\) 100.600i 0.149258i
\(675\) −282.366 1.93351i −0.418319 0.00286445i
\(676\) 251.818 0.372512
\(677\) −209.613 + 209.613i −0.309621 + 0.309621i −0.844762 0.535142i \(-0.820258\pi\)
0.535142 + 0.844762i \(0.320258\pi\)
\(678\) 32.2107 + 32.2107i 0.0475085 + 0.0475085i
\(679\) 1306.07i 1.92352i
\(680\) −244.044 102.067i −0.358888 0.150098i
\(681\) 271.673 0.398933
\(682\) −102.284 + 102.284i −0.149977 + 0.149977i
\(683\) 17.8410 + 17.8410i 0.0261215 + 0.0261215i 0.720047 0.693925i \(-0.244120\pi\)
−0.693925 + 0.720047i \(0.744120\pi\)
\(684\) 237.128i 0.346678i
\(685\) −595.234 + 244.170i −0.868954 + 0.356452i
\(686\) −606.227 −0.883712
\(687\) 13.8624 13.8624i 0.0201782 0.0201782i
\(688\) −70.8881 70.8881i −0.103035 0.103035i
\(689\) 606.273i 0.879932i
\(690\) −8.26528 20.1490i −0.0119787 0.0292014i
\(691\) 1004.98 1.45438 0.727190 0.686436i \(-0.240826\pi\)
0.727190 + 0.686436i \(0.240826\pi\)
\(692\) −119.445 + 119.445i −0.172608 + 0.172608i
\(693\) −127.548 127.548i −0.184053 0.184053i
\(694\) 572.878i 0.825472i
\(695\) 30.7872 73.6130i 0.0442981 0.105918i
\(696\) 86.1181 0.123733
\(697\) 109.799 109.799i 0.157530 0.157530i
\(698\) 240.906 + 240.906i 0.345137 + 0.345137i
\(699\) 47.8946i 0.0685188i
\(700\) −3.97659 + 580.733i −0.00568084 + 0.829618i
\(701\) −243.834 −0.347838 −0.173919 0.984760i \(-0.555643\pi\)
−0.173919 + 0.984760i \(0.555643\pi\)
\(702\) 193.966 193.966i 0.276305 0.276305i
\(703\) 50.2634 + 50.2634i 0.0714985 + 0.0714985i
\(704\) 14.4675i 0.0205504i
\(705\) −37.4495 15.6625i −0.0531199 0.0222164i
\(706\) −379.976 −0.538209
\(707\) −874.406 + 874.406i −1.23678 + 1.23678i
\(708\) 5.77581 + 5.77581i 0.00815792 + 0.00815792i
\(709\) 57.7605i 0.0814675i 0.999170 + 0.0407338i \(0.0129695\pi\)
−0.999170 + 0.0407338i \(0.987030\pi\)
\(710\) −722.273 + 296.282i −1.01729 + 0.417299i
\(711\) −697.834 −0.981482
\(712\) 262.297 262.297i 0.368394 0.368394i
\(713\) 191.802 + 191.802i 0.269007 + 0.269007i
\(714\) 197.317i 0.276354i
\(715\) −58.9318 143.663i −0.0824221 0.200928i
\(716\) 372.439 0.520166
\(717\) −58.3024 + 58.3024i −0.0813144 + 0.0813144i
\(718\) −467.461 467.461i −0.651060 0.651060i
\(719\) 24.2148i 0.0336784i 0.999858 + 0.0168392i \(0.00536033\pi\)
−0.999858 + 0.0168392i \(0.994640\pi\)
\(720\) −66.2693 + 158.452i −0.0920407 + 0.220072i
\(721\) 69.9629 0.0970359
\(722\) −170.382 + 170.382i −0.235985 + 0.235985i
\(723\) −67.5255 67.5255i −0.0933962 0.0933962i
\(724\) 487.230i 0.672970i
\(725\) −843.824 + 832.346i −1.16390 + 1.14806i
\(726\) −106.924 −0.147279
\(727\) 554.026 554.026i 0.762072 0.762072i −0.214625 0.976697i \(-0.568853\pi\)
0.976697 + 0.214625i \(0.0688529\pi\)
\(728\) −398.924 398.924i −0.547973 0.547973i
\(729\) 536.143i 0.735449i
\(730\) 670.399 + 280.381i 0.918355 + 0.384084i
\(731\) −468.797 −0.641310
\(732\) −89.8850 + 89.8850i −0.122794 + 0.122794i
\(733\) 259.853 + 259.853i 0.354507 + 0.354507i 0.861783 0.507277i \(-0.169348\pi\)
−0.507277 + 0.861783i \(0.669348\pi\)
\(734\) 792.082i 1.07913i
\(735\) −255.212 + 104.690i −0.347227 + 0.142435i
\(736\) −27.1293 −0.0368605
\(737\) 29.0594 29.0594i 0.0394294 0.0394294i
\(738\) −71.2895 71.2895i −0.0965982 0.0965982i
\(739\) 1082.77i 1.46518i 0.680668 + 0.732592i \(0.261690\pi\)
−0.680668 + 0.732592i \(0.738310\pi\)
\(740\) −19.5397 47.6335i −0.0264049 0.0643696i
\(741\) 152.266 0.205487
\(742\) 410.054 410.054i 0.552633 0.552633i
\(743\) −477.140 477.140i −0.642181 0.642181i 0.308910 0.951091i \(-0.400036\pi\)
−0.951091 + 0.308910i \(0.900036\pi\)
\(744\) 102.737i 0.138087i
\(745\) −528.403 + 1263.43i −0.709266 + 1.69587i
\(746\) 122.536 0.164257
\(747\) 605.639 605.639i 0.810761 0.810761i
\(748\) −47.8382 47.8382i −0.0639548 0.0639548i
\(749\) 366.459i 0.489265i
\(750\) 42.3655 + 105.326i 0.0564874 + 0.140435i
\(751\) 904.489 1.20438 0.602190 0.798353i \(-0.294295\pi\)
0.602190 + 0.798353i \(0.294295\pi\)
\(752\) −35.7560 + 35.7560i −0.0475479 + 0.0475479i
\(753\) −186.321 186.321i −0.247438 0.247438i
\(754\) 1151.42i 1.52708i
\(755\) −309.712 129.531i −0.410214 0.171564i
\(756\) −262.379 −0.347062
\(757\) 290.718 290.718i 0.384040 0.384040i −0.488515 0.872555i \(-0.662461\pi\)
0.872555 + 0.488515i \(0.162461\pi\)
\(758\) −2.27599 2.27599i −0.00300262 0.00300262i
\(759\) 5.56985i 0.00733840i
\(760\) −180.645 + 74.1020i −0.237691 + 0.0975026i
\(761\) −492.010 −0.646531 −0.323266 0.946308i \(-0.604781\pi\)
−0.323266 + 0.946308i \(0.604781\pi\)
\(762\) −0.425202 + 0.425202i −0.000558008 + 0.000558008i
\(763\) 1246.66 + 1246.66i 1.63390 + 1.63390i
\(764\) 650.114i 0.850935i
\(765\) 304.810 + 743.062i 0.398445 + 0.971323i
\(766\) −910.184 −1.18823
\(767\) 77.2237 77.2237i 0.100683 0.100683i
\(768\) −7.26576 7.26576i −0.00946062 0.00946062i
\(769\) 1181.65i 1.53661i −0.640086 0.768304i \(-0.721101\pi\)
0.640086 0.768304i \(-0.278899\pi\)
\(770\) −57.3082 + 137.026i −0.0744263 + 0.177955i
\(771\) 201.727 0.261643
\(772\) 379.332 379.332i 0.491362 0.491362i
\(773\) 60.7545 + 60.7545i 0.0785957 + 0.0785957i 0.745312 0.666716i \(-0.232301\pi\)
−0.666716 + 0.745312i \(0.732301\pi\)
\(774\) 304.378i 0.393254i
\(775\) −992.969 1006.66i −1.28125 1.29892i
\(776\) 318.049 0.409857
\(777\) 27.1558 27.1558i 0.0349495 0.0349495i
\(778\) −94.4517 94.4517i −0.121403 0.121403i
\(779\) 114.614i 0.147130i
\(780\) −101.746 42.5532i −0.130443 0.0545554i
\(781\) −199.660 −0.255647
\(782\) −89.7058 + 89.7058i −0.114713 + 0.114713i
\(783\) −378.652 378.652i −0.483591 0.483591i
\(784\) 343.626i 0.438299i
\(785\) 135.673 55.6541i 0.172832 0.0708969i
\(786\) −52.5934 −0.0669128
\(787\) −364.615 + 364.615i −0.463297 + 0.463297i −0.899735 0.436437i \(-0.856240\pi\)
0.436437 + 0.899735i \(0.356240\pi\)
\(788\) −59.3397 59.3397i −0.0753042 0.0753042i
\(789\) 173.908i 0.220416i
\(790\) 218.072 + 531.612i 0.276040 + 0.672927i
\(791\) −582.561 −0.736487
\(792\) −31.0602 + 31.0602i −0.0392174 + 0.0392174i
\(793\) 1201.78 + 1201.78i 1.51549 + 1.51549i
\(794\) 333.298i 0.419771i
\(795\) 43.7404 104.584i 0.0550193 0.131553i
\(796\) 143.495 0.180271
\(797\) 130.697 130.697i 0.163986 0.163986i −0.620344 0.784330i \(-0.713007\pi\)
0.784330 + 0.620344i \(0.213007\pi\)
\(798\) −102.985 102.985i −0.129054 0.129054i
\(799\) 236.461i 0.295947i
\(800\) 141.418 + 0.968365i 0.176773 + 0.00121046i
\(801\) −1126.24 −1.40605
\(802\) 56.3098 56.3098i 0.0702118 0.0702118i
\(803\) 131.414 + 131.414i 0.163653 + 0.163653i
\(804\) 29.1880i 0.0363035i
\(805\) 256.949 + 107.464i 0.319191 + 0.133496i
\(806\) 1373.61 1.70423
\(807\) −203.677 + 203.677i −0.252388 + 0.252388i
\(808\) 212.932 + 212.932i 0.263530 + 0.263530i
\(809\) 183.753i 0.227135i −0.993530 0.113568i \(-0.963772\pi\)
0.993530 0.113568i \(-0.0362279\pi\)
\(810\) 458.168 187.944i 0.565640 0.232030i
\(811\) −1246.28 −1.53672 −0.768360 0.640018i \(-0.778927\pi\)
−0.768360 + 0.640018i \(0.778927\pi\)
\(812\) −778.762 + 778.762i −0.959067 + 0.959067i
\(813\) 161.531 + 161.531i 0.198685 + 0.198685i
\(814\) 13.1675i 0.0161763i
\(815\) −13.7818 33.5970i −0.0169101 0.0412233i
\(816\) −48.0499 −0.0588847
\(817\) −244.679 + 244.679i −0.299484 + 0.299484i
\(818\) −617.869 617.869i −0.755342 0.755342i
\(819\) 1712.90i 2.09145i
\(820\) −32.0308 + 76.5864i −0.0390619 + 0.0933981i
\(821\) −50.3398 −0.0613152 −0.0306576 0.999530i \(-0.509760\pi\)
−0.0306576 + 0.999530i \(0.509760\pi\)
\(822\) −82.6352 + 82.6352i −0.100529 + 0.100529i
\(823\) −43.2603 43.2603i −0.0525642 0.0525642i 0.680336 0.732900i \(-0.261834\pi\)
−0.732900 + 0.680336i \(0.761834\pi\)
\(824\) 17.0371i 0.0206761i
\(825\) −0.198812 + 29.0342i −0.000240985 + 0.0351929i
\(826\) −104.461 −0.126466
\(827\) −412.757 + 412.757i −0.499102 + 0.499102i −0.911158 0.412057i \(-0.864811\pi\)
0.412057 + 0.911158i \(0.364811\pi\)
\(828\) 58.2437 + 58.2437i 0.0703427 + 0.0703427i
\(829\) 375.863i 0.453393i 0.973965 + 0.226697i \(0.0727926\pi\)
−0.973965 + 0.226697i \(0.927207\pi\)
\(830\) −650.639 272.117i −0.783902 0.327852i
\(831\) 67.8787 0.0816831
\(832\) −97.1447 + 97.1447i −0.116760 + 0.116760i
\(833\) 1136.23 + 1136.23i 1.36403 + 1.36403i
\(834\) 14.4937i 0.0173785i
\(835\) −28.1091 + 11.5306i −0.0336636 + 0.0138091i
\(836\) −49.9362 −0.0597324
\(837\) 451.722 451.722i 0.539692 0.539692i
\(838\) −327.397 327.397i −0.390688 0.390688i
\(839\) 21.1937i 0.0252607i 0.999920 + 0.0126304i \(0.00402047\pi\)
−0.999920 + 0.0126304i \(0.995980\pi\)
\(840\) 40.0350 + 97.5969i 0.0476607 + 0.116187i
\(841\) −1406.74 −1.67270
\(842\) −271.135 + 271.135i −0.322013 + 0.322013i
\(843\) 13.4119 + 13.4119i 0.0159097 + 0.0159097i
\(844\) 387.981i 0.459693i
\(845\) −242.906 + 580.796i −0.287463 + 0.687332i
\(846\) 153.528 0.181476
\(847\) 966.912 966.912i 1.14157 1.14157i
\(848\) −99.8549 99.8549i −0.117753 0.117753i
\(849\) 306.370i 0.360859i
\(850\) 470.815 464.411i 0.553900 0.546366i
\(851\) −24.6916 −0.0290148
\(852\) −100.272 + 100.272i −0.117690 + 0.117690i
\(853\) −53.9548 53.9548i −0.0632530 0.0632530i 0.674773 0.738026i \(-0.264242\pi\)
−0.738026 + 0.674773i \(0.764242\pi\)
\(854\) 1625.65i 1.90357i
\(855\) 546.914 + 228.736i 0.639666 + 0.267528i
\(856\) −89.2389 −0.104251
\(857\) −568.035 + 568.035i −0.662818 + 0.662818i −0.956043 0.293225i \(-0.905271\pi\)
0.293225 + 0.956043i \(0.405271\pi\)
\(858\) −19.9445 19.9445i −0.0232454 0.0232454i
\(859\) 1184.25i 1.37864i 0.724457 + 0.689320i \(0.242091\pi\)
−0.724457 + 0.689320i \(0.757909\pi\)
\(860\) 231.877 95.1176i 0.269624 0.110602i
\(861\) −61.9224 −0.0719192
\(862\) −148.281 + 148.281i −0.172019 + 0.172019i
\(863\) 781.788 + 781.788i 0.905896 + 0.905896i 0.995938 0.0900420i \(-0.0287001\pi\)
−0.0900420 + 0.995938i \(0.528700\pi\)
\(864\) 63.8935i 0.0739508i
\(865\) −160.271 390.707i −0.185285 0.451685i
\(866\) −875.273 −1.01071
\(867\) −27.6440 + 27.6440i −0.0318847 + 0.0318847i
\(868\) −929.044 929.044i −1.07033 1.07033i
\(869\) 146.955i 0.169108i
\(870\) −83.0704 + 198.624i −0.0954833 + 0.228303i
\(871\) −390.250 −0.448048
\(872\) 303.583 303.583i 0.348146 0.348146i
\(873\) −682.818 682.818i −0.782151 0.782151i
\(874\) 93.6400i 0.107140i
\(875\) −1335.57 569.353i −1.52637 0.650689i
\(876\) 131.995 0.150679
\(877\) −314.824 + 314.824i −0.358978 + 0.358978i −0.863436 0.504458i \(-0.831692\pi\)
0.504458 + 0.863436i \(0.331692\pi\)
\(878\) 387.950 + 387.950i 0.441856 + 0.441856i
\(879\) 0.658850i 0.000749545i
\(880\) 33.3680 + 13.9555i 0.0379182 + 0.0158585i
\(881\) −654.884 −0.743342 −0.371671 0.928365i \(-0.621215\pi\)
−0.371671 + 0.928365i \(0.621215\pi\)
\(882\) 737.728 737.728i 0.836427 0.836427i
\(883\) −899.338 899.338i −1.01850 1.01850i −0.999826 0.0186775i \(-0.994054\pi\)
−0.0186775 0.999826i \(-0.505946\pi\)
\(884\) 642.437i 0.726739i
\(885\) −18.8928 + 7.74997i −0.0213478 + 0.00875703i
\(886\) −67.0140 −0.0756366
\(887\) −79.8383 + 79.8383i −0.0900094 + 0.0900094i −0.750678 0.660668i \(-0.770273\pi\)
0.660668 + 0.750678i \(0.270273\pi\)
\(888\) −6.61288 6.61288i −0.00744693 0.00744693i
\(889\) 7.69017i 0.00865036i
\(890\) 351.949 + 857.977i 0.395449 + 0.964019i
\(891\) 126.653 0.142147
\(892\) −282.962 + 282.962i −0.317222 + 0.317222i
\(893\) 123.416 + 123.416i 0.138204 + 0.138204i
\(894\) 248.756i 0.278251i
\(895\) −359.258 + 858.996i −0.401406 + 0.959772i
\(896\) 131.408 0.146661
\(897\) −37.3998 + 37.3998i −0.0416943 + 0.0416943i
\(898\) 90.3725 + 90.3725i 0.100638 + 0.100638i
\(899\) 2681.50i 2.98276i
\(900\) −301.530 305.688i −0.335034 0.339654i
\(901\) −660.360 −0.732919
\(902\) −15.0127 + 15.0127i −0.0166438 + 0.0166438i
\(903\) 132.192 + 132.192i 0.146392 + 0.146392i
\(904\) 141.863i 0.156928i
\(905\) 1123.75 + 469.987i 1.24172 + 0.519323i
\(906\) −60.9792 −0.0673060
\(907\) 399.844 399.844i 0.440842 0.440842i −0.451453 0.892295i \(-0.649094\pi\)
0.892295 + 0.451453i \(0.149094\pi\)
\(908\) 598.254 + 598.254i 0.658870 + 0.658870i
\(909\) 914.285i 1.00581i
\(910\) 1304.89 535.276i 1.43394 0.588216i
\(911\) 375.905 0.412629 0.206315 0.978486i \(-0.433853\pi\)
0.206315 + 0.978486i \(0.433853\pi\)
\(912\) −25.0786 + 25.0786i −0.0274985 + 0.0274985i
\(913\) −127.540 127.540i −0.139693 0.139693i
\(914\) 865.282i 0.946698i
\(915\) −120.608 294.016i −0.131812 0.321328i
\(916\) 61.0530 0.0666518
\(917\) 475.600 475.600i 0.518648 0.518648i
\(918\) 211.270 + 211.270i 0.230142 + 0.230142i
\(919\) 218.112i 0.237336i −0.992934 0.118668i \(-0.962138\pi\)
0.992934 0.118668i \(-0.0378624\pi\)
\(920\) 26.1692 62.5713i 0.0284448 0.0680123i
\(921\) −283.380 −0.307687
\(922\) −477.708 + 477.708i −0.518121 + 0.518121i
\(923\) 1340.66 + 1340.66i 1.45250 + 1.45250i
\(924\) 26.9790i 0.0291981i
\(925\) 128.711 + 0.881350i 0.139147 + 0.000952811i
\(926\) 1019.13 1.10058
\(927\) −36.5769 + 36.5769i −0.0394573 + 0.0394573i
\(928\) 189.641 + 189.641i 0.204355 + 0.204355i
\(929\) 1273.70i 1.37104i −0.728052 0.685522i \(-0.759574\pi\)
0.728052 0.685522i \(-0.240426\pi\)
\(930\) −236.953 99.1010i −0.254788 0.106560i
\(931\) 1186.07 1.27397
\(932\) −105.469 + 105.469i −0.113164 + 0.113164i
\(933\) 200.891 + 200.891i 0.215317 + 0.215317i
\(934\) 1017.10i 1.08897i
\(935\) 156.480 64.1893i 0.167358 0.0686516i
\(936\) 417.118 0.445639
\(937\) 636.364 636.364i 0.679151 0.679151i −0.280657 0.959808i \(-0.590552\pi\)
0.959808 + 0.280657i \(0.0905525\pi\)
\(938\) 263.946 + 263.946i 0.281393 + 0.281393i
\(939\) 313.845i 0.334233i
\(940\) −47.9774 116.959i −0.0510397 0.124424i
\(941\) 1561.91 1.65984 0.829921 0.557881i \(-0.188386\pi\)
0.829921 + 0.557881i \(0.188386\pi\)
\(942\) 18.8352 18.8352i 0.0199949 0.0199949i
\(943\) 28.1517 + 28.1517i 0.0298533 + 0.0298533i
\(944\) 25.4379i 0.0269470i
\(945\) 253.093 605.152i 0.267823 0.640373i
\(946\) 64.0984 0.0677573
\(947\) 689.902 689.902i 0.728513 0.728513i −0.241810 0.970324i \(-0.577741\pi\)
0.970324 + 0.241810i \(0.0777411\pi\)
\(948\) 73.8028 + 73.8028i 0.0778510 + 0.0778510i
\(949\) 1764.80i 1.85964i
\(950\) 3.34242 488.121i 0.00351834 0.513811i
\(951\) 405.544 0.426440
\(952\) 434.513 434.513i 0.456422 0.456422i
\(953\) 1126.44 + 1126.44i 1.18200 + 1.18200i 0.979226 + 0.202771i \(0.0649946\pi\)
0.202771 + 0.979226i \(0.435005\pi\)
\(954\) 428.755i 0.449429i
\(955\) 1499.43 + 627.107i 1.57008 + 0.656657i
\(956\) −256.777 −0.268595
\(957\) −38.9348 + 38.9348i −0.0406842 + 0.0406842i
\(958\) 213.247 + 213.247i 0.222596 + 0.222596i
\(959\) 1494.53i 1.55843i
\(960\) 23.7664 9.74919i 0.0247567 0.0101554i
\(961\) 2237.97 2.32879
\(962\) −88.4155 + 88.4155i −0.0919080 + 0.0919080i
\(963\) 191.586 + 191.586i 0.198947 + 0.198947i
\(964\) 297.397i 0.308503i
\(965\) 508.987 + 1240.80i 0.527448 + 1.28581i
\(966\) 50.5908 0.0523714
\(967\) −823.547 + 823.547i −0.851651 + 0.851651i −0.990337 0.138685i \(-0.955712\pi\)
0.138685 + 0.990337i \(0.455712\pi\)
\(968\) −235.459 235.459i −0.243243 0.243243i
\(969\) 165.850i 0.171156i
\(970\) −306.794 + 733.552i −0.316282 + 0.756239i
\(971\) −1767.79 −1.82059 −0.910294 0.413963i \(-0.864144\pi\)
−0.910294 + 0.413963i \(0.864144\pi\)
\(972\) 207.367 207.367i 0.213341 0.213341i
\(973\) 131.066 + 131.066i 0.134703 + 0.134703i
\(974\) 889.455i 0.913198i
\(975\) 196.290 193.620i 0.201323 0.198585i
\(976\) −395.873 −0.405608
\(977\) −355.445 + 355.445i −0.363813 + 0.363813i −0.865215 0.501402i \(-0.832818\pi\)
0.501402 + 0.865215i \(0.332818\pi\)
\(978\) −4.66421 4.66421i −0.00476913 0.00476913i
\(979\) 237.173i 0.242261i
\(980\) −792.543 331.466i −0.808717 0.338230i
\(981\) −1303.52 −1.32877
\(982\) −488.473 + 488.473i −0.497427 + 0.497427i
\(983\) −874.521 874.521i −0.889644 0.889644i 0.104844 0.994489i \(-0.466566\pi\)
−0.994489 + 0.104844i \(0.966566\pi\)
\(984\) 15.0791i 0.0153243i
\(985\) 194.101 79.6219i 0.197057 0.0808344i
\(986\) 1254.14 1.27194
\(987\) 66.6778 66.6778i 0.0675560 0.0675560i
\(988\) 335.306 + 335.306i 0.339379 + 0.339379i
\(989\) 120.197i 0.121534i
\(990\) −41.6765 101.598i −0.0420975 0.102625i
\(991\) 1547.23 1.56128 0.780639 0.624982i \(-0.214894\pi\)
0.780639 + 0.624982i \(0.214894\pi\)
\(992\) −226.238 + 226.238i −0.228062 + 0.228062i
\(993\) −245.905 245.905i −0.247638 0.247638i
\(994\) 1813.51i 1.82446i
\(995\) −138.417 + 330.959i −0.139113 + 0.332623i
\(996\) −128.104 −0.128619
\(997\) 58.7774 58.7774i 0.0589543 0.0589543i −0.677015 0.735969i \(-0.736727\pi\)
0.735969 + 0.677015i \(0.236727\pi\)
\(998\) −727.731 727.731i −0.729189 0.729189i
\(999\) 58.1522i 0.0582104i
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 230.3.f.a.93.4 yes 20
5.2 odd 4 inner 230.3.f.a.47.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.f.a.47.4 20 5.2 odd 4 inner
230.3.f.a.93.4 yes 20 1.1 even 1 trivial