Properties

Label 156.3.f.a.79.6
Level $156$
Weight $3$
Character 156.79
Analytic conductor $4.251$
Analytic rank $0$
Dimension $24$
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] = [156,3,Mod(79,156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(156, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("156.79");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 156.f (of order \(2\), degree \(1\), 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: \(4.25069212402\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 79.6
Character \(\chi\) \(=\) 156.79
Dual form 156.3.f.a.79.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.66943 + 1.10137i) q^{2} +1.73205i q^{3} +(1.57397 - 3.67731i) q^{4} -0.251667 q^{5} +(-1.90763 - 2.89153i) q^{6} +2.33352i q^{7} +(1.42246 + 7.87252i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.66943 + 1.10137i) q^{2} +1.73205i q^{3} +(1.57397 - 3.67731i) q^{4} -0.251667 q^{5} +(-1.90763 - 2.89153i) q^{6} +2.33352i q^{7} +(1.42246 + 7.87252i) q^{8} -3.00000 q^{9} +(0.420139 - 0.277178i) q^{10} +17.3946i q^{11} +(6.36929 + 2.72619i) q^{12} -3.60555 q^{13} +(-2.57007 - 3.89564i) q^{14} -0.435900i q^{15} +(-11.0452 - 11.5759i) q^{16} -17.8176 q^{17} +(5.00828 - 3.30411i) q^{18} -5.49823i q^{19} +(-0.396116 + 0.925457i) q^{20} -4.04177 q^{21} +(-19.1579 - 29.0390i) q^{22} +30.7733i q^{23} +(-13.6356 + 2.46376i) q^{24} -24.9367 q^{25} +(6.01920 - 3.97105i) q^{26} -5.19615i q^{27} +(8.58107 + 3.67288i) q^{28} -22.8908 q^{29} +(0.480087 + 0.727702i) q^{30} -0.174889i q^{31} +(31.1886 + 7.16029i) q^{32} -30.1283 q^{33} +(29.7452 - 19.6238i) q^{34} -0.587269i q^{35} +(-4.72191 + 11.0319i) q^{36} +38.6830 q^{37} +(6.05559 + 9.17890i) q^{38} -6.24500i q^{39} +(-0.357985 - 1.98125i) q^{40} +10.7622 q^{41} +(6.74744 - 4.45149i) q^{42} +42.8900i q^{43} +(63.9653 + 27.3785i) q^{44} +0.755000 q^{45} +(-33.8928 - 51.3738i) q^{46} +36.2920i q^{47} +(20.0501 - 19.1309i) q^{48} +43.5547 q^{49} +(41.6299 - 27.4645i) q^{50} -30.8610i q^{51} +(-5.67503 + 13.2587i) q^{52} +87.4625 q^{53} +(5.72289 + 8.67459i) q^{54} -4.37764i q^{55} +(-18.3707 + 3.31932i) q^{56} +9.52322 q^{57} +(38.2145 - 25.2112i) q^{58} -94.5210i q^{59} +(-1.60294 - 0.686092i) q^{60} -26.2640 q^{61} +(0.192617 + 0.291964i) q^{62} -7.00055i q^{63} +(-59.9532 + 22.3966i) q^{64} +0.907397 q^{65} +(50.2970 - 33.1824i) q^{66} +32.3753i q^{67} +(-28.0443 + 65.5209i) q^{68} -53.3010 q^{69} +(0.646800 + 0.980402i) q^{70} +13.5128i q^{71} +(-4.26737 - 23.6176i) q^{72} +110.236 q^{73} +(-64.5784 + 42.6043i) q^{74} -43.1916i q^{75} +(-20.2187 - 8.65405i) q^{76} -40.5906 q^{77} +(6.87805 + 10.4256i) q^{78} +8.46854i q^{79} +(2.77972 + 2.91328i) q^{80} +9.00000 q^{81} +(-17.9666 + 11.8531i) q^{82} +1.61619i q^{83} +(-6.36162 + 14.8629i) q^{84} +4.48410 q^{85} +(-47.2378 - 71.6018i) q^{86} -39.6480i q^{87} +(-136.939 + 24.7430i) q^{88} -104.620 q^{89} +(-1.26042 + 0.831535i) q^{90} -8.41362i q^{91} +(113.163 + 48.4363i) q^{92} +0.302916 q^{93} +(-39.9709 - 60.5868i) q^{94} +1.38372i q^{95} +(-12.4020 + 54.0203i) q^{96} +77.5982 q^{97} +(-72.7114 + 47.9698i) q^{98} -52.1838i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.66943 + 1.10137i −0.834713 + 0.550685i
\(3\) 1.73205i 0.577350i
\(4\) 1.57397 3.67731i 0.393492 0.919328i
\(5\) −0.251667 −0.0503334 −0.0251667 0.999683i \(-0.508012\pi\)
−0.0251667 + 0.999683i \(0.508012\pi\)
\(6\) −1.90763 2.89153i −0.317938 0.481922i
\(7\) 2.33352i 0.333360i 0.986011 + 0.166680i \(0.0533046\pi\)
−0.986011 + 0.166680i \(0.946695\pi\)
\(8\) 1.42246 + 7.87252i 0.177807 + 0.984065i
\(9\) −3.00000 −0.333333
\(10\) 0.420139 0.277178i 0.0420139 0.0277178i
\(11\) 17.3946i 1.58133i 0.612252 + 0.790663i \(0.290264\pi\)
−0.612252 + 0.790663i \(0.709736\pi\)
\(12\) 6.36929 + 2.72619i 0.530774 + 0.227183i
\(13\) −3.60555 −0.277350
\(14\) −2.57007 3.89564i −0.183576 0.278260i
\(15\) 0.435900i 0.0290600i
\(16\) −11.0452 11.5759i −0.690328 0.723497i
\(17\) −17.8176 −1.04809 −0.524047 0.851689i \(-0.675578\pi\)
−0.524047 + 0.851689i \(0.675578\pi\)
\(18\) 5.00828 3.30411i 0.278238 0.183562i
\(19\) 5.49823i 0.289381i −0.989477 0.144690i \(-0.953781\pi\)
0.989477 0.144690i \(-0.0462186\pi\)
\(20\) −0.396116 + 0.925457i −0.0198058 + 0.0462729i
\(21\) −4.04177 −0.192465
\(22\) −19.1579 29.0390i −0.870812 1.31995i
\(23\) 30.7733i 1.33797i 0.743275 + 0.668985i \(0.233271\pi\)
−0.743275 + 0.668985i \(0.766729\pi\)
\(24\) −13.6356 + 2.46376i −0.568150 + 0.102657i
\(25\) −24.9367 −0.997467
\(26\) 6.01920 3.97105i 0.231508 0.152733i
\(27\) 5.19615i 0.192450i
\(28\) 8.58107 + 3.67288i 0.306467 + 0.131174i
\(29\) −22.8908 −0.789338 −0.394669 0.918823i \(-0.629141\pi\)
−0.394669 + 0.918823i \(0.629141\pi\)
\(30\) 0.480087 + 0.727702i 0.0160029 + 0.0242567i
\(31\) 0.174889i 0.00564158i −0.999996 0.00282079i \(-0.999102\pi\)
0.999996 0.00282079i \(-0.000897886\pi\)
\(32\) 31.1886 + 7.16029i 0.974644 + 0.223759i
\(33\) −30.1283 −0.912979
\(34\) 29.7452 19.6238i 0.874858 0.577170i
\(35\) 0.587269i 0.0167791i
\(36\) −4.72191 + 11.0319i −0.131164 + 0.306443i
\(37\) 38.6830 1.04549 0.522743 0.852490i \(-0.324909\pi\)
0.522743 + 0.852490i \(0.324909\pi\)
\(38\) 6.05559 + 9.17890i 0.159358 + 0.241550i
\(39\) 6.24500i 0.160128i
\(40\) −0.357985 1.98125i −0.00894962 0.0495313i
\(41\) 10.7622 0.262492 0.131246 0.991350i \(-0.458102\pi\)
0.131246 + 0.991350i \(0.458102\pi\)
\(42\) 6.74744 4.45149i 0.160653 0.105988i
\(43\) 42.8900i 0.997443i 0.866762 + 0.498721i \(0.166197\pi\)
−0.866762 + 0.498721i \(0.833803\pi\)
\(44\) 63.9653 + 27.3785i 1.45376 + 0.622239i
\(45\) 0.755000 0.0167778
\(46\) −33.8928 51.3738i −0.736800 1.11682i
\(47\) 36.2920i 0.772170i 0.922463 + 0.386085i \(0.126173\pi\)
−0.922463 + 0.386085i \(0.873827\pi\)
\(48\) 20.0501 19.1309i 0.417711 0.398561i
\(49\) 43.5547 0.888871
\(50\) 41.6299 27.4645i 0.832598 0.549290i
\(51\) 30.8610i 0.605117i
\(52\) −5.67503 + 13.2587i −0.109135 + 0.254976i
\(53\) 87.4625 1.65023 0.825117 0.564961i \(-0.191109\pi\)
0.825117 + 0.564961i \(0.191109\pi\)
\(54\) 5.72289 + 8.67459i 0.105979 + 0.160641i
\(55\) 4.37764i 0.0795934i
\(56\) −18.3707 + 3.31932i −0.328048 + 0.0592737i
\(57\) 9.52322 0.167074
\(58\) 38.2145 25.2112i 0.658871 0.434677i
\(59\) 94.5210i 1.60205i −0.598630 0.801025i \(-0.704288\pi\)
0.598630 0.801025i \(-0.295712\pi\)
\(60\) −1.60294 0.686092i −0.0267156 0.0114349i
\(61\) −26.2640 −0.430557 −0.215278 0.976553i \(-0.569066\pi\)
−0.215278 + 0.976553i \(0.569066\pi\)
\(62\) 0.192617 + 0.291964i 0.00310673 + 0.00470910i
\(63\) 7.00055i 0.111120i
\(64\) −59.9532 + 22.3966i −0.936769 + 0.349947i
\(65\) 0.907397 0.0139600
\(66\) 50.2970 33.1824i 0.762076 0.502764i
\(67\) 32.3753i 0.483214i 0.970374 + 0.241607i \(0.0776745\pi\)
−0.970374 + 0.241607i \(0.922326\pi\)
\(68\) −28.0443 + 65.5209i −0.412417 + 0.963542i
\(69\) −53.3010 −0.772478
\(70\) 0.646800 + 0.980402i 0.00924000 + 0.0140057i
\(71\) 13.5128i 0.190321i 0.995462 + 0.0951603i \(0.0303364\pi\)
−0.995462 + 0.0951603i \(0.969664\pi\)
\(72\) −4.26737 23.6176i −0.0592690 0.328022i
\(73\) 110.236 1.51008 0.755041 0.655678i \(-0.227617\pi\)
0.755041 + 0.655678i \(0.227617\pi\)
\(74\) −64.5784 + 42.6043i −0.872681 + 0.575733i
\(75\) 43.1916i 0.575888i
\(76\) −20.2187 8.65405i −0.266036 0.113869i
\(77\) −40.5906 −0.527150
\(78\) 6.87805 + 10.4256i 0.0881802 + 0.133661i
\(79\) 8.46854i 0.107197i 0.998563 + 0.0535984i \(0.0170691\pi\)
−0.998563 + 0.0535984i \(0.982931\pi\)
\(80\) 2.77972 + 2.91328i 0.0347465 + 0.0364160i
\(81\) 9.00000 0.111111
\(82\) −17.9666 + 11.8531i −0.219105 + 0.144550i
\(83\) 1.61619i 0.0194721i 0.999953 + 0.00973606i \(0.00309913\pi\)
−0.999953 + 0.00973606i \(0.996901\pi\)
\(84\) −6.36162 + 14.8629i −0.0757336 + 0.176939i
\(85\) 4.48410 0.0527541
\(86\) −47.2378 71.6018i −0.549277 0.832579i
\(87\) 39.6480i 0.455725i
\(88\) −136.939 + 24.7430i −1.55613 + 0.281171i
\(89\) −104.620 −1.17551 −0.587753 0.809040i \(-0.699987\pi\)
−0.587753 + 0.809040i \(0.699987\pi\)
\(90\) −1.26042 + 0.831535i −0.0140046 + 0.00923927i
\(91\) 8.41362i 0.0924573i
\(92\) 113.163 + 48.4363i 1.23003 + 0.526481i
\(93\) 0.302916 0.00325716
\(94\) −39.9709 60.5868i −0.425223 0.644541i
\(95\) 1.38372i 0.0145655i
\(96\) −12.4020 + 54.0203i −0.129187 + 0.562711i
\(97\) 77.5982 0.799981 0.399991 0.916519i \(-0.369013\pi\)
0.399991 + 0.916519i \(0.369013\pi\)
\(98\) −72.7114 + 47.9698i −0.741953 + 0.489488i
\(99\) 52.1838i 0.527109i
\(100\) −39.2495 + 91.6999i −0.392495 + 0.916999i
\(101\) −4.14702 −0.0410596 −0.0205298 0.999789i \(-0.506535\pi\)
−0.0205298 + 0.999789i \(0.506535\pi\)
\(102\) 33.9894 + 51.5201i 0.333229 + 0.505099i
\(103\) 73.5402i 0.713983i 0.934108 + 0.356991i \(0.116197\pi\)
−0.934108 + 0.356991i \(0.883803\pi\)
\(104\) −5.12874 28.3848i −0.0493148 0.272931i
\(105\) 1.01718 0.00968742
\(106\) −146.012 + 96.3285i −1.37747 + 0.908760i
\(107\) 81.6012i 0.762628i −0.924446 0.381314i \(-0.875472\pi\)
0.924446 0.381314i \(-0.124528\pi\)
\(108\) −19.1079 8.17858i −0.176925 0.0757276i
\(109\) 111.967 1.02722 0.513610 0.858024i \(-0.328308\pi\)
0.513610 + 0.858024i \(0.328308\pi\)
\(110\) 4.82140 + 7.30815i 0.0438309 + 0.0664377i
\(111\) 67.0009i 0.603611i
\(112\) 27.0127 25.7743i 0.241185 0.230127i
\(113\) −166.707 −1.47529 −0.737643 0.675190i \(-0.764061\pi\)
−0.737643 + 0.675190i \(0.764061\pi\)
\(114\) −15.8983 + 10.4886i −0.139459 + 0.0920052i
\(115\) 7.74462i 0.0673446i
\(116\) −36.0294 + 84.1766i −0.310598 + 0.725661i
\(117\) 10.8167 0.0924500
\(118\) 104.103 + 157.796i 0.882225 + 1.33725i
\(119\) 41.5777i 0.349392i
\(120\) 3.43163 0.620048i 0.0285969 0.00516706i
\(121\) −181.572 −1.50059
\(122\) 43.8458 28.9263i 0.359391 0.237101i
\(123\) 18.6406i 0.151550i
\(124\) −0.643121 0.275270i −0.00518646 0.00221992i
\(125\) 12.5674 0.100539
\(126\) 7.71020 + 11.6869i 0.0611921 + 0.0927532i
\(127\) 94.8943i 0.747199i −0.927590 0.373600i \(-0.878123\pi\)
0.927590 0.373600i \(-0.121877\pi\)
\(128\) 75.4206 103.420i 0.589223 0.807970i
\(129\) −74.2877 −0.575874
\(130\) −1.51483 + 0.999380i −0.0116526 + 0.00768754i
\(131\) 223.567i 1.70662i −0.521405 0.853310i \(-0.674592\pi\)
0.521405 0.853310i \(-0.325408\pi\)
\(132\) −47.4210 + 110.791i −0.359250 + 0.839327i
\(133\) 12.8302 0.0964679
\(134\) −35.6572 54.0482i −0.266099 0.403345i
\(135\) 1.30770i 0.00968666i
\(136\) −25.3447 140.269i −0.186358 1.03139i
\(137\) 189.094 1.38025 0.690124 0.723692i \(-0.257556\pi\)
0.690124 + 0.723692i \(0.257556\pi\)
\(138\) 88.9821 58.7041i 0.644797 0.425392i
\(139\) 114.967i 0.827098i −0.910482 0.413549i \(-0.864289\pi\)
0.910482 0.413549i \(-0.135711\pi\)
\(140\) −2.15957 0.924343i −0.0154255 0.00660245i
\(141\) −62.8596 −0.445813
\(142\) −14.8826 22.5586i −0.104807 0.158863i
\(143\) 62.7171i 0.438581i
\(144\) 33.1357 + 34.7278i 0.230109 + 0.241166i
\(145\) 5.76085 0.0397300
\(146\) −184.031 + 121.411i −1.26049 + 0.831579i
\(147\) 75.4389i 0.513190i
\(148\) 60.8858 142.249i 0.411390 0.961144i
\(149\) 148.971 0.999807 0.499903 0.866081i \(-0.333369\pi\)
0.499903 + 0.866081i \(0.333369\pi\)
\(150\) 47.5699 + 72.1051i 0.317133 + 0.480701i
\(151\) 253.205i 1.67685i 0.545014 + 0.838427i \(0.316524\pi\)
−0.545014 + 0.838427i \(0.683476\pi\)
\(152\) 43.2850 7.82099i 0.284770 0.0514539i
\(153\) 53.4528 0.349365
\(154\) 67.7630 44.7052i 0.440019 0.290294i
\(155\) 0.0440137i 0.000283959i
\(156\) −22.9648 9.82943i −0.147210 0.0630092i
\(157\) 274.330 1.74732 0.873662 0.486534i \(-0.161739\pi\)
0.873662 + 0.486534i \(0.161739\pi\)
\(158\) −9.32700 14.1376i −0.0590316 0.0894785i
\(159\) 151.489i 0.952764i
\(160\) −7.84914 1.80201i −0.0490571 0.0112626i
\(161\) −71.8101 −0.446026
\(162\) −15.0248 + 9.91233i −0.0927459 + 0.0611872i
\(163\) 157.871i 0.968533i 0.874920 + 0.484267i \(0.160914\pi\)
−0.874920 + 0.484267i \(0.839086\pi\)
\(164\) 16.9393 39.5758i 0.103288 0.241316i
\(165\) 7.58229 0.0459533
\(166\) −1.78002 2.69810i −0.0107230 0.0162536i
\(167\) 95.1205i 0.569584i 0.958589 + 0.284792i \(0.0919245\pi\)
−0.958589 + 0.284792i \(0.908076\pi\)
\(168\) −5.74924 31.8189i −0.0342217 0.189398i
\(169\) 13.0000 0.0769231
\(170\) −7.48587 + 4.93865i −0.0440345 + 0.0290509i
\(171\) 16.4947i 0.0964602i
\(172\) 157.720 + 67.5076i 0.916977 + 0.392486i
\(173\) −129.298 −0.747386 −0.373693 0.927552i \(-0.621909\pi\)
−0.373693 + 0.927552i \(0.621909\pi\)
\(174\) 43.6672 + 66.1895i 0.250961 + 0.380399i
\(175\) 58.1901i 0.332515i
\(176\) 201.359 192.127i 1.14408 1.09163i
\(177\) 163.715 0.924945
\(178\) 174.656 115.225i 0.981211 0.647334i
\(179\) 32.4167i 0.181099i −0.995892 0.0905494i \(-0.971138\pi\)
0.995892 0.0905494i \(-0.0288623\pi\)
\(180\) 1.18835 2.77637i 0.00660193 0.0154243i
\(181\) −88.3270 −0.487995 −0.243997 0.969776i \(-0.578459\pi\)
−0.243997 + 0.969776i \(0.578459\pi\)
\(182\) 9.26651 + 14.0459i 0.0509149 + 0.0771754i
\(183\) 45.4905i 0.248582i
\(184\) −242.264 + 43.7737i −1.31665 + 0.237900i
\(185\) −9.73522 −0.0526228
\(186\) −0.505697 + 0.333623i −0.00271880 + 0.00179367i
\(187\) 309.930i 1.65738i
\(188\) 133.457 + 57.1225i 0.709878 + 0.303843i
\(189\) 12.1253 0.0641551
\(190\) −1.52399 2.31002i −0.00802100 0.0121580i
\(191\) 195.231i 1.02215i 0.859536 + 0.511076i \(0.170753\pi\)
−0.859536 + 0.511076i \(0.829247\pi\)
\(192\) −38.7921 103.842i −0.202042 0.540844i
\(193\) −88.5332 −0.458721 −0.229361 0.973341i \(-0.573664\pi\)
−0.229361 + 0.973341i \(0.573664\pi\)
\(194\) −129.544 + 85.4643i −0.667755 + 0.440538i
\(195\) 1.57166i 0.00805979i
\(196\) 68.5537 160.164i 0.349764 0.817164i
\(197\) −193.536 −0.982415 −0.491208 0.871043i \(-0.663444\pi\)
−0.491208 + 0.871043i \(0.663444\pi\)
\(198\) 57.4736 + 87.1169i 0.290271 + 0.439985i
\(199\) 372.542i 1.87207i 0.351904 + 0.936036i \(0.385534\pi\)
−0.351904 + 0.936036i \(0.614466\pi\)
\(200\) −35.4713 196.314i −0.177356 0.981572i
\(201\) −56.0757 −0.278984
\(202\) 6.92315 4.56741i 0.0342730 0.0226109i
\(203\) 53.4161i 0.263134i
\(204\) −113.485 48.5742i −0.556301 0.238109i
\(205\) −2.70848 −0.0132121
\(206\) −80.9950 122.770i −0.393179 0.595971i
\(207\) 92.3200i 0.445990i
\(208\) 39.8242 + 41.7377i 0.191462 + 0.200662i
\(209\) 95.6395 0.457605
\(210\) −1.69811 + 1.12029i −0.00808622 + 0.00533472i
\(211\) 284.334i 1.34755i −0.738935 0.673777i \(-0.764671\pi\)
0.738935 0.673777i \(-0.235329\pi\)
\(212\) 137.663 321.627i 0.649355 1.51711i
\(213\) −23.4048 −0.109882
\(214\) 89.8731 + 136.227i 0.419968 + 0.636576i
\(215\) 10.7940i 0.0502046i
\(216\) 40.9068 7.39129i 0.189383 0.0342190i
\(217\) 0.408106 0.00188067
\(218\) −186.921 + 123.317i −0.857434 + 0.565675i
\(219\) 190.934i 0.871846i
\(220\) −16.0979 6.89027i −0.0731725 0.0313194i
\(221\) 64.2423 0.290689
\(222\) −73.7927 111.853i −0.332400 0.503842i
\(223\) 21.0036i 0.0941863i −0.998891 0.0470932i \(-0.985004\pi\)
0.998891 0.0470932i \(-0.0149958\pi\)
\(224\) −16.7087 + 72.7792i −0.0745923 + 0.324907i
\(225\) 74.8100 0.332489
\(226\) 278.306 183.607i 1.23144 0.812418i
\(227\) 428.034i 1.88561i 0.333340 + 0.942807i \(0.391824\pi\)
−0.333340 + 0.942807i \(0.608176\pi\)
\(228\) 14.9893 35.0199i 0.0657423 0.153596i
\(229\) −299.946 −1.30981 −0.654903 0.755713i \(-0.727291\pi\)
−0.654903 + 0.755713i \(0.727291\pi\)
\(230\) 8.52970 + 12.9291i 0.0370856 + 0.0562134i
\(231\) 70.3049i 0.304350i
\(232\) −32.5611 180.208i −0.140350 0.776760i
\(233\) −343.608 −1.47471 −0.737356 0.675504i \(-0.763926\pi\)
−0.737356 + 0.675504i \(0.763926\pi\)
\(234\) −18.0576 + 11.9131i −0.0771693 + 0.0509108i
\(235\) 9.13349i 0.0388659i
\(236\) −347.583 148.773i −1.47281 0.630395i
\(237\) −14.6679 −0.0618901
\(238\) 45.7924 + 69.4109i 0.192405 + 0.291642i
\(239\) 11.0123i 0.0460765i −0.999735 0.0230383i \(-0.992666\pi\)
0.999735 0.0230383i \(-0.00733396\pi\)
\(240\) −5.04595 + 4.81462i −0.0210248 + 0.0200609i
\(241\) 273.663 1.13553 0.567766 0.823190i \(-0.307808\pi\)
0.567766 + 0.823190i \(0.307808\pi\)
\(242\) 303.120 199.977i 1.25256 0.826353i
\(243\) 15.5885i 0.0641500i
\(244\) −41.3387 + 96.5808i −0.169421 + 0.395823i
\(245\) −10.9613 −0.0447399
\(246\) −20.5302 31.1191i −0.0834561 0.126500i
\(247\) 19.8242i 0.0802598i
\(248\) 1.37682 0.248772i 0.00555168 0.00100311i
\(249\) −2.79932 −0.0112422
\(250\) −20.9803 + 13.8414i −0.0839214 + 0.0553654i
\(251\) 184.717i 0.735926i 0.929840 + 0.367963i \(0.119945\pi\)
−0.929840 + 0.367963i \(0.880055\pi\)
\(252\) −25.7432 11.0187i −0.102156 0.0437248i
\(253\) −535.289 −2.11577
\(254\) 104.514 + 158.419i 0.411471 + 0.623697i
\(255\) 7.76669i 0.0304576i
\(256\) −12.0052 + 255.718i −0.0468952 + 0.998900i
\(257\) 426.793 1.66067 0.830337 0.557261i \(-0.188148\pi\)
0.830337 + 0.557261i \(0.188148\pi\)
\(258\) 124.018 81.8183i 0.480690 0.317125i
\(259\) 90.2674i 0.348523i
\(260\) 1.42822 3.33678i 0.00549314 0.0128338i
\(261\) 68.6724 0.263113
\(262\) 246.230 + 373.229i 0.939809 + 1.42454i
\(263\) 173.214i 0.658609i 0.944224 + 0.329304i \(0.106814\pi\)
−0.944224 + 0.329304i \(0.893186\pi\)
\(264\) −42.8562 237.186i −0.162334 0.898431i
\(265\) −22.0114 −0.0830619
\(266\) −21.4191 + 14.1308i −0.0805230 + 0.0531234i
\(267\) 181.207i 0.678679i
\(268\) 119.054 + 50.9578i 0.444232 + 0.190141i
\(269\) 375.485 1.39585 0.697927 0.716169i \(-0.254106\pi\)
0.697927 + 0.716169i \(0.254106\pi\)
\(270\) −1.44026 2.18311i −0.00533430 0.00808558i
\(271\) 451.566i 1.66629i 0.553051 + 0.833147i \(0.313463\pi\)
−0.553051 + 0.833147i \(0.686537\pi\)
\(272\) 196.800 + 206.256i 0.723528 + 0.758293i
\(273\) 14.5728 0.0533803
\(274\) −315.678 + 208.262i −1.15211 + 0.760081i
\(275\) 433.763i 1.57732i
\(276\) −83.8941 + 196.004i −0.303964 + 0.710161i
\(277\) −480.894 −1.73608 −0.868039 0.496496i \(-0.834620\pi\)
−0.868039 + 0.496496i \(0.834620\pi\)
\(278\) 126.621 + 191.928i 0.455470 + 0.690389i
\(279\) 0.524666i 0.00188053i
\(280\) 4.62329 0.835364i 0.0165117 0.00298344i
\(281\) −251.688 −0.895688 −0.447844 0.894112i \(-0.647808\pi\)
−0.447844 + 0.894112i \(0.647808\pi\)
\(282\) 104.939 69.2317i 0.372126 0.245502i
\(283\) 366.709i 1.29579i −0.761729 0.647896i \(-0.775649\pi\)
0.761729 0.647896i \(-0.224351\pi\)
\(284\) 49.6906 + 21.2687i 0.174967 + 0.0748897i
\(285\) −2.39668 −0.00840940
\(286\) 69.0747 + 104.702i 0.241520 + 0.366089i
\(287\) 25.1137i 0.0875041i
\(288\) −93.5659 21.4809i −0.324881 0.0745864i
\(289\) 28.4669 0.0985012
\(290\) −9.61732 + 6.34483i −0.0331632 + 0.0218787i
\(291\) 134.404i 0.461869i
\(292\) 173.508 405.372i 0.594205 1.38826i
\(293\) −84.9216 −0.289835 −0.144917 0.989444i \(-0.546292\pi\)
−0.144917 + 0.989444i \(0.546292\pi\)
\(294\) −83.0862 125.940i −0.282606 0.428367i
\(295\) 23.7878i 0.0806366i
\(296\) 55.0248 + 304.533i 0.185895 + 1.02883i
\(297\) 90.3849 0.304326
\(298\) −248.696 + 164.072i −0.834552 + 0.550578i
\(299\) 110.955i 0.371086i
\(300\) −158.829 67.9822i −0.529430 0.226607i
\(301\) −100.085 −0.332507
\(302\) −278.872 422.707i −0.923418 1.39969i
\(303\) 7.18285i 0.0237058i
\(304\) −63.6473 + 60.7293i −0.209366 + 0.199768i
\(305\) 6.60977 0.0216714
\(306\) −89.2355 + 58.8713i −0.291619 + 0.192390i
\(307\) 146.019i 0.475633i 0.971310 + 0.237816i \(0.0764316\pi\)
−0.971310 + 0.237816i \(0.923568\pi\)
\(308\) −63.8883 + 149.264i −0.207430 + 0.484624i
\(309\) −127.375 −0.412218
\(310\) −0.0484754 0.0734776i −0.000156372 0.000237025i
\(311\) 193.433i 0.621971i 0.950415 + 0.310985i \(0.100659\pi\)
−0.950415 + 0.310985i \(0.899341\pi\)
\(312\) 49.1639 8.88323i 0.157577 0.0284719i
\(313\) −328.534 −1.04963 −0.524814 0.851217i \(-0.675865\pi\)
−0.524814 + 0.851217i \(0.675865\pi\)
\(314\) −457.973 + 302.139i −1.45851 + 0.962225i
\(315\) 1.76181i 0.00559304i
\(316\) 31.1415 + 13.3292i 0.0985489 + 0.0421811i
\(317\) 516.505 1.62935 0.814676 0.579916i \(-0.196915\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(318\) −166.846 252.900i −0.524673 0.795284i
\(319\) 398.176i 1.24820i
\(320\) 15.0882 5.63649i 0.0471507 0.0176140i
\(321\) 141.337 0.440303
\(322\) 119.882 79.0895i 0.372303 0.245620i
\(323\) 97.9653i 0.303298i
\(324\) 14.1657 33.0958i 0.0437214 0.102148i
\(325\) 89.9104 0.276647
\(326\) −173.874 263.554i −0.533357 0.808447i
\(327\) 193.932i 0.593066i
\(328\) 15.3087 + 84.7253i 0.0466728 + 0.258309i
\(329\) −84.6881 −0.257411
\(330\) −12.6581 + 8.35091i −0.0383578 + 0.0253058i
\(331\) 525.675i 1.58814i −0.607824 0.794071i \(-0.707958\pi\)
0.607824 0.794071i \(-0.292042\pi\)
\(332\) 5.94322 + 2.54383i 0.0179013 + 0.00766213i
\(333\) −116.049 −0.348495
\(334\) −104.763 158.797i −0.313661 0.475439i
\(335\) 8.14780i 0.0243218i
\(336\) 44.6424 + 46.7873i 0.132864 + 0.139248i
\(337\) 201.872 0.599026 0.299513 0.954092i \(-0.403176\pi\)
0.299513 + 0.954092i \(0.403176\pi\)
\(338\) −21.7025 + 14.3178i −0.0642087 + 0.0423604i
\(339\) 288.746i 0.851757i
\(340\) 7.05783 16.4894i 0.0207583 0.0484983i
\(341\) 3.04212 0.00892117
\(342\) −18.1668 27.5367i −0.0531192 0.0805166i
\(343\) 215.978i 0.629674i
\(344\) −337.653 + 61.0092i −0.981549 + 0.177352i
\(345\) 13.4141 0.0388814
\(346\) 215.853 142.405i 0.623853 0.411574i
\(347\) 23.9745i 0.0690907i −0.999403 0.0345453i \(-0.989002\pi\)
0.999403 0.0345453i \(-0.0109983\pi\)
\(348\) −145.798 62.4048i −0.418960 0.179324i
\(349\) −0.403468 −0.00115607 −0.000578035 1.00000i \(-0.500184\pi\)
−0.000578035 1.00000i \(0.500184\pi\)
\(350\) 64.0889 + 97.1442i 0.183111 + 0.277555i
\(351\) 18.7350i 0.0533761i
\(352\) −124.550 + 542.513i −0.353836 + 1.54123i
\(353\) 174.107 0.493221 0.246610 0.969115i \(-0.420683\pi\)
0.246610 + 0.969115i \(0.420683\pi\)
\(354\) −273.310 + 180.311i −0.772063 + 0.509353i
\(355\) 3.40071i 0.00957947i
\(356\) −164.669 + 384.721i −0.462553 + 1.08068i
\(357\) 72.0147 0.201722
\(358\) 35.7028 + 54.1173i 0.0997284 + 0.151166i
\(359\) 200.471i 0.558415i −0.960231 0.279208i \(-0.909928\pi\)
0.960231 0.279208i \(-0.0900718\pi\)
\(360\) 1.07395 + 5.94376i 0.00298321 + 0.0165104i
\(361\) 330.769 0.916259
\(362\) 147.455 97.2807i 0.407335 0.268731i
\(363\) 314.491i 0.866367i
\(364\) −30.9395 13.2428i −0.0849986 0.0363812i
\(365\) −27.7427 −0.0760075
\(366\) 50.1019 + 75.9431i 0.136890 + 0.207495i
\(367\) 661.977i 1.80375i −0.431995 0.901876i \(-0.642190\pi\)
0.431995 0.901876i \(-0.357810\pi\)
\(368\) 356.230 339.899i 0.968018 0.923638i
\(369\) −32.2865 −0.0874972
\(370\) 16.2522 10.7221i 0.0439249 0.0289786i
\(371\) 204.095i 0.550122i
\(372\) 0.476781 1.11392i 0.00128167 0.00299440i
\(373\) −136.647 −0.366346 −0.183173 0.983081i \(-0.558637\pi\)
−0.183173 + 0.983081i \(0.558637\pi\)
\(374\) 341.347 + 517.405i 0.912693 + 1.38344i
\(375\) 21.7674i 0.0580463i
\(376\) −285.710 + 51.6238i −0.759866 + 0.137297i
\(377\) 82.5340 0.218923
\(378\) −20.2423 + 13.3545i −0.0535511 + 0.0353292i
\(379\) 171.247i 0.451838i −0.974146 0.225919i \(-0.927462\pi\)
0.974146 0.225919i \(-0.0725384\pi\)
\(380\) 5.08838 + 2.17794i 0.0133905 + 0.00573141i
\(381\) 164.362 0.431396
\(382\) −215.022 325.924i −0.562884 0.853204i
\(383\) 488.106i 1.27443i 0.770687 + 0.637214i \(0.219913\pi\)
−0.770687 + 0.637214i \(0.780087\pi\)
\(384\) 179.129 + 130.632i 0.466482 + 0.340188i
\(385\) 10.2153 0.0265332
\(386\) 147.800 97.5078i 0.382901 0.252611i
\(387\) 128.670i 0.332481i
\(388\) 122.137 285.353i 0.314786 0.735445i
\(389\) 741.544 1.90628 0.953141 0.302525i \(-0.0978296\pi\)
0.953141 + 0.302525i \(0.0978296\pi\)
\(390\) −1.73098 2.62377i −0.00443840 0.00672761i
\(391\) 548.307i 1.40232i
\(392\) 61.9546 + 342.885i 0.158047 + 0.874708i
\(393\) 387.230 0.985317
\(394\) 323.094 213.155i 0.820035 0.541001i
\(395\) 2.13125i 0.00539557i
\(396\) −191.896 82.1356i −0.484586 0.207413i
\(397\) 344.631 0.868088 0.434044 0.900892i \(-0.357086\pi\)
0.434044 + 0.900892i \(0.357086\pi\)
\(398\) −410.307 621.932i −1.03092 1.56264i
\(399\) 22.2226i 0.0556958i
\(400\) 275.432 + 288.666i 0.688579 + 0.721664i
\(401\) −401.952 −1.00237 −0.501187 0.865339i \(-0.667103\pi\)
−0.501187 + 0.865339i \(0.667103\pi\)
\(402\) 93.6143 61.7601i 0.232871 0.153632i
\(403\) 0.630571i 0.00156469i
\(404\) −6.52728 + 15.2499i −0.0161566 + 0.0377473i
\(405\) −2.26500 −0.00559259
\(406\) 58.8309 + 89.1742i 0.144904 + 0.219641i
\(407\) 672.874i 1.65325i
\(408\) 242.954 43.8984i 0.595475 0.107594i
\(409\) −251.492 −0.614895 −0.307447 0.951565i \(-0.599475\pi\)
−0.307447 + 0.951565i \(0.599475\pi\)
\(410\) 4.52160 2.98303i 0.0110283 0.00727569i
\(411\) 327.520i 0.796886i
\(412\) 270.430 + 115.750i 0.656384 + 0.280947i
\(413\) 220.566 0.534059
\(414\) 101.678 + 154.121i 0.245600 + 0.372274i
\(415\) 0.406740i 0.000980098i
\(416\) −112.452 25.8168i −0.270318 0.0620596i
\(417\) 199.128 0.477525
\(418\) −159.663 + 105.334i −0.381969 + 0.251996i
\(419\) 453.214i 1.08166i −0.841133 0.540829i \(-0.818111\pi\)
0.841133 0.540829i \(-0.181889\pi\)
\(420\) 1.60101 3.74049i 0.00381193 0.00890592i
\(421\) 239.355 0.568539 0.284270 0.958744i \(-0.408249\pi\)
0.284270 + 0.958744i \(0.408249\pi\)
\(422\) 313.157 + 474.675i 0.742078 + 1.12482i
\(423\) 108.876i 0.257390i
\(424\) 124.411 + 688.550i 0.293423 + 1.62394i
\(425\) 444.311 1.04544
\(426\) 39.0726 25.7773i 0.0917197 0.0605102i
\(427\) 61.2874i 0.143530i
\(428\) −300.073 128.438i −0.701105 0.300088i
\(429\) 108.629 0.253215
\(430\) 11.8882 + 18.0198i 0.0276469 + 0.0419065i
\(431\) 582.956i 1.35257i −0.736642 0.676283i \(-0.763590\pi\)
0.736642 0.676283i \(-0.236410\pi\)
\(432\) −60.1504 + 57.3928i −0.139237 + 0.132854i
\(433\) −38.8680 −0.0897643 −0.0448822 0.998992i \(-0.514291\pi\)
−0.0448822 + 0.998992i \(0.514291\pi\)
\(434\) −0.681303 + 0.449476i −0.00156982 + 0.00103566i
\(435\) 9.97809i 0.0229381i
\(436\) 176.233 411.737i 0.404203 0.944352i
\(437\) 169.199 0.387183
\(438\) −210.289 318.751i −0.480112 0.727741i
\(439\) 374.232i 0.852464i −0.904614 0.426232i \(-0.859841\pi\)
0.904614 0.426232i \(-0.140159\pi\)
\(440\) 34.4631 6.22700i 0.0783251 0.0141523i
\(441\) −130.664 −0.296290
\(442\) −107.248 + 70.7545i −0.242642 + 0.160078i
\(443\) 196.055i 0.442562i −0.975210 0.221281i \(-0.928976\pi\)
0.975210 0.221281i \(-0.0710238\pi\)
\(444\) 246.383 + 105.457i 0.554917 + 0.237516i
\(445\) 26.3294 0.0591672
\(446\) 23.1327 + 35.0639i 0.0518670 + 0.0786186i
\(447\) 258.026i 0.577239i
\(448\) −52.2629 139.902i −0.116658 0.312281i
\(449\) −858.959 −1.91305 −0.956524 0.291653i \(-0.905795\pi\)
−0.956524 + 0.291653i \(0.905795\pi\)
\(450\) −124.890 + 82.3935i −0.277533 + 0.183097i
\(451\) 187.203i 0.415085i
\(452\) −262.392 + 613.035i −0.580514 + 1.35627i
\(453\) −438.564 −0.968132
\(454\) −471.424 714.572i −1.03838 1.57395i
\(455\) 2.11743i 0.00465369i
\(456\) 13.5464 + 74.9718i 0.0297069 + 0.164412i
\(457\) 356.728 0.780586 0.390293 0.920691i \(-0.372374\pi\)
0.390293 + 0.920691i \(0.372374\pi\)
\(458\) 500.737 330.351i 1.09331 0.721291i
\(459\) 92.5830i 0.201706i
\(460\) −28.4794 12.1898i −0.0619117 0.0264996i
\(461\) −9.54824 −0.0207120 −0.0103560 0.999946i \(-0.503296\pi\)
−0.0103560 + 0.999946i \(0.503296\pi\)
\(462\) 77.4317 + 117.369i 0.167601 + 0.254045i
\(463\) 767.584i 1.65785i 0.559360 + 0.828925i \(0.311047\pi\)
−0.559360 + 0.828925i \(0.688953\pi\)
\(464\) 252.835 + 264.983i 0.544902 + 0.571084i
\(465\) −0.0762340 −0.000163944
\(466\) 573.628 378.439i 1.23096 0.812102i
\(467\) 11.3023i 0.0242019i 0.999927 + 0.0121009i \(0.00385194\pi\)
−0.999927 + 0.0121009i \(0.996148\pi\)
\(468\) 17.0251 39.7762i 0.0363784 0.0849919i
\(469\) −75.5484 −0.161084
\(470\) 10.0594 + 15.2477i 0.0214029 + 0.0324419i
\(471\) 475.153i 1.00882i
\(472\) 744.119 134.452i 1.57652 0.284856i
\(473\) −746.055 −1.57728
\(474\) 24.4870 16.1548i 0.0516604 0.0340819i
\(475\) 137.108i 0.288648i
\(476\) −152.894 65.4420i −0.321206 0.137483i
\(477\) −262.387 −0.550078
\(478\) 12.1286 + 18.3842i 0.0253737 + 0.0384607i
\(479\) 418.204i 0.873077i −0.899686 0.436538i \(-0.856204\pi\)
0.899686 0.436538i \(-0.143796\pi\)
\(480\) 3.12117 13.5951i 0.00650244 0.0283231i
\(481\) −139.473 −0.289966
\(482\) −456.861 + 301.405i −0.947844 + 0.625321i
\(483\) 124.379i 0.257513i
\(484\) −285.788 + 667.695i −0.590471 + 1.37954i
\(485\) −19.5289 −0.0402657
\(486\) −17.1687 26.0238i −0.0353265 0.0535469i
\(487\) 422.152i 0.866842i −0.901192 0.433421i \(-0.857306\pi\)
0.901192 0.433421i \(-0.142694\pi\)
\(488\) −37.3593 206.764i −0.0765560 0.423696i
\(489\) −273.440 −0.559183
\(490\) 18.2990 12.0724i 0.0373450 0.0246376i
\(491\) 13.0273i 0.0265321i −0.999912 0.0132661i \(-0.995777\pi\)
0.999912 0.0132661i \(-0.00422285\pi\)
\(492\) 68.5473 + 29.3397i 0.139324 + 0.0596336i
\(493\) 407.859 0.827301
\(494\) −21.8337 33.0950i −0.0441978 0.0669939i
\(495\) 13.1329i 0.0265311i
\(496\) −2.02450 + 1.93169i −0.00408166 + 0.00389454i
\(497\) −31.5323 −0.0634452
\(498\) 4.67325 3.08308i 0.00938405 0.00619093i
\(499\) 354.534i 0.710489i 0.934773 + 0.355245i \(0.115602\pi\)
−0.934773 + 0.355245i \(0.884398\pi\)
\(500\) 19.7807 46.2142i 0.0395614 0.0924285i
\(501\) −164.753 −0.328849
\(502\) −203.442 308.372i −0.405263 0.614287i
\(503\) 290.412i 0.577360i −0.957426 0.288680i \(-0.906784\pi\)
0.957426 0.288680i \(-0.0932164\pi\)
\(504\) 55.1120 9.95797i 0.109349 0.0197579i
\(505\) 1.04367 0.00206667
\(506\) 893.626 589.552i 1.76606 1.16512i
\(507\) 22.5167i 0.0444116i
\(508\) −348.956 149.361i −0.686921 0.294017i
\(509\) 4.57807 0.00899424 0.00449712 0.999990i \(-0.498569\pi\)
0.00449712 + 0.999990i \(0.498569\pi\)
\(510\) −8.55399 12.9659i −0.0167725 0.0254234i
\(511\) 257.238i 0.503400i
\(512\) −261.599 440.125i −0.510935 0.859619i
\(513\) −28.5697 −0.0556913
\(514\) −712.500 + 470.057i −1.38619 + 0.914508i
\(515\) 18.5076i 0.0359371i
\(516\) −116.927 + 273.179i −0.226602 + 0.529417i
\(517\) −631.284 −1.22105
\(518\) −99.4178 150.695i −0.191926 0.290917i
\(519\) 223.950i 0.431503i
\(520\) 1.29073 + 7.14351i 0.00248218 + 0.0137375i
\(521\) −162.675 −0.312235 −0.156118 0.987738i \(-0.549898\pi\)
−0.156118 + 0.987738i \(0.549898\pi\)
\(522\) −114.644 + 75.6337i −0.219624 + 0.144892i
\(523\) 655.375i 1.25311i 0.779379 + 0.626553i \(0.215535\pi\)
−0.779379 + 0.626553i \(0.784465\pi\)
\(524\) −822.126 351.888i −1.56894 0.671541i
\(525\) 100.788 0.191978
\(526\) −190.773 289.168i −0.362686 0.549749i
\(527\) 3.11610i 0.00591290i
\(528\) 332.774 + 348.764i 0.630255 + 0.660537i
\(529\) −417.998 −0.790166
\(530\) 36.7464 24.2427i 0.0693328 0.0457409i
\(531\) 283.563i 0.534017i
\(532\) 20.1944 47.1807i 0.0379594 0.0886856i
\(533\) −38.8035 −0.0728021
\(534\) 199.576 + 302.512i 0.373738 + 0.566502i
\(535\) 20.5363i 0.0383856i
\(536\) −254.876 + 46.0525i −0.475514 + 0.0859188i
\(537\) 56.1473 0.104557
\(538\) −626.844 + 413.548i −1.16514 + 0.768676i
\(539\) 757.616i 1.40560i
\(540\) 4.80882 + 2.05828i 0.00890522 + 0.00381162i
\(541\) −447.595 −0.827347 −0.413673 0.910425i \(-0.635754\pi\)
−0.413673 + 0.910425i \(0.635754\pi\)
\(542\) −497.341 753.856i −0.917603 1.39088i
\(543\) 152.987i 0.281744i
\(544\) −555.706 127.579i −1.02152 0.234521i
\(545\) −28.1784 −0.0517034
\(546\) −24.3282 + 16.0501i −0.0445572 + 0.0293957i
\(547\) 1066.95i 1.95056i 0.220980 + 0.975278i \(0.429074\pi\)
−0.220980 + 0.975278i \(0.570926\pi\)
\(548\) 297.628 695.357i 0.543117 1.26890i
\(549\) 78.7919 0.143519
\(550\) 477.733 + 724.135i 0.868606 + 1.31661i
\(551\) 125.859i 0.228419i
\(552\) −75.8183 419.613i −0.137352 0.760169i
\(553\) −19.7615 −0.0357351
\(554\) 802.817 529.642i 1.44913 0.956032i
\(555\) 16.8619i 0.0303818i
\(556\) −422.768 180.954i −0.760374 0.325457i
\(557\) −617.405 −1.10845 −0.554224 0.832368i \(-0.686985\pi\)
−0.554224 + 0.832368i \(0.686985\pi\)
\(558\) −0.577852 0.875892i −0.00103558 0.00156970i
\(559\) 154.642i 0.276641i
\(560\) −6.79819 + 6.48653i −0.0121396 + 0.0115831i
\(561\) 536.814 0.956888
\(562\) 420.175 277.202i 0.747643 0.493242i
\(563\) 372.544i 0.661713i 0.943681 + 0.330856i \(0.107338\pi\)
−0.943681 + 0.330856i \(0.892662\pi\)
\(564\) −98.9391 + 231.154i −0.175424 + 0.409848i
\(565\) 41.9547 0.0742561
\(566\) 403.882 + 612.193i 0.713573 + 1.08161i
\(567\) 21.0017i 0.0370400i
\(568\) −106.380 + 19.2213i −0.187288 + 0.0338403i
\(569\) −87.3586 −0.153530 −0.0767650 0.997049i \(-0.524459\pi\)
−0.0767650 + 0.997049i \(0.524459\pi\)
\(570\) 4.00108 2.63963i 0.00701943 0.00463093i
\(571\) 603.066i 1.05616i 0.849195 + 0.528079i \(0.177087\pi\)
−0.849195 + 0.528079i \(0.822913\pi\)
\(572\) −230.630 98.7147i −0.403200 0.172578i
\(573\) −338.150 −0.590140
\(574\) −27.6594 41.9254i −0.0481872 0.0730408i
\(575\) 767.384i 1.33458i
\(576\) 179.860 67.1899i 0.312256 0.116649i
\(577\) 245.153 0.424875 0.212437 0.977175i \(-0.431860\pi\)
0.212437 + 0.977175i \(0.431860\pi\)
\(578\) −47.5233 + 31.3525i −0.0822203 + 0.0542431i
\(579\) 153.344i 0.264843i
\(580\) 9.06741 21.1845i 0.0156335 0.0365249i
\(581\) −3.77140 −0.00649122
\(582\) −148.029 224.378i −0.254345 0.385528i
\(583\) 1521.37i 2.60956i
\(584\) 156.806 + 867.835i 0.268503 + 1.48602i
\(585\) −2.72219 −0.00465332
\(586\) 141.770 93.5301i 0.241929 0.159608i
\(587\) 751.196i 1.27972i −0.768491 0.639860i \(-0.778992\pi\)
0.768491 0.639860i \(-0.221008\pi\)
\(588\) 277.413 + 118.739i 0.471790 + 0.201936i
\(589\) −0.961580 −0.00163256
\(590\) −26.1992 39.7120i −0.0444054 0.0673084i
\(591\) 335.214i 0.567198i
\(592\) −427.263 447.792i −0.721728 0.756405i
\(593\) −820.636 −1.38387 −0.691936 0.721959i \(-0.743242\pi\)
−0.691936 + 0.721959i \(0.743242\pi\)
\(594\) −150.891 + 99.5472i −0.254025 + 0.167588i
\(595\) 10.4637i 0.0175861i
\(596\) 234.476 547.814i 0.393416 0.919150i
\(597\) −645.262 −1.08084
\(598\) 122.202 + 185.231i 0.204352 + 0.309751i
\(599\) 370.633i 0.618752i 0.950940 + 0.309376i \(0.100120\pi\)
−0.950940 + 0.309376i \(0.899880\pi\)
\(600\) 340.027 61.4381i 0.566711 0.102397i
\(601\) 282.638 0.470279 0.235139 0.971962i \(-0.424445\pi\)
0.235139 + 0.971962i \(0.424445\pi\)
\(602\) 167.084 110.230i 0.277548 0.183107i
\(603\) 97.1260i 0.161071i
\(604\) 931.113 + 398.537i 1.54158 + 0.659829i
\(605\) 45.6955 0.0755298
\(606\) 7.91098 + 11.9912i 0.0130544 + 0.0197875i
\(607\) 878.042i 1.44653i −0.690572 0.723263i \(-0.742641\pi\)
0.690572 0.723263i \(-0.257359\pi\)
\(608\) 39.3690 171.482i 0.0647516 0.282043i
\(609\) 92.5194 0.151920
\(610\) −11.0345 + 7.27980i −0.0180894 + 0.0119341i
\(611\) 130.853i 0.214162i
\(612\) 84.1330 196.563i 0.137472 0.321181i
\(613\) 748.062 1.22033 0.610164 0.792275i \(-0.291103\pi\)
0.610164 + 0.792275i \(0.291103\pi\)
\(614\) −160.821 243.768i −0.261924 0.397017i
\(615\) 4.69122i 0.00762800i
\(616\) −57.7383 319.550i −0.0937310 0.518750i
\(617\) −66.8574 −0.108359 −0.0541794 0.998531i \(-0.517254\pi\)
−0.0541794 + 0.998531i \(0.517254\pi\)
\(618\) 212.644 140.287i 0.344084 0.227002i
\(619\) 419.308i 0.677396i −0.940895 0.338698i \(-0.890014\pi\)
0.940895 0.338698i \(-0.109986\pi\)
\(620\) 0.161852 + 0.0692762i 0.000261052 + 0.000111736i
\(621\) 159.903 0.257493
\(622\) −213.041 322.922i −0.342510 0.519167i
\(623\) 244.133i 0.391867i
\(624\) −72.2918 + 68.9775i −0.115852 + 0.110541i
\(625\) 620.254 0.992406
\(626\) 548.463 361.837i 0.876139 0.578015i
\(627\) 165.652i 0.264199i
\(628\) 431.786 1008.80i 0.687558 1.60636i
\(629\) −689.238 −1.09577
\(630\) −1.94040 2.94121i −0.00308000 0.00466858i
\(631\) 1104.22i 1.74996i 0.484163 + 0.874978i \(0.339124\pi\)
−0.484163 + 0.874978i \(0.660876\pi\)
\(632\) −66.6688 + 12.0461i −0.105489 + 0.0190603i
\(633\) 492.481 0.778011
\(634\) −862.267 + 568.863i −1.36004 + 0.897260i
\(635\) 23.8817i 0.0376090i
\(636\) 557.074 + 238.440i 0.875902 + 0.374905i
\(637\) −157.039 −0.246529
\(638\) 438.539 + 664.726i 0.687365 + 1.04189i
\(639\) 40.5383i 0.0634402i
\(640\) −18.9808 + 26.0274i −0.0296576 + 0.0406679i
\(641\) 257.680 0.401996 0.200998 0.979592i \(-0.435581\pi\)
0.200998 + 0.979592i \(0.435581\pi\)
\(642\) −235.952 + 155.665i −0.367527 + 0.242468i
\(643\) 288.864i 0.449244i 0.974446 + 0.224622i \(0.0721147\pi\)
−0.974446 + 0.224622i \(0.927885\pi\)
\(644\) −113.027 + 264.068i −0.175508 + 0.410044i
\(645\) 18.6958 0.0289857
\(646\) −107.896 163.546i −0.167022 0.253167i
\(647\) 83.0624i 0.128381i −0.997938 0.0641904i \(-0.979553\pi\)
0.997938 0.0641904i \(-0.0204465\pi\)
\(648\) 12.8021 + 70.8527i 0.0197563 + 0.109341i
\(649\) 1644.15 2.53336
\(650\) −150.099 + 99.0246i −0.230921 + 0.152346i
\(651\) 0.706861i 0.00108581i
\(652\) 580.541 + 248.484i 0.890400 + 0.381110i
\(653\) 763.163 1.16870 0.584352 0.811501i \(-0.301349\pi\)
0.584352 + 0.811501i \(0.301349\pi\)
\(654\) −213.591 323.756i −0.326592 0.495040i
\(655\) 56.2644i 0.0858999i
\(656\) −118.871 124.582i −0.181205 0.189912i
\(657\) −330.708 −0.503361
\(658\) 141.380 93.2729i 0.214864 0.141752i
\(659\) 901.575i 1.36810i 0.729437 + 0.684048i \(0.239782\pi\)
−0.729437 + 0.684048i \(0.760218\pi\)
\(660\) 11.9343 27.8825i 0.0180823 0.0422461i
\(661\) 1056.46 1.59828 0.799141 0.601144i \(-0.205288\pi\)
0.799141 + 0.601144i \(0.205288\pi\)
\(662\) 578.963 + 877.576i 0.874566 + 1.32564i
\(663\) 111.271i 0.167829i
\(664\) −12.7235 + 2.29895i −0.0191618 + 0.00346228i
\(665\) −3.22894 −0.00485555
\(666\) 193.735 127.813i 0.290894 0.191911i
\(667\) 704.426i 1.05611i
\(668\) 349.788 + 149.717i 0.523634 + 0.224127i
\(669\) 36.3792 0.0543785
\(670\) 8.97374 + 13.6021i 0.0133936 + 0.0203017i
\(671\) 456.851i 0.680851i
\(672\) −126.057 28.9403i −0.187585 0.0430659i
\(673\) −748.492 −1.11217 −0.556086 0.831124i \(-0.687698\pi\)
−0.556086 + 0.831124i \(0.687698\pi\)
\(674\) −337.010 + 222.335i −0.500015 + 0.329875i
\(675\) 129.575i 0.191963i
\(676\) 20.4616 47.8051i 0.0302686 0.0707175i
\(677\) 918.698 1.35701 0.678507 0.734594i \(-0.262627\pi\)
0.678507 + 0.734594i \(0.262627\pi\)
\(678\) 318.016 + 482.040i 0.469050 + 0.710973i
\(679\) 181.077i 0.266682i
\(680\) 6.37843 + 35.3012i 0.00938004 + 0.0519135i
\(681\) −741.377 −1.08866
\(682\) −5.07859 + 3.35050i −0.00744662 + 0.00491275i
\(683\) 711.777i 1.04213i −0.853516 0.521066i \(-0.825534\pi\)
0.853516 0.521066i \(-0.174466\pi\)
\(684\) 60.6562 + 25.9621i 0.0886786 + 0.0379564i
\(685\) −47.5886 −0.0694725
\(686\) −237.872 360.559i −0.346752 0.525597i
\(687\) 519.521i 0.756217i
\(688\) 496.493 473.731i 0.721647 0.688563i
\(689\) −315.350 −0.457693
\(690\) −22.3938 + 14.7739i −0.0324548 + 0.0214114i
\(691\) 55.6041i 0.0804690i 0.999190 + 0.0402345i \(0.0128105\pi\)
−0.999190 + 0.0402345i \(0.987190\pi\)
\(692\) −203.511 + 475.468i −0.294091 + 0.687093i
\(693\) 121.772 0.175717
\(694\) 26.4048 + 40.0236i 0.0380472 + 0.0576709i
\(695\) 28.9333i 0.0416306i
\(696\) 312.130 56.3976i 0.448463 0.0810310i
\(697\) −191.756 −0.275116
\(698\) 0.673561 0.444368i 0.000964987 0.000636630i
\(699\) 595.146i 0.851425i
\(700\) −213.983 91.5895i −0.305690 0.130842i
\(701\) −398.266 −0.568140 −0.284070 0.958803i \(-0.591685\pi\)
−0.284070 + 0.958803i \(0.591685\pi\)
\(702\) −20.6342 31.2767i −0.0293934 0.0445537i
\(703\) 212.688i 0.302543i
\(704\) −389.580 1042.86i −0.553381 1.48134i
\(705\) 15.8197 0.0224393
\(706\) −290.659 + 191.756i −0.411698 + 0.271609i
\(707\) 9.67715i 0.0136876i
\(708\) 257.683 602.032i 0.363958 0.850327i
\(709\) 194.214 0.273927 0.136964 0.990576i \(-0.456266\pi\)
0.136964 + 0.990576i \(0.456266\pi\)
\(710\) 3.74544 + 5.67724i 0.00527527 + 0.00799611i
\(711\) 25.4056i 0.0357322i
\(712\) −148.817 823.624i −0.209013 1.15678i
\(713\) 5.38191 0.00754826
\(714\) −120.223 + 79.3148i −0.168380 + 0.111085i
\(715\) 15.7838i 0.0220752i
\(716\) −119.206 51.0229i −0.166489 0.0712610i
\(717\) 19.0738 0.0266023
\(718\) 220.793 + 334.672i 0.307511 + 0.466117i
\(719\) 798.804i 1.11099i −0.831519 0.555496i \(-0.812528\pi\)
0.831519 0.555496i \(-0.187472\pi\)
\(720\) −8.33916 8.73984i −0.0115822 0.0121387i
\(721\) −171.607 −0.238013
\(722\) −552.195 + 364.299i −0.764813 + 0.504570i
\(723\) 473.999i 0.655600i
\(724\) −139.024 + 324.806i −0.192022 + 0.448627i
\(725\) 570.820 0.787338
\(726\) 346.371 + 525.020i 0.477095 + 0.723168i
\(727\) 1133.48i 1.55912i −0.626325 0.779562i \(-0.715442\pi\)
0.626325 0.779562i \(-0.284558\pi\)
\(728\) 66.2364 11.9680i 0.0909841 0.0164396i
\(729\) −27.0000 −0.0370370
\(730\) 46.3144 30.5550i 0.0634444 0.0418562i
\(731\) 764.198i 1.04541i
\(732\) −167.283 71.6007i −0.228528 0.0978151i
\(733\) −582.095 −0.794126 −0.397063 0.917791i \(-0.629971\pi\)
−0.397063 + 0.917791i \(0.629971\pi\)
\(734\) 729.081 + 1105.12i 0.993299 + 1.50562i
\(735\) 18.9855i 0.0258306i
\(736\) −220.346 + 959.778i −0.299383 + 1.30405i
\(737\) −563.156 −0.764119
\(738\) 53.8999 35.5593i 0.0730350 0.0481834i
\(739\) 373.621i 0.505576i −0.967522 0.252788i \(-0.918653\pi\)
0.967522 0.252788i \(-0.0813475\pi\)
\(740\) −15.3229 + 35.7994i −0.0207067 + 0.0483776i
\(741\) −34.3365 −0.0463380
\(742\) −224.784 340.722i −0.302944 0.459194i
\(743\) 529.876i 0.713158i 0.934265 + 0.356579i \(0.116057\pi\)
−0.934265 + 0.356579i \(0.883943\pi\)
\(744\) 0.430885 + 2.38472i 0.000579146 + 0.00320526i
\(745\) −37.4911 −0.0503236
\(746\) 228.122 150.499i 0.305793 0.201741i
\(747\) 4.84856i 0.00649071i
\(748\) −1139.71 487.820i −1.52367 0.652165i
\(749\) 190.418 0.254229
\(750\) −23.9739 36.3390i −0.0319652 0.0484520i
\(751\) 925.306i 1.23210i −0.787707 0.616050i \(-0.788732\pi\)
0.787707 0.616050i \(-0.211268\pi\)
\(752\) 420.114 400.854i 0.558663 0.533051i
\(753\) −319.940 −0.424887
\(754\) −137.784 + 90.9004i −0.182738 + 0.120558i
\(755\) 63.7233i 0.0844017i
\(756\) 19.0849 44.5886i 0.0252445 0.0589796i
\(757\) −1082.42 −1.42988 −0.714940 0.699186i \(-0.753546\pi\)
−0.714940 + 0.699186i \(0.753546\pi\)
\(758\) 188.606 + 285.883i 0.248820 + 0.377155i
\(759\) 927.148i 1.22154i
\(760\) −10.8934 + 1.96828i −0.0143334 + 0.00258985i
\(761\) −505.561 −0.664338 −0.332169 0.943220i \(-0.607780\pi\)
−0.332169 + 0.943220i \(0.607780\pi\)
\(762\) −274.390 + 181.023i −0.360092 + 0.237563i
\(763\) 261.277i 0.342434i
\(764\) 717.925 + 307.288i 0.939693 + 0.402209i
\(765\) −13.4523 −0.0175847
\(766\) −537.585 814.857i −0.701808 1.06378i
\(767\) 340.800i 0.444329i
\(768\) −442.917 20.7936i −0.576715 0.0270749i
\(769\) 1500.21 1.95086 0.975430 0.220311i \(-0.0707072\pi\)
0.975430 + 0.220311i \(0.0707072\pi\)
\(770\) −17.0537 + 11.2508i −0.0221476 + 0.0146115i
\(771\) 739.228i 0.958791i
\(772\) −139.349 + 325.564i −0.180503 + 0.421715i
\(773\) 1376.68 1.78096 0.890478 0.455025i \(-0.150370\pi\)
0.890478 + 0.455025i \(0.150370\pi\)
\(774\) 141.713 + 214.805i 0.183092 + 0.277526i
\(775\) 4.36114i 0.00562728i
\(776\) 110.380 + 610.894i 0.142242 + 0.787234i
\(777\) −156.348 −0.201220
\(778\) −1237.95 + 816.714i −1.59120 + 1.04976i
\(779\) 59.1728i 0.0759600i
\(780\) 5.77948 + 2.47374i 0.00740959 + 0.00317146i
\(781\) −235.049 −0.300959
\(782\) 603.889 + 915.358i 0.772236 + 1.17053i
\(783\) 118.944i 0.151908i
\(784\) −481.072 504.187i −0.613613 0.643096i
\(785\) −69.0397 −0.0879486
\(786\) −646.451 + 426.483i −0.822457 + 0.542599i
\(787\) 401.463i 0.510119i 0.966925 + 0.255059i \(0.0820950\pi\)
−0.966925 + 0.255059i \(0.917905\pi\)
\(788\) −304.619 + 711.692i −0.386573 + 0.903162i
\(789\) −300.016 −0.380248
\(790\) 2.34729 + 3.55797i 0.00297126 + 0.00450375i
\(791\) 389.015i 0.491801i
\(792\) 410.818 74.2291i 0.518709 0.0937236i
\(793\) 94.6961 0.119415
\(794\) −575.336 + 379.566i −0.724604 + 0.478043i
\(795\) 38.1249i 0.0479558i
\(796\) 1369.95 + 586.370i 1.72105 + 0.736646i
\(797\) 8.24350 0.0103432 0.00517158 0.999987i \(-0.498354\pi\)
0.00517158 + 0.999987i \(0.498354\pi\)
\(798\) −24.4753 37.0990i −0.0306708 0.0464900i
\(799\) 646.637i 0.809307i
\(800\) −777.740 178.554i −0.972175 0.223192i
\(801\) 313.860 0.391836
\(802\) 671.029 442.698i 0.836695 0.551992i
\(803\) 1917.51i 2.38793i
\(804\) −88.2615 + 206.208i −0.109778 + 0.256478i
\(805\) 18.0722 0.0224500
\(806\) −0.694492 1.05269i −0.000861652 0.00130607i
\(807\) 650.359i 0.805897i
\(808\) −5.89895 32.6475i −0.00730069 0.0404054i
\(809\) −34.8089 −0.0430270 −0.0215135 0.999769i \(-0.506848\pi\)
−0.0215135 + 0.999769i \(0.506848\pi\)
\(810\) 3.78125 2.49460i 0.00466821 0.00307976i
\(811\) 209.233i 0.257994i 0.991645 + 0.128997i \(0.0411757\pi\)
−0.991645 + 0.128997i \(0.958824\pi\)
\(812\) −196.428 84.0753i −0.241906 0.103541i
\(813\) −782.135 −0.962035
\(814\) −741.083 1123.31i −0.910422 1.37999i
\(815\) 39.7309i 0.0487495i
\(816\) −357.245 + 340.867i −0.437800 + 0.417729i
\(817\) 235.819 0.288641
\(818\) 419.847 276.986i 0.513261 0.338613i
\(819\) 25.2409i 0.0308191i
\(820\) −4.26306 + 9.95991i −0.00519885 + 0.0121462i
\(821\) 789.296 0.961384 0.480692 0.876889i \(-0.340386\pi\)
0.480692 + 0.876889i \(0.340386\pi\)
\(822\) −360.721 546.771i −0.438833 0.665171i
\(823\) 591.495i 0.718706i −0.933202 0.359353i \(-0.882997\pi\)
0.933202 0.359353i \(-0.117003\pi\)
\(824\) −578.947 + 104.608i −0.702605 + 0.126951i
\(825\) 751.299 0.910666
\(826\) −368.219 + 242.925i −0.445786 + 0.294098i
\(827\) 623.715i 0.754189i 0.926175 + 0.377095i \(0.123077\pi\)
−0.926175 + 0.377095i \(0.876923\pi\)
\(828\) −339.489 145.309i −0.410011 0.175494i
\(829\) 1315.38 1.58671 0.793353 0.608762i \(-0.208334\pi\)
0.793353 + 0.608762i \(0.208334\pi\)
\(830\) 0.447972 + 0.679023i 0.000539725 + 0.000818100i
\(831\) 832.932i 1.00233i
\(832\) 216.164 80.7522i 0.259813 0.0970579i
\(833\) −776.040 −0.931621
\(834\) −332.429 + 219.314i −0.398596 + 0.262966i
\(835\) 23.9387i 0.0286691i
\(836\) 150.534 351.696i 0.180064 0.420689i
\(837\) −0.908749 −0.00108572
\(838\) 499.157 + 756.608i 0.595652 + 0.902874i
\(839\) 379.400i 0.452205i −0.974104 0.226103i \(-0.927402\pi\)
0.974104 0.226103i \(-0.0725984\pi\)
\(840\) 1.44689 + 8.00777i 0.00172249 + 0.00953306i
\(841\) −317.011 −0.376945
\(842\) −399.586 + 263.618i −0.474567 + 0.313086i
\(843\) 435.937i 0.517126i
\(844\) −1045.58 447.533i −1.23884 0.530252i
\(845\) −3.27167 −0.00387180
\(846\) 119.913 + 181.761i 0.141741 + 0.214847i
\(847\) 423.701i 0.500237i
\(848\) −966.044 1012.46i −1.13920 1.19394i
\(849\) 635.158 0.748125
\(850\) −741.745 + 489.351i −0.872642 + 0.575707i
\(851\) 1190.40i 1.39883i
\(852\) −36.8384 + 86.0667i −0.0432376 + 0.101017i
\(853\) 1112.16 1.30382 0.651909 0.758297i \(-0.273969\pi\)
0.651909 + 0.758297i \(0.273969\pi\)
\(854\) 67.5001 + 102.315i 0.0790400 + 0.119807i
\(855\) 4.15117i 0.00485517i
\(856\) 642.407 116.074i 0.750476 0.135601i
\(857\) 384.695 0.448886 0.224443 0.974487i \(-0.427944\pi\)
0.224443 + 0.974487i \(0.427944\pi\)
\(858\) −181.348 + 119.641i −0.211362 + 0.139442i
\(859\) 1229.85i 1.43172i −0.698242 0.715861i \(-0.746034\pi\)
0.698242 0.715861i \(-0.253966\pi\)
\(860\) −39.6929 16.9894i −0.0461545 0.0197551i
\(861\) −43.4982 −0.0505205
\(862\) 642.050 + 973.202i 0.744838 + 1.12900i
\(863\) 274.288i 0.317831i −0.987292 0.158915i \(-0.949200\pi\)
0.987292 0.158915i \(-0.0507997\pi\)
\(864\) 37.2060 162.061i 0.0430625 0.187570i
\(865\) 32.5399 0.0376184
\(866\) 64.8872 42.8080i 0.0749275 0.0494319i
\(867\) 49.3060i 0.0568697i
\(868\) 0.642346 1.50073i 0.000740030 0.00172896i
\(869\) −147.307 −0.169513
\(870\) −10.9896 16.6577i −0.0126317 0.0191468i
\(871\) 116.731i 0.134019i
\(872\) 159.268 + 881.463i 0.182647 + 1.01085i
\(873\) −232.795 −0.266660
\(874\) −282.465 + 186.351i −0.323187 + 0.213216i
\(875\) 29.3262i 0.0335157i
\(876\) 702.125 + 300.525i 0.801512 + 0.343065i
\(877\) −1335.73 −1.52307 −0.761535 0.648124i \(-0.775554\pi\)
−0.761535 + 0.648124i \(0.775554\pi\)
\(878\) 412.168 + 624.753i 0.469439 + 0.711563i
\(879\) 147.089i 0.167336i
\(880\) −50.6753 + 48.3521i −0.0575856 + 0.0549456i
\(881\) −1187.95 −1.34841 −0.674206 0.738544i \(-0.735514\pi\)
−0.674206 + 0.738544i \(0.735514\pi\)
\(882\) 218.134 143.909i 0.247318 0.163163i
\(883\) 397.325i 0.449972i 0.974362 + 0.224986i \(0.0722337\pi\)
−0.974362 + 0.224986i \(0.927766\pi\)
\(884\) 101.115 236.239i 0.114384 0.267239i
\(885\) −41.2017 −0.0465556
\(886\) 215.929 + 327.299i 0.243712 + 0.369412i
\(887\) 435.697i 0.491203i 0.969371 + 0.245602i \(0.0789855\pi\)
−0.969371 + 0.245602i \(0.921015\pi\)
\(888\) −527.466 + 95.3057i −0.593993 + 0.107326i
\(889\) 221.438 0.249086
\(890\) −43.9550 + 28.9984i −0.0493876 + 0.0325825i
\(891\) 156.551i 0.175703i
\(892\) −77.2366 33.0589i −0.0865881 0.0370616i
\(893\) 199.542 0.223451
\(894\) −284.182 430.755i −0.317877 0.481829i
\(895\) 8.15820i 0.00911531i
\(896\) 241.333 + 175.995i 0.269345 + 0.196423i
\(897\) 192.179 0.214247
\(898\) 1433.97 946.031i 1.59685 1.05349i
\(899\) 4.00335i 0.00445311i
\(900\) 117.749 275.100i 0.130832 0.305666i
\(901\) −1558.37 −1.72960
\(902\) −206.180 312.522i −0.228581 0.346477i
\(903\) 173.352i 0.191973i
\(904\) −237.134 1312.41i −0.262316 1.45178i
\(905\) 22.2290 0.0245624
\(906\) 732.150 483.021i 0.808112 0.533136i
\(907\) 1247.02i 1.37489i 0.726238 + 0.687444i \(0.241267\pi\)
−0.726238 + 0.687444i \(0.758733\pi\)
\(908\) 1574.02 + 673.712i 1.73350 + 0.741974i
\(909\) 12.4411 0.0136865
\(910\) −2.33207 3.53489i −0.00256272 0.00388449i
\(911\) 547.306i 0.600775i −0.953817 0.300387i \(-0.902884\pi\)
0.953817 0.300387i \(-0.0971159\pi\)
\(912\) −105.186 110.240i −0.115336 0.120878i
\(913\) −28.1129 −0.0307918
\(914\) −595.531 + 392.889i −0.651566 + 0.429857i
\(915\) 11.4485i 0.0125120i
\(916\) −472.105 + 1102.99i −0.515399 + 1.20414i
\(917\) 521.698 0.568918
\(918\) −101.968 154.560i −0.111076 0.168366i
\(919\) 315.834i 0.343672i −0.985126 0.171836i \(-0.945030\pi\)
0.985126 0.171836i \(-0.0549698\pi\)
\(920\) 60.9697 11.0164i 0.0662715 0.0119743i
\(921\) −252.913 −0.274607
\(922\) 15.9401 10.5161i 0.0172886 0.0114058i
\(923\) 48.7210i 0.0527854i
\(924\) −258.533 110.658i −0.279798 0.119760i
\(925\) −964.624 −1.04284
\(926\) −845.394 1281.43i −0.912953 1.38383i
\(927\) 220.621i 0.237994i
\(928\) −713.933 163.905i −0.769324 0.176622i
\(929\) 1106.19 1.19073 0.595366 0.803455i \(-0.297007\pi\)
0.595366 + 0.803455i \(0.297007\pi\)
\(930\) 0.127267 0.0839618i 0.000136846 9.02815e-5i
\(931\) 239.474i 0.257222i
\(932\) −540.828 + 1263.55i −0.580288 + 1.35574i
\(933\) −335.036 −0.359095
\(934\) −12.4480 18.8683i −0.0133276 0.0202016i
\(935\) 77.9990i 0.0834214i
\(936\) 15.3862 + 85.1544i 0.0164383 + 0.0909769i
\(937\) −1597.85 −1.70528 −0.852641 0.522496i \(-0.825001\pi\)
−0.852641 + 0.522496i \(0.825001\pi\)
\(938\) 126.123 83.2068i 0.134459 0.0887066i
\(939\) 569.037i 0.606003i
\(940\) −33.5867 14.3758i −0.0357305 0.0152934i
\(941\) −15.4424 −0.0164106 −0.00820529 0.999966i \(-0.502612\pi\)
−0.00820529 + 0.999966i \(0.502612\pi\)
\(942\) −523.319 793.233i −0.555541 0.842073i
\(943\) 331.187i 0.351206i
\(944\) −1094.17 + 1044.01i −1.15908 + 1.10594i
\(945\) −3.05154 −0.00322914
\(946\) 1245.48 821.682i 1.31658 0.868586i
\(947\) 145.749i 0.153906i 0.997035 + 0.0769531i \(0.0245192\pi\)
−0.997035 + 0.0769531i \(0.975481\pi\)
\(948\) −23.0869 + 53.9386i −0.0243533 + 0.0568973i
\(949\) −397.461 −0.418821
\(950\) −151.006 228.891i −0.158954 0.240938i
\(951\) 894.613i 0.940707i
\(952\) 327.321 59.1424i 0.343825 0.0621244i
\(953\) 1507.81 1.58217 0.791086 0.611705i \(-0.209516\pi\)
0.791086 + 0.611705i \(0.209516\pi\)
\(954\) 438.036 288.986i 0.459158 0.302920i
\(955\) 49.1332i 0.0514483i
\(956\) −40.4956 17.3330i −0.0423594 0.0181308i
\(957\) 689.661 0.720649
\(958\) 460.597 + 698.160i 0.480790 + 0.728769i
\(959\) 441.254i 0.460119i
\(960\) 9.76268 + 26.1336i 0.0101695 + 0.0272225i
\(961\) 960.969 0.999968
\(962\) 232.841 153.612i 0.242038 0.159680i
\(963\) 244.804i 0.254209i
\(964\) 430.738 1006.35i 0.446823 1.04393i
\(965\) 22.2809 0.0230890
\(966\) 136.987 + 207.641i 0.141809 + 0.214949i
\(967\) 900.400i 0.931127i 0.885015 + 0.465563i \(0.154148\pi\)
−0.885015 + 0.465563i \(0.845852\pi\)
\(968\) −258.277 1429.43i −0.266816 1.47668i
\(969\) −169.681 −0.175109
\(970\) 32.6020 21.5085i 0.0336103 0.0221737i
\(971\) 253.545i 0.261118i −0.991441 0.130559i \(-0.958323\pi\)
0.991441 0.130559i \(-0.0416772\pi\)
\(972\) 57.3236 + 24.5357i 0.0589749 + 0.0252425i
\(973\) 268.277 0.275721
\(974\) 464.945 + 704.752i 0.477357 + 0.723564i
\(975\) 155.729i 0.159722i
\(976\) 290.092 + 304.030i 0.297225 + 0.311506i
\(977\) −421.348 −0.431267 −0.215634 0.976474i \(-0.569182\pi\)
−0.215634 + 0.976474i \(0.569182\pi\)
\(978\) 456.489 301.159i 0.466757 0.307934i
\(979\) 1819.82i 1.85886i
\(980\) −17.2527 + 40.3080i −0.0176048 + 0.0411306i
\(981\) −335.901 −0.342407
\(982\) 14.3479 + 21.7481i 0.0146109 + 0.0221467i
\(983\) 587.872i 0.598038i 0.954247 + 0.299019i \(0.0966594\pi\)
−0.954247 + 0.299019i \(0.903341\pi\)
\(984\) −146.749 + 26.5154i −0.149135 + 0.0269466i
\(985\) 48.7065 0.0494483
\(986\) −680.891 + 449.204i −0.690559 + 0.455582i
\(987\) 146.684i 0.148616i
\(988\) 72.8996 + 31.2026i 0.0737851 + 0.0315816i
\(989\) −1319.87 −1.33455
\(990\) −14.4642 21.9244i −0.0146103 0.0221459i
\(991\) 555.559i 0.560604i 0.959912 + 0.280302i \(0.0904346\pi\)
−0.959912 + 0.280302i \(0.909565\pi\)
\(992\) 1.25226 5.45454i 0.00126235 0.00549853i
\(993\) 910.496 0.916915
\(994\) 52.6408 34.7287i 0.0529586 0.0349383i
\(995\) 93.7565i 0.0942277i
\(996\) −4.40604 + 10.2940i −0.00442373 + 0.0103353i
\(997\) −1312.59 −1.31654 −0.658272 0.752780i \(-0.728712\pi\)
−0.658272 + 0.752780i \(0.728712\pi\)
\(998\) −390.473 591.868i −0.391256 0.593055i
\(999\) 201.003i 0.201204i
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 156.3.f.a.79.6 yes 24
3.2 odd 2 468.3.f.b.235.19 24
4.3 odd 2 inner 156.3.f.a.79.5 24
8.3 odd 2 2496.3.k.e.703.14 24
8.5 even 2 2496.3.k.e.703.13 24
12.11 even 2 468.3.f.b.235.20 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.3.f.a.79.5 24 4.3 odd 2 inner
156.3.f.a.79.6 yes 24 1.1 even 1 trivial
468.3.f.b.235.19 24 3.2 odd 2
468.3.f.b.235.20 24 12.11 even 2
2496.3.k.e.703.13 24 8.5 even 2
2496.3.k.e.703.14 24 8.3 odd 2