Properties

Label 28.3.c.a.15.5
Level $28$
Weight $3$
Character 28.15
Analytic conductor $0.763$
Analytic rank $0$
Dimension $6$
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] = [28,3,Mod(15,28)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28, base_ring=CyclotomicField(2))
 
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("28.15");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.c (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: \(0.762944740209\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.1539727.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 3x^{3} - 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 15.5
Root \(-1.20134 - 0.746179i\) of defining polynomial
Character \(\chi\) \(=\) 28.15
Dual form 28.3.c.a.15.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58777 - 1.21613i) q^{2} +2.98472i q^{3} +(1.04204 - 3.86188i) q^{4} -6.80536 q^{5} +(3.62981 + 4.73905i) q^{6} -2.64575i q^{7} +(-3.04204 - 7.39905i) q^{8} +0.0914622 q^{9} +O(q^{10})\) \(q+(1.58777 - 1.21613i) q^{2} +2.98472i q^{3} +(1.04204 - 3.86188i) q^{4} -6.80536 q^{5} +(3.62981 + 4.73905i) q^{6} -2.64575i q^{7} +(-3.04204 - 7.39905i) q^{8} +0.0914622 q^{9} +(-10.8054 + 8.27622i) q^{10} +14.3426i q^{11} +(11.5266 + 3.11020i) q^{12} +4.62243 q^{13} +(-3.21759 - 4.20085i) q^{14} -20.3121i q^{15} +(-13.8283 - 8.04848i) q^{16} +11.6107 q^{17} +(0.145221 - 0.111230i) q^{18} -22.4428i q^{19} +(-7.09146 + 26.2815i) q^{20} +7.89682 q^{21} +(17.4426 + 22.7728i) q^{22} -0.853941i q^{23} +(22.0841 - 9.07963i) q^{24} +21.3129 q^{25} +(7.33937 - 5.62149i) q^{26} +27.1354i q^{27} +(-10.2176 - 2.75698i) q^{28} -42.8321 q^{29} +(-24.7022 - 32.2509i) q^{30} +1.54982i q^{31} +(-31.7442 + 4.03789i) q^{32} -42.8087 q^{33} +(18.4352 - 14.1202i) q^{34} +18.0053i q^{35} +(0.0953074 - 0.353217i) q^{36} +45.0151 q^{37} +(-27.2935 - 35.6341i) q^{38} +13.7967i q^{39} +(20.7022 + 50.3532i) q^{40} -36.6492 q^{41} +(12.5384 - 9.60358i) q^{42} +27.9894i q^{43} +(55.3896 + 14.9456i) q^{44} -0.622433 q^{45} +(-1.03851 - 1.35586i) q^{46} -42.1740i q^{47} +(24.0225 - 41.2736i) q^{48} -7.00000 q^{49} +(33.8400 - 25.9193i) q^{50} +34.6547i q^{51} +(4.81677 - 17.8513i) q^{52} +43.4044 q^{53} +(33.0003 + 43.0849i) q^{54} -97.6068i q^{55} +(-19.5761 + 8.04848i) q^{56} +66.9856 q^{57} +(-68.0077 + 52.0896i) q^{58} +53.9979i q^{59} +(-78.4429 - 21.1660i) q^{60} -15.9498 q^{61} +(1.88479 + 2.46077i) q^{62} -0.241986i q^{63} +(-45.4920 + 45.0164i) q^{64} -31.4573 q^{65} +(-67.9705 + 52.0611i) q^{66} -91.9453i q^{67} +(12.0988 - 44.8392i) q^{68} +2.54877 q^{69} +(21.8968 + 28.5883i) q^{70} -16.3585i q^{71} +(-0.278232 - 0.676734i) q^{72} +9.58728 q^{73} +(71.4737 - 54.7443i) q^{74} +63.6130i q^{75} +(-86.6717 - 23.3864i) q^{76} +37.9470 q^{77} +(16.7786 + 21.9059i) q^{78} +56.9826i q^{79} +(94.1065 + 54.7728i) q^{80} -80.1685 q^{81} +(-58.1906 + 44.5703i) q^{82} -14.3077i q^{83} +(8.22881 - 30.4966i) q^{84} -79.0151 q^{85} +(34.0388 + 44.4408i) q^{86} -127.842i q^{87} +(106.122 - 43.6309i) q^{88} +100.136 q^{89} +(-0.988282 + 0.756962i) q^{90} -12.2298i q^{91} +(-3.29782 - 0.889842i) q^{92} -4.62579 q^{93} +(-51.2891 - 66.9626i) q^{94} +152.732i q^{95} +(-12.0520 - 94.7475i) q^{96} +68.2834 q^{97} +(-11.1144 + 8.51293i) q^{98} +1.31181i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.58777 1.21613i 0.793886 0.608066i
\(3\) 2.98472i 0.994906i 0.867491 + 0.497453i \(0.165731\pi\)
−0.867491 + 0.497453i \(0.834269\pi\)
\(4\) 1.04204 3.86188i 0.260510 0.965471i
\(5\) −6.80536 −1.36107 −0.680536 0.732715i \(-0.738253\pi\)
−0.680536 + 0.732715i \(0.738253\pi\)
\(6\) 3.62981 + 4.73905i 0.604969 + 0.789842i
\(7\) 2.64575i 0.377964i
\(8\) −3.04204 7.39905i −0.380255 0.924882i
\(9\) 0.0914622 0.0101625
\(10\) −10.8054 + 8.27622i −1.08054 + 0.827622i
\(11\) 14.3426i 1.30388i 0.758272 + 0.651938i \(0.226044\pi\)
−0.758272 + 0.651938i \(0.773956\pi\)
\(12\) 11.5266 + 3.11020i 0.960553 + 0.259183i
\(13\) 4.62243 0.355572 0.177786 0.984069i \(-0.443107\pi\)
0.177786 + 0.984069i \(0.443107\pi\)
\(14\) −3.21759 4.20085i −0.229828 0.300061i
\(15\) 20.3121i 1.35414i
\(16\) −13.8283 8.04848i −0.864269 0.503030i
\(17\) 11.6107 0.682983 0.341492 0.939885i \(-0.389068\pi\)
0.341492 + 0.939885i \(0.389068\pi\)
\(18\) 0.145221 0.111230i 0.00806784 0.00617946i
\(19\) 22.4428i 1.18120i −0.806964 0.590601i \(-0.798891\pi\)
0.806964 0.590601i \(-0.201109\pi\)
\(20\) −7.09146 + 26.2815i −0.354573 + 1.31408i
\(21\) 7.89682 0.376039
\(22\) 17.4426 + 22.7728i 0.792843 + 1.03513i
\(23\) 0.853941i 0.0371279i −0.999828 0.0185639i \(-0.994091\pi\)
0.999828 0.0185639i \(-0.00590943\pi\)
\(24\) 22.0841 9.07963i 0.920170 0.378318i
\(25\) 21.3129 0.852516
\(26\) 7.33937 5.62149i 0.282283 0.216211i
\(27\) 27.1354i 1.00502i
\(28\) −10.2176 2.75698i −0.364914 0.0984636i
\(29\) −42.8321 −1.47697 −0.738485 0.674270i \(-0.764459\pi\)
−0.738485 + 0.674270i \(0.764459\pi\)
\(30\) −24.7022 32.2509i −0.823406 1.07503i
\(31\) 1.54982i 0.0499943i 0.999688 + 0.0249972i \(0.00795767\pi\)
−0.999688 + 0.0249972i \(0.992042\pi\)
\(32\) −31.7442 + 4.03789i −0.992007 + 0.126184i
\(33\) −42.8087 −1.29723
\(34\) 18.4352 14.1202i 0.542211 0.415299i
\(35\) 18.0053i 0.514437i
\(36\) 0.0953074 0.353217i 0.00264743 0.00981157i
\(37\) 45.0151 1.21662 0.608312 0.793698i \(-0.291847\pi\)
0.608312 + 0.793698i \(0.291847\pi\)
\(38\) −27.2935 35.6341i −0.718250 0.937740i
\(39\) 13.7967i 0.353760i
\(40\) 20.7022 + 50.3532i 0.517554 + 1.25883i
\(41\) −36.6492 −0.893883 −0.446942 0.894563i \(-0.647487\pi\)
−0.446942 + 0.894563i \(0.647487\pi\)
\(42\) 12.5384 9.60358i 0.298532 0.228657i
\(43\) 27.9894i 0.650916i 0.945557 + 0.325458i \(0.105518\pi\)
−0.945557 + 0.325458i \(0.894482\pi\)
\(44\) 55.3896 + 14.9456i 1.25885 + 0.339673i
\(45\) −0.622433 −0.0138318
\(46\) −1.03851 1.35586i −0.0225762 0.0294753i
\(47\) 42.1740i 0.897318i −0.893703 0.448659i \(-0.851902\pi\)
0.893703 0.448659i \(-0.148098\pi\)
\(48\) 24.0225 41.2736i 0.500468 0.859866i
\(49\) −7.00000 −0.142857
\(50\) 33.8400 25.9193i 0.676800 0.518386i
\(51\) 34.6547i 0.679504i
\(52\) 4.81677 17.8513i 0.0926301 0.343294i
\(53\) 43.4044 0.818950 0.409475 0.912321i \(-0.365712\pi\)
0.409475 + 0.912321i \(0.365712\pi\)
\(54\) 33.0003 + 43.0849i 0.611117 + 0.797869i
\(55\) 97.6068i 1.77467i
\(56\) −19.5761 + 8.04848i −0.349572 + 0.143723i
\(57\) 66.9856 1.17519
\(58\) −68.0077 + 52.0896i −1.17255 + 0.898096i
\(59\) 53.9979i 0.915219i 0.889153 + 0.457609i \(0.151294\pi\)
−0.889153 + 0.457609i \(0.848706\pi\)
\(60\) −78.4429 21.1660i −1.30738 0.352767i
\(61\) −15.9498 −0.261472 −0.130736 0.991417i \(-0.541734\pi\)
−0.130736 + 0.991417i \(0.541734\pi\)
\(62\) 1.88479 + 2.46077i 0.0303999 + 0.0396898i
\(63\) 0.241986i 0.00384105i
\(64\) −45.4920 + 45.0164i −0.710812 + 0.703382i
\(65\) −31.4573 −0.483959
\(66\) −67.9705 + 52.0611i −1.02986 + 0.788804i
\(67\) 91.9453i 1.37232i −0.727452 0.686159i \(-0.759295\pi\)
0.727452 0.686159i \(-0.240705\pi\)
\(68\) 12.0988 44.8392i 0.177924 0.659401i
\(69\) 2.54877 0.0369387
\(70\) 21.8968 + 28.5883i 0.312812 + 0.408404i
\(71\) 16.3585i 0.230401i −0.993342 0.115201i \(-0.963249\pi\)
0.993342 0.115201i \(-0.0367511\pi\)
\(72\) −0.278232 0.676734i −0.00386433 0.00939908i
\(73\) 9.58728 0.131333 0.0656663 0.997842i \(-0.479083\pi\)
0.0656663 + 0.997842i \(0.479083\pi\)
\(74\) 71.4737 54.7443i 0.965861 0.739788i
\(75\) 63.6130i 0.848173i
\(76\) −86.6717 23.3864i −1.14042 0.307715i
\(77\) 37.9470 0.492819
\(78\) 16.7786 + 21.9059i 0.215110 + 0.280845i
\(79\) 56.9826i 0.721299i 0.932701 + 0.360649i \(0.117445\pi\)
−0.932701 + 0.360649i \(0.882555\pi\)
\(80\) 94.1065 + 54.7728i 1.17633 + 0.684660i
\(81\) −80.1685 −0.989734
\(82\) −58.1906 + 44.5703i −0.709642 + 0.543541i
\(83\) 14.3077i 0.172381i −0.996279 0.0861907i \(-0.972531\pi\)
0.996279 0.0861907i \(-0.0274694\pi\)
\(84\) 8.22881 30.4966i 0.0979620 0.363055i
\(85\) −79.0151 −0.929589
\(86\) 34.0388 + 44.4408i 0.395800 + 0.516753i
\(87\) 127.842i 1.46945i
\(88\) 106.122 43.6309i 1.20593 0.495805i
\(89\) 100.136 1.12512 0.562562 0.826755i \(-0.309816\pi\)
0.562562 + 0.826755i \(0.309816\pi\)
\(90\) −0.988282 + 0.756962i −0.0109809 + 0.00841068i
\(91\) 12.2298i 0.134394i
\(92\) −3.29782 0.889842i −0.0358459 0.00967219i
\(93\) −4.62579 −0.0497396
\(94\) −51.2891 66.9626i −0.545629 0.712369i
\(95\) 152.732i 1.60770i
\(96\) −12.0520 94.7475i −0.125541 0.986953i
\(97\) 68.2834 0.703952 0.351976 0.936009i \(-0.385510\pi\)
0.351976 + 0.936009i \(0.385510\pi\)
\(98\) −11.1144 + 8.51293i −0.113412 + 0.0868666i
\(99\) 1.31181i 0.0132506i
\(100\) 22.2089 82.3079i 0.222089 0.823079i
\(101\) −28.1628 −0.278840 −0.139420 0.990233i \(-0.544524\pi\)
−0.139420 + 0.990233i \(0.544524\pi\)
\(102\) 42.1447 + 55.0238i 0.413184 + 0.539449i
\(103\) 160.243i 1.55575i 0.628416 + 0.777877i \(0.283703\pi\)
−0.628416 + 0.777877i \(0.716297\pi\)
\(104\) −14.0616 34.2016i −0.135208 0.328862i
\(105\) −53.7407 −0.511816
\(106\) 68.9162 52.7855i 0.650153 0.497976i
\(107\) 118.923i 1.11143i −0.831374 0.555713i \(-0.812445\pi\)
0.831374 0.555713i \(-0.187555\pi\)
\(108\) 104.794 + 28.2762i 0.970314 + 0.261817i
\(109\) −98.2666 −0.901529 −0.450764 0.892643i \(-0.648849\pi\)
−0.450764 + 0.892643i \(0.648849\pi\)
\(110\) −118.703 154.977i −1.07912 1.40888i
\(111\) 134.357i 1.21043i
\(112\) −21.2943 + 36.5862i −0.190128 + 0.326663i
\(113\) 96.9977 0.858387 0.429193 0.903213i \(-0.358798\pi\)
0.429193 + 0.903213i \(0.358798\pi\)
\(114\) 106.358 81.4633i 0.932963 0.714591i
\(115\) 5.81138i 0.0505337i
\(116\) −44.6329 + 165.413i −0.384766 + 1.42597i
\(117\) 0.422778 0.00361349
\(118\) 65.6686 + 85.7364i 0.556514 + 0.726579i
\(119\) 30.7191i 0.258143i
\(120\) −150.290 + 61.7901i −1.25242 + 0.514918i
\(121\) −84.7112 −0.700092
\(122\) −25.3246 + 19.3970i −0.207579 + 0.158992i
\(123\) 109.388i 0.889330i
\(124\) 5.98524 + 1.61498i 0.0482681 + 0.0130240i
\(125\) 25.0921 0.200737
\(126\) −0.294288 0.384219i −0.00233562 0.00304936i
\(127\) 71.8712i 0.565915i 0.959132 + 0.282958i \(0.0913156\pi\)
−0.959132 + 0.282958i \(0.908684\pi\)
\(128\) −17.4849 + 126.800i −0.136601 + 0.990626i
\(129\) −83.5404 −0.647600
\(130\) −49.9470 + 38.2563i −0.384208 + 0.294279i
\(131\) 209.837i 1.60181i −0.598791 0.800906i \(-0.704352\pi\)
0.598791 0.800906i \(-0.295648\pi\)
\(132\) −44.6084 + 165.322i −0.337943 + 1.25244i
\(133\) −59.3782 −0.446453
\(134\) −111.818 145.988i −0.834460 1.08946i
\(135\) 184.666i 1.36790i
\(136\) −35.3203 85.9083i −0.259708 0.631679i
\(137\) −18.1650 −0.132591 −0.0662954 0.997800i \(-0.521118\pi\)
−0.0662954 + 0.997800i \(0.521118\pi\)
\(138\) 4.04687 3.09965i 0.0293252 0.0224612i
\(139\) 134.084i 0.964635i 0.875996 + 0.482318i \(0.160205\pi\)
−0.875996 + 0.482318i \(0.839795\pi\)
\(140\) 69.5343 + 18.7622i 0.496674 + 0.134016i
\(141\) 125.877 0.892747
\(142\) −19.8941 25.9735i −0.140099 0.182912i
\(143\) 66.2979i 0.463621i
\(144\) −1.26477 0.736132i −0.00878311 0.00511203i
\(145\) 291.488 2.01026
\(146\) 15.2224 11.6594i 0.104263 0.0798590i
\(147\) 20.8930i 0.142129i
\(148\) 46.9076 173.843i 0.316943 1.17461i
\(149\) −20.7618 −0.139341 −0.0696706 0.997570i \(-0.522195\pi\)
−0.0696706 + 0.997570i \(0.522195\pi\)
\(150\) 77.3618 + 101.003i 0.515745 + 0.673353i
\(151\) 93.1090i 0.616616i −0.951287 0.308308i \(-0.900237\pi\)
0.951287 0.308308i \(-0.0997628\pi\)
\(152\) −166.056 + 68.2721i −1.09247 + 0.449158i
\(153\) 1.06194 0.00694080
\(154\) 60.2513 46.1487i 0.391242 0.299667i
\(155\) 10.5471i 0.0680458i
\(156\) 53.2811 + 14.3767i 0.341545 + 0.0921582i
\(157\) 159.337 1.01489 0.507444 0.861685i \(-0.330590\pi\)
0.507444 + 0.861685i \(0.330590\pi\)
\(158\) 69.2984 + 90.4754i 0.438598 + 0.572629i
\(159\) 129.550i 0.814778i
\(160\) 216.031 27.4793i 1.35019 0.171746i
\(161\) −2.25932 −0.0140330
\(162\) −127.289 + 97.4955i −0.785736 + 0.601824i
\(163\) 45.8277i 0.281152i −0.990070 0.140576i \(-0.955105\pi\)
0.990070 0.140576i \(-0.0448954\pi\)
\(164\) −38.1900 + 141.535i −0.232866 + 0.863019i
\(165\) 291.329 1.76563
\(166\) −17.4000 22.7173i −0.104819 0.136851i
\(167\) 15.5845i 0.0933203i 0.998911 + 0.0466602i \(0.0148578\pi\)
−0.998911 + 0.0466602i \(0.985142\pi\)
\(168\) −24.0225 58.4290i −0.142991 0.347792i
\(169\) −147.633 −0.873569
\(170\) −125.458 + 96.0928i −0.737988 + 0.565252i
\(171\) 2.05267i 0.0120039i
\(172\) 108.092 + 29.1661i 0.628441 + 0.169570i
\(173\) −266.021 −1.53770 −0.768848 0.639432i \(-0.779170\pi\)
−0.768848 + 0.639432i \(0.779170\pi\)
\(174\) −155.473 202.984i −0.893521 1.16657i
\(175\) 56.3886i 0.322221i
\(176\) 115.436 198.334i 0.655889 1.12690i
\(177\) −161.168 −0.910556
\(178\) 158.993 121.779i 0.893220 0.684150i
\(179\) 44.5059i 0.248636i −0.992242 0.124318i \(-0.960326\pi\)
0.992242 0.124318i \(-0.0396744\pi\)
\(180\) −0.648601 + 2.40376i −0.00360334 + 0.0133542i
\(181\) −168.111 −0.928787 −0.464394 0.885629i \(-0.653728\pi\)
−0.464394 + 0.885629i \(0.653728\pi\)
\(182\) −14.8731 19.4182i −0.0817202 0.106693i
\(183\) 47.6056i 0.260140i
\(184\) −6.31836 + 2.59772i −0.0343389 + 0.0141181i
\(185\) −306.344 −1.65591
\(186\) −7.34469 + 5.62557i −0.0394876 + 0.0302450i
\(187\) 166.528i 0.890525i
\(188\) −162.871 43.9470i −0.866335 0.233761i
\(189\) 71.7936 0.379861
\(190\) 185.742 + 242.503i 0.977589 + 1.27633i
\(191\) 353.607i 1.85134i 0.378328 + 0.925672i \(0.376499\pi\)
−0.378328 + 0.925672i \(0.623501\pi\)
\(192\) −134.361 135.781i −0.699799 0.707191i
\(193\) −348.574 −1.80608 −0.903042 0.429553i \(-0.858671\pi\)
−0.903042 + 0.429553i \(0.858671\pi\)
\(194\) 108.418 83.0417i 0.558858 0.428050i
\(195\) 93.8912i 0.481493i
\(196\) −7.29429 + 27.0332i −0.0372158 + 0.137924i
\(197\) −26.9314 −0.136707 −0.0683537 0.997661i \(-0.521775\pi\)
−0.0683537 + 0.997661i \(0.521775\pi\)
\(198\) 1.59533 + 2.08285i 0.00805725 + 0.0105195i
\(199\) 231.560i 1.16362i 0.813326 + 0.581809i \(0.197655\pi\)
−0.813326 + 0.581809i \(0.802345\pi\)
\(200\) −64.8347 157.695i −0.324173 0.788476i
\(201\) 274.431 1.36533
\(202\) −44.7162 + 34.2498i −0.221367 + 0.169553i
\(203\) 113.323i 0.558242i
\(204\) 133.832 + 36.1116i 0.656041 + 0.177018i
\(205\) 249.411 1.21664
\(206\) 194.876 + 254.429i 0.946002 + 1.23509i
\(207\) 0.0781034i 0.000377311i
\(208\) −63.9204 37.2036i −0.307310 0.178863i
\(209\) 321.890 1.54014
\(210\) −85.3280 + 65.3558i −0.406324 + 0.311218i
\(211\) 79.6903i 0.377679i −0.982008 0.188840i \(-0.939527\pi\)
0.982008 0.188840i \(-0.0604726\pi\)
\(212\) 45.2291 167.623i 0.213345 0.790673i
\(213\) 48.8254 0.229227
\(214\) −144.626 188.822i −0.675821 0.882346i
\(215\) 190.478i 0.885943i
\(216\) 200.777 82.5471i 0.929521 0.382163i
\(217\) 4.10045 0.0188961
\(218\) −156.025 + 119.505i −0.715711 + 0.548189i
\(219\) 28.6153i 0.130664i
\(220\) −376.946 101.710i −1.71339 0.462319i
\(221\) 53.6698 0.242850
\(222\) 163.396 + 213.329i 0.736019 + 0.960940i
\(223\) 264.367i 1.18550i −0.805386 0.592750i \(-0.798042\pi\)
0.805386 0.592750i \(-0.201958\pi\)
\(224\) 10.6833 + 83.9873i 0.0476931 + 0.374943i
\(225\) 1.94932 0.00866367
\(226\) 154.010 117.962i 0.681461 0.521956i
\(227\) 431.324i 1.90011i −0.312088 0.950053i \(-0.601028\pi\)
0.312088 0.950053i \(-0.398972\pi\)
\(228\) 69.8017 258.690i 0.306148 1.13461i
\(229\) −424.901 −1.85546 −0.927732 0.373247i \(-0.878244\pi\)
−0.927732 + 0.373247i \(0.878244\pi\)
\(230\) 7.06741 + 9.22714i 0.0307279 + 0.0401180i
\(231\) 113.261i 0.490308i
\(232\) 130.297 + 316.917i 0.561626 + 1.36602i
\(233\) 218.828 0.939176 0.469588 0.882886i \(-0.344403\pi\)
0.469588 + 0.882886i \(0.344403\pi\)
\(234\) 0.671275 0.514154i 0.00286870 0.00219724i
\(235\) 287.009i 1.22131i
\(236\) 208.534 + 56.2680i 0.883617 + 0.238424i
\(237\) −170.077 −0.717625
\(238\) −37.3585 48.7749i −0.156968 0.204936i
\(239\) 90.1656i 0.377262i 0.982048 + 0.188631i \(0.0604050\pi\)
−0.982048 + 0.188631i \(0.939595\pi\)
\(240\) −163.481 + 280.881i −0.681172 + 1.17034i
\(241\) 375.944 1.55994 0.779968 0.625820i \(-0.215236\pi\)
0.779968 + 0.625820i \(0.215236\pi\)
\(242\) −134.502 + 103.020i −0.555794 + 0.425703i
\(243\) 4.93877i 0.0203242i
\(244\) −16.6203 + 61.5962i −0.0681161 + 0.252443i
\(245\) 47.6375 0.194439
\(246\) −133.030 173.683i −0.540772 0.706027i
\(247\) 103.741i 0.420002i
\(248\) 11.4672 4.71463i 0.0462388 0.0190106i
\(249\) 42.7043 0.171503
\(250\) 39.8405 30.5153i 0.159362 0.122061i
\(251\) 319.525i 1.27301i −0.771274 0.636503i \(-0.780380\pi\)
0.771274 0.636503i \(-0.219620\pi\)
\(252\) −0.934523 0.252160i −0.00370843 0.00100063i
\(253\) 12.2478 0.0484101
\(254\) 87.4050 + 114.115i 0.344114 + 0.449272i
\(255\) 235.838i 0.924854i
\(256\) 126.444 + 222.594i 0.493921 + 0.869507i
\(257\) −167.466 −0.651618 −0.325809 0.945436i \(-0.605637\pi\)
−0.325809 + 0.945436i \(0.605637\pi\)
\(258\) −132.643 + 101.596i −0.514121 + 0.393784i
\(259\) 119.099i 0.459840i
\(260\) −32.7798 + 121.484i −0.126076 + 0.467248i
\(261\) −3.91752 −0.0150097
\(262\) −255.190 333.174i −0.974008 1.27166i
\(263\) 86.1276i 0.327481i 0.986503 + 0.163741i \(0.0523560\pi\)
−0.986503 + 0.163741i \(0.947644\pi\)
\(264\) 130.226 + 316.744i 0.493280 + 1.19979i
\(265\) −295.382 −1.11465
\(266\) −94.2790 + 72.2118i −0.354432 + 0.271473i
\(267\) 298.878i 1.11939i
\(268\) −355.082 95.8108i −1.32493 0.357503i
\(269\) 269.343 1.00128 0.500638 0.865657i \(-0.333099\pi\)
0.500638 + 0.865657i \(0.333099\pi\)
\(270\) −224.579 293.208i −0.831774 1.08596i
\(271\) 318.318i 1.17460i −0.809368 0.587302i \(-0.800190\pi\)
0.809368 0.587302i \(-0.199810\pi\)
\(272\) −160.556 93.4487i −0.590281 0.343561i
\(273\) 36.5025 0.133709
\(274\) −28.8418 + 22.0910i −0.105262 + 0.0806241i
\(275\) 305.683i 1.11157i
\(276\) 2.65593 9.84307i 0.00962292 0.0356633i
\(277\) 356.597 1.28735 0.643677 0.765298i \(-0.277408\pi\)
0.643677 + 0.765298i \(0.277408\pi\)
\(278\) 163.064 + 212.895i 0.586562 + 0.765810i
\(279\) 0.141750i 0.000508066i
\(280\) 133.222 54.7728i 0.475793 0.195617i
\(281\) 109.846 0.390911 0.195455 0.980713i \(-0.437381\pi\)
0.195455 + 0.980713i \(0.437381\pi\)
\(282\) 199.865 153.084i 0.708740 0.542850i
\(283\) 514.582i 1.81831i 0.416457 + 0.909155i \(0.363272\pi\)
−0.416457 + 0.909155i \(0.636728\pi\)
\(284\) −63.1746 17.0462i −0.222446 0.0600219i
\(285\) −455.861 −1.59951
\(286\) 80.6270 + 105.266i 0.281913 + 0.368063i
\(287\) 96.9647i 0.337856i
\(288\) −2.90340 + 0.369315i −0.0100812 + 0.00128234i
\(289\) −154.191 −0.533534
\(290\) 462.817 354.488i 1.59592 1.22237i
\(291\) 203.807i 0.700366i
\(292\) 9.99034 37.0250i 0.0342135 0.126798i
\(293\) −133.002 −0.453931 −0.226965 0.973903i \(-0.572880\pi\)
−0.226965 + 0.973903i \(0.572880\pi\)
\(294\) −25.4087 33.1734i −0.0864241 0.112835i
\(295\) 367.475i 1.24568i
\(296\) −136.938 333.069i −0.462627 1.12523i
\(297\) −389.194 −1.31042
\(298\) −32.9651 + 25.2492i −0.110621 + 0.0847287i
\(299\) 3.94729i 0.0132016i
\(300\) 245.666 + 66.2873i 0.818886 + 0.220958i
\(301\) 74.0530 0.246023
\(302\) −113.233 147.836i −0.374944 0.489523i
\(303\) 84.0581i 0.277420i
\(304\) −180.631 + 310.346i −0.594181 + 1.02088i
\(305\) 108.544 0.355882
\(306\) 1.68612 1.29146i 0.00551020 0.00422047i
\(307\) 382.811i 1.24694i 0.781847 + 0.623471i \(0.214278\pi\)
−0.781847 + 0.623471i \(0.785722\pi\)
\(308\) 39.5424 146.547i 0.128384 0.475802i
\(309\) −478.279 −1.54783
\(310\) −12.8267 16.7464i −0.0413764 0.0540206i
\(311\) 196.374i 0.631426i 0.948855 + 0.315713i \(0.102244\pi\)
−0.948855 + 0.315713i \(0.897756\pi\)
\(312\) 102.082 41.9700i 0.327187 0.134519i
\(313\) 427.045 1.36436 0.682181 0.731183i \(-0.261032\pi\)
0.682181 + 0.731183i \(0.261032\pi\)
\(314\) 252.991 193.775i 0.805705 0.617119i
\(315\) 1.64680i 0.00522795i
\(316\) 220.060 + 59.3782i 0.696393 + 0.187906i
\(317\) 111.049 0.350314 0.175157 0.984541i \(-0.443957\pi\)
0.175157 + 0.984541i \(0.443957\pi\)
\(318\) 157.550 + 205.695i 0.495439 + 0.646841i
\(319\) 614.326i 1.92579i
\(320\) 309.589 306.353i 0.967466 0.957353i
\(321\) 354.951 1.10577
\(322\) −3.58728 + 2.74763i −0.0111406 + 0.00853301i
\(323\) 260.577i 0.806741i
\(324\) −83.5388 + 309.601i −0.257836 + 0.955560i
\(325\) 98.5174 0.303131
\(326\) −55.7326 72.7640i −0.170959 0.223202i
\(327\) 293.298i 0.896936i
\(328\) 111.488 + 271.170i 0.339904 + 0.826736i
\(329\) −111.582 −0.339154
\(330\) 462.563 354.294i 1.40171 1.07362i
\(331\) 119.629i 0.361416i 0.983537 + 0.180708i \(0.0578388\pi\)
−0.983537 + 0.180708i \(0.942161\pi\)
\(332\) −55.2545 14.9092i −0.166429 0.0449071i
\(333\) 4.11718 0.0123639
\(334\) 18.9528 + 24.7446i 0.0567450 + 0.0740857i
\(335\) 625.721i 1.86782i
\(336\) −109.200 63.5574i −0.324999 0.189159i
\(337\) −57.3636 −0.170218 −0.0851092 0.996372i \(-0.527124\pi\)
−0.0851092 + 0.996372i \(0.527124\pi\)
\(338\) −234.408 + 179.541i −0.693514 + 0.531188i
\(339\) 289.511i 0.854014i
\(340\) −82.3369 + 305.147i −0.242167 + 0.897491i
\(341\) −22.2286 −0.0651864
\(342\) −2.49632 3.25918i −0.00729919 0.00952976i
\(343\) 18.5203i 0.0539949i
\(344\) 207.095 85.1449i 0.602020 0.247514i
\(345\) −17.3453 −0.0502763
\(346\) −422.381 + 323.517i −1.22076 + 0.935021i
\(347\) 268.774i 0.774566i 0.921961 + 0.387283i \(0.126586\pi\)
−0.921961 + 0.387283i \(0.873414\pi\)
\(348\) −493.710 133.216i −1.41871 0.382806i
\(349\) 97.0498 0.278080 0.139040 0.990287i \(-0.455598\pi\)
0.139040 + 0.990287i \(0.455598\pi\)
\(350\) −68.5761 89.5323i −0.195932 0.255806i
\(351\) 125.432i 0.357356i
\(352\) −57.9140 455.296i −0.164528 1.29345i
\(353\) −316.928 −0.897813 −0.448907 0.893579i \(-0.648186\pi\)
−0.448907 + 0.893579i \(0.648186\pi\)
\(354\) −255.899 + 196.002i −0.722878 + 0.553679i
\(355\) 111.325i 0.313592i
\(356\) 104.346 386.714i 0.293106 1.08627i
\(357\) 91.6877 0.256828
\(358\) −54.1251 70.6653i −0.151187 0.197389i
\(359\) 590.194i 1.64399i −0.569492 0.821997i \(-0.692860\pi\)
0.569492 0.821997i \(-0.307140\pi\)
\(360\) 1.89347 + 4.60542i 0.00525963 + 0.0127928i
\(361\) −142.681 −0.395239
\(362\) −266.921 + 204.445i −0.737351 + 0.564764i
\(363\) 252.839i 0.696526i
\(364\) −47.2301 12.7440i −0.129753 0.0350109i
\(365\) −65.2449 −0.178753
\(366\) −57.8947 75.5868i −0.158182 0.206521i
\(367\) 175.544i 0.478321i −0.970980 0.239160i \(-0.923128\pi\)
0.970980 0.239160i \(-0.0768722\pi\)
\(368\) −6.87293 + 11.8086i −0.0186764 + 0.0320885i
\(369\) −3.35202 −0.00908406
\(370\) −486.404 + 372.555i −1.31461 + 1.00690i
\(371\) 114.837i 0.309534i
\(372\) −4.82026 + 17.8642i −0.0129577 + 0.0480222i
\(373\) 554.016 1.48530 0.742649 0.669681i \(-0.233569\pi\)
0.742649 + 0.669681i \(0.233569\pi\)
\(374\) 202.520 + 264.409i 0.541499 + 0.706976i
\(375\) 74.8928i 0.199714i
\(376\) −312.047 + 128.295i −0.829913 + 0.341210i
\(377\) −197.989 −0.525169
\(378\) 113.992 87.3106i 0.301566 0.230980i
\(379\) 749.909i 1.97865i −0.145723 0.989325i \(-0.546551\pi\)
0.145723 0.989325i \(-0.453449\pi\)
\(380\) 589.832 + 159.153i 1.55219 + 0.418823i
\(381\) −214.515 −0.563032
\(382\) 430.033 + 561.447i 1.12574 + 1.46976i
\(383\) 246.230i 0.642899i 0.946927 + 0.321450i \(0.104170\pi\)
−0.946927 + 0.321450i \(0.895830\pi\)
\(384\) −378.463 52.1875i −0.985580 0.135905i
\(385\) −258.243 −0.670762
\(386\) −553.456 + 423.912i −1.43382 + 1.09822i
\(387\) 2.55997i 0.00661491i
\(388\) 71.1541 263.702i 0.183387 0.679646i
\(389\) 298.019 0.766115 0.383058 0.923724i \(-0.374871\pi\)
0.383058 + 0.923724i \(0.374871\pi\)
\(390\) −114.184 149.078i −0.292780 0.382251i
\(391\) 9.91487i 0.0253577i
\(392\) 21.2943 + 51.7934i 0.0543222 + 0.132126i
\(393\) 626.305 1.59365
\(394\) −42.7609 + 32.7521i −0.108530 + 0.0831272i
\(395\) 387.787i 0.981739i
\(396\) 5.06606 + 1.36696i 0.0127931 + 0.00345192i
\(397\) 127.823 0.321971 0.160986 0.986957i \(-0.448533\pi\)
0.160986 + 0.986957i \(0.448533\pi\)
\(398\) 281.608 + 367.664i 0.707557 + 0.923779i
\(399\) 177.227i 0.444178i
\(400\) −294.721 171.536i −0.736803 0.428841i
\(401\) −774.286 −1.93089 −0.965444 0.260609i \(-0.916077\pi\)
−0.965444 + 0.260609i \(0.916077\pi\)
\(402\) 435.733 333.744i 1.08391 0.830210i
\(403\) 7.16396i 0.0177766i
\(404\) −29.3468 + 108.762i −0.0726407 + 0.269212i
\(405\) 545.575 1.34710
\(406\) 137.816 + 179.931i 0.339448 + 0.443181i
\(407\) 645.635i 1.58633i
\(408\) 256.412 105.421i 0.628461 0.258385i
\(409\) 666.884 1.63052 0.815262 0.579093i \(-0.196593\pi\)
0.815262 + 0.579093i \(0.196593\pi\)
\(410\) 396.008 303.317i 0.965873 0.739798i
\(411\) 54.2172i 0.131915i
\(412\) 618.839 + 166.979i 1.50204 + 0.405290i
\(413\) 142.865 0.345920
\(414\) −0.0949841 0.124010i −0.000229430 0.000299542i
\(415\) 97.3687i 0.234623i
\(416\) −146.736 + 18.6649i −0.352730 + 0.0448675i
\(417\) −400.204 −0.959721
\(418\) 511.087 391.460i 1.22270 0.936508i
\(419\) 95.3634i 0.227598i 0.993504 + 0.113799i \(0.0363019\pi\)
−0.993504 + 0.113799i \(0.963698\pi\)
\(420\) −56.0000 + 207.540i −0.133333 + 0.494144i
\(421\) −279.158 −0.663083 −0.331541 0.943441i \(-0.607569\pi\)
−0.331541 + 0.943441i \(0.607569\pi\)
\(422\) −96.9140 126.530i −0.229654 0.299834i
\(423\) 3.85732i 0.00911897i
\(424\) −132.038 321.151i −0.311410 0.757432i
\(425\) 247.458 0.582254
\(426\) 77.5237 59.3782i 0.181980 0.139386i
\(427\) 42.1991i 0.0988270i
\(428\) −459.266 123.922i −1.07305 0.289538i
\(429\) −197.880 −0.461260
\(430\) −231.646 302.435i −0.538712 0.703338i
\(431\) 169.374i 0.392978i −0.980506 0.196489i \(-0.937046\pi\)
0.980506 0.196489i \(-0.0629540\pi\)
\(432\) 218.399 375.237i 0.505554 0.868604i
\(433\) −295.214 −0.681787 −0.340894 0.940102i \(-0.610730\pi\)
−0.340894 + 0.940102i \(0.610730\pi\)
\(434\) 6.51058 4.98669i 0.0150013 0.0114901i
\(435\) 870.010i 2.00002i
\(436\) −102.398 + 379.494i −0.234858 + 0.870400i
\(437\) −19.1649 −0.0438555
\(438\) 34.8000 + 45.4346i 0.0794521 + 0.103732i
\(439\) 326.773i 0.744357i 0.928161 + 0.372179i \(0.121389\pi\)
−0.928161 + 0.372179i \(0.878611\pi\)
\(440\) −722.198 + 296.924i −1.64136 + 0.674827i
\(441\) −0.640236 −0.00145178
\(442\) 85.2153 65.2696i 0.192795 0.147669i
\(443\) 514.789i 1.16205i −0.813885 0.581026i \(-0.802651\pi\)
0.813885 0.581026i \(-0.197349\pi\)
\(444\) 518.872 + 140.006i 1.16863 + 0.315328i
\(445\) −681.462 −1.53137
\(446\) −321.505 419.754i −0.720863 0.941153i
\(447\) 61.9682i 0.138631i
\(448\) 119.102 + 120.360i 0.265853 + 0.268662i
\(449\) 602.217 1.34124 0.670620 0.741801i \(-0.266028\pi\)
0.670620 + 0.741801i \(0.266028\pi\)
\(450\) 3.09508 2.37064i 0.00687796 0.00526808i
\(451\) 525.646i 1.16551i
\(452\) 101.076 374.594i 0.223619 0.828748i
\(453\) 277.904 0.613475
\(454\) −524.548 684.845i −1.15539 1.50847i
\(455\) 83.2282i 0.182919i
\(456\) −203.773 495.630i −0.446870 1.08691i
\(457\) −264.634 −0.579069 −0.289534 0.957168i \(-0.593500\pi\)
−0.289534 + 0.957168i \(0.593500\pi\)
\(458\) −674.646 + 516.736i −1.47303 + 1.12825i
\(459\) 315.062i 0.686409i
\(460\) 22.4429 + 6.05569i 0.0487888 + 0.0131645i
\(461\) −434.788 −0.943140 −0.471570 0.881829i \(-0.656313\pi\)
−0.471570 + 0.881829i \(0.656313\pi\)
\(462\) 137.741 + 179.833i 0.298140 + 0.389249i
\(463\) 193.258i 0.417403i 0.977979 + 0.208702i \(0.0669237\pi\)
−0.977979 + 0.208702i \(0.933076\pi\)
\(464\) 592.296 + 344.734i 1.27650 + 0.742961i
\(465\) 31.4801 0.0676992
\(466\) 347.449 266.124i 0.745598 0.571081i
\(467\) 655.297i 1.40320i 0.712569 + 0.701602i \(0.247532\pi\)
−0.712569 + 0.701602i \(0.752468\pi\)
\(468\) 0.440552 1.63272i 0.000941351 0.00348872i
\(469\) −243.264 −0.518687
\(470\) 349.041 + 455.705i 0.742640 + 0.969585i
\(471\) 475.577i 1.00972i
\(472\) 399.533 164.264i 0.846469 0.348017i
\(473\) −401.442 −0.848714
\(474\) −270.044 + 206.836i −0.569712 + 0.436363i
\(475\) 478.322i 1.00699i
\(476\) −118.633 32.0105i −0.249230 0.0672490i
\(477\) 3.96986 0.00832256
\(478\) 109.653 + 143.162i 0.229400 + 0.299503i
\(479\) 102.660i 0.214322i 0.994242 + 0.107161i \(0.0341761\pi\)
−0.994242 + 0.107161i \(0.965824\pi\)
\(480\) 82.0180 + 644.791i 0.170871 + 1.34331i
\(481\) 208.079 0.432597
\(482\) 596.914 457.198i 1.23841 0.948544i
\(483\) 6.74342i 0.0139615i
\(484\) −88.2725 + 327.145i −0.182381 + 0.675919i
\(485\) −464.693 −0.958129
\(486\) 6.00620 + 7.84164i 0.0123584 + 0.0161351i
\(487\) 150.652i 0.309347i 0.987966 + 0.154674i \(0.0494326\pi\)
−0.987966 + 0.154674i \(0.950567\pi\)
\(488\) 48.5199 + 118.013i 0.0994260 + 0.241830i
\(489\) 136.783 0.279720
\(490\) 75.6375 57.9335i 0.154362 0.118232i
\(491\) 118.795i 0.241946i −0.992656 0.120973i \(-0.961399\pi\)
0.992656 0.120973i \(-0.0386014\pi\)
\(492\) −422.442 113.986i −0.858622 0.231680i
\(493\) −497.312 −1.00875
\(494\) −126.162 164.716i −0.255389 0.333434i
\(495\) 8.92733i 0.0180350i
\(496\) 12.4737 21.4314i 0.0251487 0.0432085i
\(497\) −43.2805 −0.0870834
\(498\) 67.8047 51.9341i 0.136154 0.104285i
\(499\) 546.431i 1.09505i 0.836789 + 0.547526i \(0.184430\pi\)
−0.836789 + 0.547526i \(0.815570\pi\)
\(500\) 26.1470 96.9027i 0.0522940 0.193805i
\(501\) −46.5153 −0.0928449
\(502\) −388.584 507.332i −0.774073 1.01062i
\(503\) 520.718i 1.03522i −0.855615 0.517612i \(-0.826821\pi\)
0.855615 0.517612i \(-0.173179\pi\)
\(504\) −1.79047 + 0.736132i −0.00355252 + 0.00146058i
\(505\) 191.658 0.379521
\(506\) 19.4467 14.8949i 0.0384321 0.0294366i
\(507\) 440.643i 0.869119i
\(508\) 277.558 + 74.8928i 0.546375 + 0.147427i
\(509\) 601.427 1.18159 0.590793 0.806823i \(-0.298815\pi\)
0.590793 + 0.806823i \(0.298815\pi\)
\(510\) −286.810 374.456i −0.562372 0.734228i
\(511\) 25.3656i 0.0496391i
\(512\) 471.468 + 199.656i 0.920835 + 0.389952i
\(513\) 608.997 1.18713
\(514\) −265.898 + 203.661i −0.517311 + 0.396227i
\(515\) 1090.51i 2.11749i
\(516\) −87.0525 + 322.623i −0.168706 + 0.625239i
\(517\) 604.886 1.16999
\(518\) −144.840 189.102i −0.279614 0.365061i
\(519\) 793.998i 1.52986i
\(520\) 95.6944 + 232.754i 0.184028 + 0.447604i
\(521\) −582.268 −1.11760 −0.558798 0.829304i \(-0.688737\pi\)
−0.558798 + 0.829304i \(0.688737\pi\)
\(522\) −6.22014 + 4.76423i −0.0119160 + 0.00912688i
\(523\) 143.593i 0.274557i 0.990533 + 0.137278i \(0.0438355\pi\)
−0.990533 + 0.137278i \(0.956165\pi\)
\(524\) −810.367 218.659i −1.54650 0.417288i
\(525\) 168.304 0.320579
\(526\) 104.743 + 136.751i 0.199130 + 0.259983i
\(527\) 17.9946i 0.0341453i
\(528\) 591.972 + 344.545i 1.12116 + 0.652548i
\(529\) 528.271 0.998622
\(530\) −469.000 + 359.224i −0.884905 + 0.677781i
\(531\) 4.93877i 0.00930088i
\(532\) −61.8745 + 229.312i −0.116305 + 0.431037i
\(533\) −169.409 −0.317840
\(534\) 363.475 + 474.550i 0.680665 + 0.888670i
\(535\) 809.311i 1.51273i
\(536\) −680.308 + 279.701i −1.26923 + 0.521831i
\(537\) 132.838 0.247370
\(538\) 427.656 327.557i 0.794899 0.608842i
\(539\) 100.398i 0.186268i
\(540\) −713.160 192.430i −1.32067 0.356352i
\(541\) 833.097 1.53992 0.769960 0.638092i \(-0.220276\pi\)
0.769960 + 0.638092i \(0.220276\pi\)
\(542\) −387.117 505.416i −0.714238 0.932502i
\(543\) 501.762i 0.924056i
\(544\) −368.573 + 46.8828i −0.677524 + 0.0861817i
\(545\) 668.740 1.22705
\(546\) 57.9577 44.3919i 0.106150 0.0813039i
\(547\) 356.858i 0.652391i 0.945302 + 0.326196i \(0.105767\pi\)
−0.945302 + 0.326196i \(0.894233\pi\)
\(548\) −18.9286 + 70.1509i −0.0345413 + 0.128013i
\(549\) −1.45880 −0.00265720
\(550\) 371.751 + 485.355i 0.675911 + 0.882464i
\(551\) 961.275i 1.74460i
\(552\) −7.75347 18.8585i −0.0140461 0.0341640i
\(553\) 150.762 0.272625
\(554\) 566.195 433.669i 1.02201 0.782796i
\(555\) 914.349i 1.64748i
\(556\) 517.818 + 139.721i 0.931327 + 0.251297i
\(557\) 324.859 0.583230 0.291615 0.956536i \(-0.405807\pi\)
0.291615 + 0.956536i \(0.405807\pi\)
\(558\) 0.172387 + 0.225067i 0.000308938 + 0.000403346i
\(559\) 129.379i 0.231447i
\(560\) 144.915 248.982i 0.258777 0.444612i
\(561\) −497.040 −0.885989
\(562\) 174.410 133.587i 0.310339 0.237700i
\(563\) 85.2531i 0.151427i 0.997130 + 0.0757133i \(0.0241234\pi\)
−0.997130 + 0.0757133i \(0.975877\pi\)
\(564\) 131.169 486.124i 0.232570 0.861922i
\(565\) −660.104 −1.16833
\(566\) 625.800 + 817.039i 1.10565 + 1.44353i
\(567\) 212.106i 0.374084i
\(568\) −121.037 + 49.7632i −0.213094 + 0.0876112i
\(569\) −28.7512 −0.0505293 −0.0252647 0.999681i \(-0.508043\pi\)
−0.0252647 + 0.999681i \(0.508043\pi\)
\(570\) −723.803 + 554.387i −1.26983 + 0.972609i
\(571\) 677.532i 1.18657i −0.804992 0.593286i \(-0.797830\pi\)
0.804992 0.593286i \(-0.202170\pi\)
\(572\) 256.035 + 69.0851i 0.447613 + 0.120778i
\(573\) −1055.42 −1.84191
\(574\) 117.922 + 153.958i 0.205439 + 0.268219i
\(575\) 18.2000i 0.0316521i
\(576\) −4.16080 + 4.11730i −0.00722361 + 0.00714810i
\(577\) −20.6675 −0.0358189 −0.0179095 0.999840i \(-0.505701\pi\)
−0.0179095 + 0.999840i \(0.505701\pi\)
\(578\) −244.821 + 187.517i −0.423565 + 0.324424i
\(579\) 1040.40i 1.79688i
\(580\) 303.743 1125.69i 0.523694 1.94085i
\(581\) −37.8545 −0.0651541
\(582\) 247.856 + 323.598i 0.425869 + 0.556011i
\(583\) 622.533i 1.06781i
\(584\) −29.1649 70.9368i −0.0499399 0.121467i
\(585\) −2.87716 −0.00491822
\(586\) −211.176 + 161.748i −0.360369 + 0.276020i
\(587\) 551.489i 0.939504i 0.882798 + 0.469752i \(0.155657\pi\)
−0.882798 + 0.469752i \(0.844343\pi\)
\(588\) −80.6864 21.7714i −0.137222 0.0370262i
\(589\) 34.7825 0.0590534
\(590\) −446.899 583.467i −0.757455 0.988927i
\(591\) 80.3825i 0.136011i
\(592\) −622.482 362.303i −1.05149 0.611998i
\(593\) 45.9313 0.0774558 0.0387279 0.999250i \(-0.487669\pi\)
0.0387279 + 0.999250i \(0.487669\pi\)
\(594\) −617.951 + 473.311i −1.04032 + 0.796821i
\(595\) 209.054i 0.351352i
\(596\) −21.6347 + 80.1798i −0.0362998 + 0.134530i
\(597\) −691.141 −1.15769
\(598\) −4.80043 6.26739i −0.00802747 0.0104806i
\(599\) 662.449i 1.10593i 0.833206 + 0.552963i \(0.186503\pi\)
−0.833206 + 0.552963i \(0.813497\pi\)
\(600\) 470.676 193.513i 0.784459 0.322522i
\(601\) −840.257 −1.39810 −0.699049 0.715074i \(-0.746393\pi\)
−0.699049 + 0.715074i \(0.746393\pi\)
\(602\) 117.579 90.0582i 0.195314 0.149598i
\(603\) 8.40952i 0.0139461i
\(604\) −359.576 97.0234i −0.595325 0.160635i
\(605\) 576.490 0.952876
\(606\) −102.226 133.465i −0.168690 0.220240i
\(607\) 1024.92i 1.68850i −0.535951 0.844249i \(-0.680047\pi\)
0.535951 0.844249i \(-0.319953\pi\)
\(608\) 90.6218 + 712.431i 0.149049 + 1.17176i
\(609\) −338.238 −0.555399
\(610\) 172.343 132.004i 0.282530 0.216400i
\(611\) 194.946i 0.319061i
\(612\) 1.10659 4.10110i 0.00180815 0.00670114i
\(613\) −109.148 −0.178055 −0.0890276 0.996029i \(-0.528376\pi\)
−0.0890276 + 0.996029i \(0.528376\pi\)
\(614\) 465.549 + 607.817i 0.758223 + 0.989929i
\(615\) 744.422i 1.21044i
\(616\) −115.436 280.772i −0.187397 0.455799i
\(617\) 78.9177 0.127905 0.0639527 0.997953i \(-0.479629\pi\)
0.0639527 + 0.997953i \(0.479629\pi\)
\(618\) −759.398 + 581.651i −1.22880 + 0.941183i
\(619\) 715.995i 1.15670i 0.815790 + 0.578348i \(0.196302\pi\)
−0.815790 + 0.578348i \(0.803698\pi\)
\(620\) −40.7317 10.9905i −0.0656963 0.0177266i
\(621\) 23.1721 0.0373141
\(622\) 238.816 + 311.796i 0.383949 + 0.501281i
\(623\) 264.935i 0.425257i
\(624\) 111.042 190.784i 0.177952 0.305744i
\(625\) −703.583 −1.12573
\(626\) 678.051 519.344i 1.08315 0.829623i
\(627\) 960.749i 1.53230i
\(628\) 166.036 615.343i 0.264389 0.979845i
\(629\) 522.657 0.830933
\(630\) 2.00273 + 2.61475i 0.00317894 + 0.00415039i
\(631\) 849.316i 1.34598i 0.739650 + 0.672992i \(0.234991\pi\)
−0.739650 + 0.672992i \(0.765009\pi\)
\(632\) 421.617 173.343i 0.667116 0.274278i
\(633\) 237.853 0.375755
\(634\) 176.321 135.051i 0.278109 0.213014i
\(635\) 489.109i 0.770251i
\(636\) 500.306 + 134.996i 0.786645 + 0.212258i
\(637\) −32.3570 −0.0507960
\(638\) −747.102 975.409i −1.17101 1.52885i
\(639\) 1.49618i 0.00234144i
\(640\) 118.991 862.920i 0.185923 1.34831i
\(641\) 488.089 0.761450 0.380725 0.924688i \(-0.375674\pi\)
0.380725 + 0.924688i \(0.375674\pi\)
\(642\) 563.581 431.667i 0.877851 0.672379i
\(643\) 257.106i 0.399854i −0.979811 0.199927i \(-0.935930\pi\)
0.979811 0.199927i \(-0.0640705\pi\)
\(644\) −2.35430 + 8.72522i −0.00365575 + 0.0135485i
\(645\) 568.522 0.881430
\(646\) −316.897 413.738i −0.490552 0.640461i
\(647\) 699.536i 1.08120i −0.841280 0.540600i \(-0.818197\pi\)
0.841280 0.540600i \(-0.181803\pi\)
\(648\) 243.876 + 593.171i 0.376352 + 0.915387i
\(649\) −774.472 −1.19333
\(650\) 156.423 119.810i 0.240651 0.184324i
\(651\) 12.2387i 0.0187998i
\(652\) −176.981 47.7544i −0.271444 0.0732429i
\(653\) 277.629 0.425160 0.212580 0.977144i \(-0.431813\pi\)
0.212580 + 0.977144i \(0.431813\pi\)
\(654\) −356.690 465.691i −0.545397 0.712065i
\(655\) 1428.02i 2.18018i
\(656\) 506.796 + 294.971i 0.772556 + 0.449650i
\(657\) 0.876874 0.00133466
\(658\) −177.167 + 135.698i −0.269250 + 0.206228i
\(659\) 522.721i 0.793204i −0.917991 0.396602i \(-0.870189\pi\)
0.917991 0.396602i \(-0.129811\pi\)
\(660\) 303.576 1125.08i 0.459964 1.70466i
\(661\) 515.922 0.780518 0.390259 0.920705i \(-0.372385\pi\)
0.390259 + 0.920705i \(0.372385\pi\)
\(662\) 145.484 + 189.943i 0.219765 + 0.286923i
\(663\) 160.189i 0.241612i
\(664\) −105.863 + 43.5245i −0.159432 + 0.0655489i
\(665\) 404.090 0.607654
\(666\) 6.53714 5.00704i 0.00981553 0.00751807i
\(667\) 36.5761i 0.0548368i
\(668\) 60.1855 + 16.2397i 0.0900981 + 0.0243109i
\(669\) 789.060 1.17946
\(670\) 760.959 + 993.502i 1.13576 + 1.48284i
\(671\) 228.762i 0.340927i
\(672\) −250.678 + 31.8865i −0.373033 + 0.0474502i
\(673\) −1231.64 −1.83008 −0.915041 0.403361i \(-0.867842\pi\)
−0.915041 + 0.403361i \(0.867842\pi\)
\(674\) −91.0803 + 69.7617i −0.135134 + 0.103504i
\(675\) 578.335i 0.856792i
\(676\) −153.840 + 570.142i −0.227574 + 0.843405i
\(677\) −576.563 −0.851645 −0.425822 0.904807i \(-0.640015\pi\)
−0.425822 + 0.904807i \(0.640015\pi\)
\(678\) 352.084 + 459.677i 0.519297 + 0.677990i
\(679\) 180.661i 0.266069i
\(680\) 240.367 + 584.637i 0.353481 + 0.859760i
\(681\) 1287.38 1.89043
\(682\) −35.2939 + 27.0329i −0.0517506 + 0.0396377i
\(683\) 161.395i 0.236302i −0.992996 0.118151i \(-0.962303\pi\)
0.992996 0.118151i \(-0.0376968\pi\)
\(684\) −7.92718 2.13897i −0.0115895 0.00312715i
\(685\) 123.619 0.180466
\(686\) 22.5231 + 29.4060i 0.0328325 + 0.0428658i
\(687\) 1268.21i 1.84601i
\(688\) 225.272 387.046i 0.327430 0.562566i
\(689\) 200.634 0.291196
\(690\) −27.5404 + 21.0942i −0.0399136 + 0.0305713i
\(691\) 113.661i 0.164488i −0.996612 0.0822442i \(-0.973791\pi\)
0.996612 0.0822442i \(-0.0262087\pi\)
\(692\) −277.205 + 1027.34i −0.400585 + 1.48460i
\(693\) 3.47072 0.00500826
\(694\) 326.865 + 426.753i 0.470988 + 0.614917i
\(695\) 912.491i 1.31294i
\(696\) −945.909 + 388.900i −1.35906 + 0.558765i
\(697\) −425.524 −0.610507
\(698\) 154.093 118.025i 0.220764 0.169091i
\(699\) 653.140i 0.934391i
\(700\) −217.766 58.7593i −0.311095 0.0839418i
\(701\) 331.011 0.472198 0.236099 0.971729i \(-0.424131\pi\)
0.236099 + 0.971729i \(0.424131\pi\)
\(702\) 152.542 + 199.157i 0.217296 + 0.283700i
\(703\) 1010.27i 1.43708i
\(704\) −645.654 652.475i −0.917123 0.926811i
\(705\) −856.640 −1.21509
\(706\) −503.210 + 385.427i −0.712761 + 0.545930i
\(707\) 74.5119i 0.105392i
\(708\) −167.944 + 622.414i −0.237209 + 0.879116i
\(709\) −591.351 −0.834063 −0.417032 0.908892i \(-0.636930\pi\)
−0.417032 + 0.908892i \(0.636930\pi\)
\(710\) 135.386 + 176.759i 0.190685 + 0.248957i
\(711\) 5.21176i 0.00733018i
\(712\) −304.618 740.912i −0.427834 1.04061i
\(713\) 1.32346 0.00185618
\(714\) 145.579 111.504i 0.203892 0.156169i
\(715\) 451.181i 0.631022i
\(716\) −171.877 46.3770i −0.240051 0.0647724i
\(717\) −269.119 −0.375340
\(718\) −717.754 937.093i −0.999658 1.30514i
\(719\) 483.600i 0.672600i −0.941755 0.336300i \(-0.890824\pi\)
0.941755 0.336300i \(-0.109176\pi\)
\(720\) 8.60719 + 5.00964i 0.0119544 + 0.00695784i
\(721\) 423.962 0.588020
\(722\) −226.545 + 173.519i −0.313775 + 0.240332i
\(723\) 1122.09i 1.55199i
\(724\) −175.178 + 649.223i −0.241959 + 0.896717i
\(725\) −912.877 −1.25914
\(726\) −307.486 401.451i −0.423534 0.552962i
\(727\) 659.508i 0.907163i −0.891215 0.453582i \(-0.850146\pi\)
0.891215 0.453582i \(-0.149854\pi\)
\(728\) −90.4890 + 37.2036i −0.124298 + 0.0511038i
\(729\) −736.257 −1.00995
\(730\) −103.594 + 79.3464i −0.141910 + 0.108694i
\(731\) 324.977i 0.444565i
\(732\) −183.847 49.6070i −0.251157 0.0677691i
\(733\) 211.776 0.288916 0.144458 0.989511i \(-0.453856\pi\)
0.144458 + 0.989511i \(0.453856\pi\)
\(734\) −213.484 278.723i −0.290851 0.379732i
\(735\) 142.184i 0.193448i
\(736\) 3.44812 + 27.1077i 0.00468495 + 0.0368311i
\(737\) 1318.74 1.78933
\(738\) −5.32224 + 4.07650i −0.00721171 + 0.00552371i
\(739\) 246.912i 0.334116i 0.985947 + 0.167058i \(0.0534267\pi\)
−0.985947 + 0.167058i \(0.946573\pi\)
\(740\) −319.223 + 1183.06i −0.431382 + 1.59873i
\(741\) 309.636 0.417863
\(742\) −139.657 182.335i −0.188217 0.245735i
\(743\) 333.126i 0.448352i 0.974549 + 0.224176i \(0.0719691\pi\)
−0.974549 + 0.224176i \(0.928031\pi\)
\(744\) 14.0718 + 34.2264i 0.0189138 + 0.0460033i
\(745\) 141.292 0.189653
\(746\) 879.651 673.757i 1.17916 0.903160i
\(747\) 1.30861i 0.00175182i
\(748\) 643.113 + 173.529i 0.859776 + 0.231991i
\(749\) −314.640 −0.420080
\(750\) 91.0796 + 118.913i 0.121439 + 0.158550i
\(751\) 609.916i 0.812139i −0.913842 0.406069i \(-0.866899\pi\)
0.913842 0.406069i \(-0.133101\pi\)
\(752\) −339.436 + 583.194i −0.451378 + 0.775524i
\(753\) 953.691 1.26652
\(754\) −314.361 + 240.781i −0.416924 + 0.319338i
\(755\) 633.640i 0.839259i
\(756\) 74.8119 277.259i 0.0989576 0.366744i
\(757\) 439.344 0.580375 0.290187 0.956970i \(-0.406282\pi\)
0.290187 + 0.956970i \(0.406282\pi\)
\(758\) −911.989 1190.68i −1.20315 1.57082i
\(759\) 36.5561i 0.0481635i
\(760\) 1130.07 464.616i 1.48693 0.611337i
\(761\) −460.968 −0.605740 −0.302870 0.953032i \(-0.597945\pi\)
−0.302870 + 0.953032i \(0.597945\pi\)
\(762\) −340.601 + 260.879i −0.446984 + 0.342361i
\(763\) 259.989i 0.340746i
\(764\) 1365.59 + 368.473i 1.78742 + 0.482294i
\(765\) −7.22689 −0.00944692
\(766\) 299.449 + 390.958i 0.390925 + 0.510389i
\(767\) 249.602i 0.325426i
\(768\) −664.379 + 377.399i −0.865077 + 0.491405i
\(769\) 1431.37 1.86134 0.930670 0.365859i \(-0.119225\pi\)
0.930670 + 0.365859i \(0.119225\pi\)
\(770\) −410.031 + 314.058i −0.532508 + 0.407868i
\(771\) 499.838i 0.648299i
\(772\) −363.229 + 1346.15i −0.470503 + 1.74372i
\(773\) 245.480 0.317568 0.158784 0.987313i \(-0.449243\pi\)
0.158784 + 0.987313i \(0.449243\pi\)
\(774\) 3.11327 + 4.06465i 0.00402231 + 0.00525149i
\(775\) 33.0312i 0.0426209i
\(776\) −207.721 505.232i −0.267681 0.651073i
\(777\) 355.476 0.457498
\(778\) 473.186 362.431i 0.608208 0.465849i
\(779\) 822.513i 1.05586i
\(780\) −362.597 97.8385i −0.464868 0.125434i
\(781\) 234.624 0.300414
\(782\) −12.0578 15.7426i −0.0154192 0.0201311i
\(783\) 1162.27i 1.48438i
\(784\) 96.7981 + 56.3394i 0.123467 + 0.0718615i
\(785\) −1084.35 −1.38134
\(786\) 994.430 761.670i 1.26518 0.969046i
\(787\) 579.993i 0.736967i 0.929634 + 0.368483i \(0.120123\pi\)
−0.929634 + 0.368483i \(0.879877\pi\)
\(788\) −28.0636 + 104.006i −0.0356137 + 0.131987i
\(789\) −257.067 −0.325813
\(790\) −471.601 615.718i −0.596963 0.779389i
\(791\) 256.632i 0.324440i
\(792\) 9.70615 3.99058i 0.0122552 0.00503861i
\(793\) −73.7268 −0.0929720
\(794\) 202.953 155.449i 0.255608 0.195780i
\(795\) 881.632i 1.10897i
\(796\) 894.257 + 241.295i 1.12344 + 0.303134i
\(797\) −1348.22 −1.69162 −0.845810 0.533484i \(-0.820882\pi\)
−0.845810 + 0.533484i \(0.820882\pi\)
\(798\) −215.532 281.396i −0.270090 0.352627i
\(799\) 489.670i 0.612853i
\(800\) −676.561 + 86.0592i −0.845701 + 0.107574i
\(801\) 9.15867 0.0114340
\(802\) −1229.39 + 941.635i −1.53291 + 1.17411i
\(803\) 137.507i 0.171241i
\(804\) 285.968 1059.82i 0.355682 1.31818i
\(805\) 15.3755 0.0190999
\(806\) 8.71232 + 11.3747i 0.0108093 + 0.0141126i
\(807\) 803.913i 0.996175i
\(808\) 85.6725 + 208.378i 0.106030 + 0.257894i
\(809\) −697.465 −0.862132 −0.431066 0.902320i \(-0.641862\pi\)
−0.431066 + 0.902320i \(0.641862\pi\)
\(810\) 866.249 663.492i 1.06944 0.819126i
\(811\) 482.271i 0.594662i −0.954774 0.297331i \(-0.903903\pi\)
0.954774 0.297331i \(-0.0960965\pi\)
\(812\) 437.641 + 118.087i 0.538967 + 0.145428i
\(813\) 950.089 1.16862
\(814\) 785.178 + 1025.12i 0.964592 + 1.25936i
\(815\) 311.874i 0.382668i
\(816\) 278.918 479.216i 0.341811 0.587274i
\(817\) 628.161 0.768863
\(818\) 1058.86 811.020i 1.29445 0.991467i
\(819\) 1.11857i 0.00136577i
\(820\) 259.897 963.197i 0.316947 1.17463i
\(821\) −386.345 −0.470579 −0.235289 0.971925i \(-0.575604\pi\)
−0.235289 + 0.971925i \(0.575604\pi\)
\(822\) −65.9354 86.0846i −0.0802134 0.104726i
\(823\) 354.386i 0.430603i −0.976548 0.215301i \(-0.930927\pi\)
0.976548 0.215301i \(-0.0690734\pi\)
\(824\) 1185.64 487.465i 1.43889 0.591584i
\(825\) −912.377 −1.10591
\(826\) 226.837 173.743i 0.274621 0.210342i
\(827\) 1260.47i 1.52414i 0.647493 + 0.762072i \(0.275818\pi\)
−0.647493 + 0.762072i \(0.724182\pi\)
\(828\) −0.301626 0.0813869i −0.000364283 9.82934e-5i
\(829\) −1443.69 −1.74148 −0.870739 0.491746i \(-0.836359\pi\)
−0.870739 + 0.491746i \(0.836359\pi\)
\(830\) 118.413 + 154.599i 0.142667 + 0.186264i
\(831\) 1064.34i 1.28080i
\(832\) −210.284 + 208.086i −0.252745 + 0.250103i
\(833\) −81.2750 −0.0975690
\(834\) −635.432 + 486.701i −0.761909 + 0.583574i
\(835\) 106.058i 0.127016i
\(836\) 335.422 1243.10i 0.401223 1.48696i
\(837\) −42.0552 −0.0502451
\(838\) 115.975 + 151.415i 0.138394 + 0.180687i
\(839\) 44.6511i 0.0532194i −0.999646 0.0266097i \(-0.991529\pi\)
0.999646 0.0266097i \(-0.00847114\pi\)
\(840\) 163.481 + 397.630i 0.194621 + 0.473369i
\(841\) 993.593 1.18144
\(842\) −443.239 + 339.493i −0.526412 + 0.403198i
\(843\) 327.859i 0.388920i
\(844\) −307.755 83.0406i −0.364638 0.0983893i
\(845\) 1004.70 1.18899
\(846\) −4.69102 6.12455i −0.00554494 0.00723942i
\(847\) 224.125i 0.264610i
\(848\) −600.208 349.339i −0.707793 0.411957i
\(849\) −1535.88 −1.80905
\(850\) 392.907 300.942i 0.462243 0.354049i
\(851\) 38.4402i 0.0451707i
\(852\) 50.8781 188.558i 0.0597161 0.221312i
\(853\) −118.167 −0.138531 −0.0692655 0.997598i \(-0.522066\pi\)
−0.0692655 + 0.997598i \(0.522066\pi\)
\(854\) 51.3198 + 67.0026i 0.0600934 + 0.0784574i
\(855\) 13.9692i 0.0163382i
\(856\) −879.915 + 361.768i −1.02794 + 0.422626i
\(857\) −153.130 −0.178682 −0.0893408 0.996001i \(-0.528476\pi\)
−0.0893408 + 0.996001i \(0.528476\pi\)
\(858\) −314.189 + 240.649i −0.366188 + 0.280477i
\(859\) 136.656i 0.159087i 0.996831 + 0.0795437i \(0.0253463\pi\)
−0.996831 + 0.0795437i \(0.974654\pi\)
\(860\) −735.603 198.486i −0.855353 0.230797i
\(861\) −289.412 −0.336135
\(862\) −205.981 268.927i −0.238957 0.311980i
\(863\) 1462.52i 1.69470i 0.531036 + 0.847349i \(0.321803\pi\)
−0.531036 + 0.847349i \(0.678197\pi\)
\(864\) −109.570 861.394i −0.126817 0.996983i
\(865\) 1810.37 2.09291
\(866\) −468.732 + 359.019i −0.541261 + 0.414572i
\(867\) 460.217i 0.530816i
\(868\) 4.27284 15.8355i 0.00492262 0.0182436i
\(869\) −817.281 −0.940484
\(870\) 1058.05 + 1381.38i 1.21615 + 1.58779i
\(871\) 425.011i 0.487957i
\(872\) 298.931 + 727.080i 0.342811 + 0.833807i
\(873\) 6.24535 0.00715389
\(874\) −30.4295 + 23.3070i −0.0348163 + 0.0266671i
\(875\) 66.3874i 0.0758713i
\(876\) 110.509 + 29.8183i 0.126152 + 0.0340392i
\(877\) 29.8881 0.0340799 0.0170399 0.999855i \(-0.494576\pi\)
0.0170399 + 0.999855i \(0.494576\pi\)
\(878\) 397.399 + 518.841i 0.452619 + 0.590935i
\(879\) 396.972i 0.451618i
\(880\) −785.586 + 1349.74i −0.892712 + 1.53379i
\(881\) −497.832 −0.565076 −0.282538 0.959256i \(-0.591176\pi\)
−0.282538 + 0.959256i \(0.591176\pi\)
\(882\) −1.01655 + 0.778612i −0.00115255 + 0.000882780i
\(883\) 1430.98i 1.62059i 0.586022 + 0.810295i \(0.300693\pi\)
−0.586022 + 0.810295i \(0.699307\pi\)
\(884\) 55.9261 207.266i 0.0632648 0.234464i
\(885\) 1096.81 1.23933
\(886\) −626.052 817.368i −0.706605 0.922538i
\(887\) 1187.21i 1.33846i −0.743057 0.669228i \(-0.766625\pi\)
0.743057 0.669228i \(-0.233375\pi\)
\(888\) 994.117 408.720i 1.11950 0.460271i
\(889\) 190.153 0.213896
\(890\) −1082.01 + 828.748i −1.21574 + 0.931178i
\(891\) 1149.83i 1.29049i
\(892\) −1020.95 275.481i −1.14457 0.308835i
\(893\) −946.504 −1.05991
\(894\) −75.3616 98.3914i −0.0842971 0.110058i
\(895\) 302.879i 0.338412i
\(896\) 335.482 + 46.2607i 0.374422 + 0.0516302i
\(897\) 11.7815 0.0131344
\(898\) 956.183 732.376i 1.06479 0.815563i
\(899\) 66.3823i 0.0738401i
\(900\) 2.03128 7.52807i 0.00225697 0.00836452i
\(901\) 503.956 0.559329
\(902\) −639.256 834.607i −0.708709 0.925285i
\(903\) 221.027i 0.244770i
\(904\) −295.071 717.691i −0.326406 0.793906i
\(905\) 1144.05 1.26415
\(906\) 441.249 337.968i 0.487029 0.373034i
\(907\) 818.659i 0.902601i −0.892372 0.451301i \(-0.850960\pi\)
0.892372 0.451301i \(-0.149040\pi\)
\(908\) −1665.72 449.457i −1.83450 0.494997i
\(909\) −2.57584 −0.00283370
\(910\) 101.217 + 132.147i 0.111227 + 0.145217i
\(911\) 774.905i 0.850610i 0.905050 + 0.425305i \(0.139833\pi\)
−0.905050 + 0.425305i \(0.860167\pi\)
\(912\) −926.296 539.132i −1.01568 0.591154i
\(913\) 205.210 0.224764
\(914\) −420.179 + 321.831i −0.459715 + 0.352112i
\(915\) 323.973i 0.354069i
\(916\) −442.765 + 1640.92i −0.483367 + 1.79140i
\(917\) −555.177 −0.605428
\(918\) 383.157 + 500.247i 0.417383 + 0.544931i
\(919\) 1695.99i 1.84547i −0.385437 0.922734i \(-0.625949\pi\)
0.385437 0.922734i \(-0.374051\pi\)
\(920\) 42.9987 17.6784i 0.0467377 0.0192157i
\(921\) −1142.58 −1.24059
\(922\) −690.344 + 528.760i −0.748746 + 0.573492i
\(923\) 75.6160i 0.0819241i
\(924\) 437.402 + 118.023i 0.473378 + 0.127730i
\(925\) 959.401 1.03719
\(926\) 235.027 + 306.849i 0.253809 + 0.331370i
\(927\) 14.6562i 0.0158103i
\(928\) 1359.67 172.952i 1.46516 0.186370i
\(929\) −1173.31 −1.26298 −0.631491 0.775383i \(-0.717557\pi\)
−0.631491 + 0.775383i \(0.717557\pi\)
\(930\) 49.9833 38.2840i 0.0537455 0.0411656i
\(931\) 157.100i 0.168743i
\(932\) 228.028 845.088i 0.244665 0.906747i
\(933\) −586.120 −0.628210
\(934\) 796.928 + 1040.46i 0.853242 + 1.11398i
\(935\) 1133.28i 1.21207i
\(936\) −1.28611 3.12816i −0.00137405 0.00334205i
\(937\) −315.505 −0.336719 −0.168359 0.985726i \(-0.553847\pi\)
−0.168359 + 0.985726i \(0.553847\pi\)
\(938\) −386.248 + 295.842i −0.411779 + 0.315396i
\(939\) 1274.61i 1.35741i
\(940\) 1108.40 + 299.075i 1.17914 + 0.318165i
\(941\) −423.505 −0.450058 −0.225029 0.974352i \(-0.572248\pi\)
−0.225029 + 0.974352i \(0.572248\pi\)
\(942\) 578.365 + 755.108i 0.613976 + 0.801601i
\(943\) 31.2963i 0.0331880i
\(944\) 434.601 746.699i 0.460383 0.790995i
\(945\) −488.581 −0.517017
\(946\) −637.398 + 488.206i −0.673782 + 0.516074i
\(947\) 1147.28i 1.21149i −0.795660 0.605743i \(-0.792876\pi\)
0.795660 0.605743i \(-0.207124\pi\)
\(948\) −177.227 + 656.818i −0.186949 + 0.692846i
\(949\) 44.3166 0.0466982
\(950\) −581.703 759.466i −0.612319 0.799438i
\(951\) 331.451i 0.348529i
\(952\) −227.292 + 93.4487i −0.238752 + 0.0981604i
\(953\) 736.494 0.772816 0.386408 0.922328i \(-0.373716\pi\)
0.386408 + 0.922328i \(0.373716\pi\)
\(954\) 6.30323 4.82788i 0.00660716 0.00506067i
\(955\) 2406.42i 2.51981i
\(956\) 348.209 + 93.9563i 0.364235 + 0.0982806i
\(957\) 1833.59 1.91598
\(958\) 124.849 + 163.001i 0.130322 + 0.170148i
\(959\) 48.0599i 0.0501146i
\(960\) 914.377 + 924.036i 0.952476 + 0.962538i
\(961\) 958.598 0.997501
\(962\) 330.382 253.052i 0.343433 0.263048i
\(963\) 10.8769i 0.0112948i
\(964\) 391.749 1451.85i 0.406379 1.50607i
\(965\) 2372.17 2.45821
\(966\) −8.20090 10.7070i −0.00848954 0.0110839i
\(967\) 1147.66i 1.18682i −0.804899 0.593411i \(-0.797781\pi\)
0.804899 0.593411i \(-0.202219\pi\)
\(968\) 257.695 + 626.782i 0.266214 + 0.647502i
\(969\) 777.750 0.802632
\(970\) −737.826 + 565.128i −0.760646 + 0.582606i
\(971\) 1108.64i 1.14175i 0.821036 + 0.570876i \(0.193396\pi\)
−0.821036 + 0.570876i \(0.806604\pi\)
\(972\) 19.0730 + 5.14640i 0.0196224 + 0.00529465i
\(973\) 354.754 0.364598
\(974\) 183.213 + 239.201i 0.188104 + 0.245586i
\(975\) 294.047i 0.301586i
\(976\) 220.558 + 128.372i 0.225982 + 0.131528i
\(977\) 779.026 0.797366 0.398683 0.917089i \(-0.369467\pi\)
0.398683 + 0.917089i \(0.369467\pi\)
\(978\) 217.180 166.346i 0.222065 0.170088i
\(979\) 1436.21i 1.46702i
\(980\) 49.6402 183.971i 0.0506533 0.187725i
\(981\) −8.98769 −0.00916176
\(982\) −144.471 188.620i −0.147119 0.192077i
\(983\) 79.5940i 0.0809705i 0.999180 + 0.0404853i \(0.0128904\pi\)
−0.999180 + 0.0404853i \(0.987110\pi\)
\(984\) −809.364 + 332.761i −0.822525 + 0.338172i
\(985\) 183.277 0.186069
\(986\) −789.618 + 604.797i −0.800830 + 0.613385i
\(987\) 333.040i 0.337427i
\(988\) −400.634 108.102i −0.405500 0.109415i
\(989\) 23.9013 0.0241671
\(990\) −10.8568 14.1746i −0.0109665 0.0143177i
\(991\) 644.244i 0.650095i 0.945698 + 0.325047i \(0.105380\pi\)
−0.945698 + 0.325047i \(0.894620\pi\)
\(992\) −6.25802 49.1979i −0.00630849 0.0495947i
\(993\) −357.057 −0.359574
\(994\) −68.7195 + 52.6348i −0.0691343 + 0.0529525i
\(995\) 1575.85i 1.58377i
\(996\) 44.4997 164.919i 0.0446784 0.165581i
\(997\) −1739.99 −1.74523 −0.872615 0.488409i \(-0.837578\pi\)
−0.872615 + 0.488409i \(0.837578\pi\)
\(998\) 664.533 + 867.608i 0.665864 + 0.869346i
\(999\) 1221.50i 1.22273i
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 28.3.c.a.15.5 6
3.2 odd 2 252.3.g.a.127.2 6
4.3 odd 2 inner 28.3.c.a.15.6 yes 6
7.2 even 3 196.3.g.k.67.1 12
7.3 odd 6 196.3.g.j.79.3 12
7.4 even 3 196.3.g.k.79.3 12
7.5 odd 6 196.3.g.j.67.1 12
7.6 odd 2 196.3.c.g.99.5 6
8.3 odd 2 448.3.d.d.127.5 6
8.5 even 2 448.3.d.d.127.2 6
12.11 even 2 252.3.g.a.127.1 6
16.3 odd 4 1792.3.g.g.127.10 12
16.5 even 4 1792.3.g.g.127.9 12
16.11 odd 4 1792.3.g.g.127.3 12
16.13 even 4 1792.3.g.g.127.4 12
28.3 even 6 196.3.g.j.79.1 12
28.11 odd 6 196.3.g.k.79.1 12
28.19 even 6 196.3.g.j.67.3 12
28.23 odd 6 196.3.g.k.67.3 12
28.27 even 2 196.3.c.g.99.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.3.c.a.15.5 6 1.1 even 1 trivial
28.3.c.a.15.6 yes 6 4.3 odd 2 inner
196.3.c.g.99.5 6 7.6 odd 2
196.3.c.g.99.6 6 28.27 even 2
196.3.g.j.67.1 12 7.5 odd 6
196.3.g.j.67.3 12 28.19 even 6
196.3.g.j.79.1 12 28.3 even 6
196.3.g.j.79.3 12 7.3 odd 6
196.3.g.k.67.1 12 7.2 even 3
196.3.g.k.67.3 12 28.23 odd 6
196.3.g.k.79.1 12 28.11 odd 6
196.3.g.k.79.3 12 7.4 even 3
252.3.g.a.127.1 6 12.11 even 2
252.3.g.a.127.2 6 3.2 odd 2
448.3.d.d.127.2 6 8.5 even 2
448.3.d.d.127.5 6 8.3 odd 2
1792.3.g.g.127.3 12 16.11 odd 4
1792.3.g.g.127.4 12 16.13 even 4
1792.3.g.g.127.9 12 16.5 even 4
1792.3.g.g.127.10 12 16.3 odd 4