Properties

Label 12.6.b.a.11.7
Level $12$
Weight $6$
Character 12.11
Analytic conductor $1.925$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [12,6,Mod(11,12)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(12, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("12.11");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 12.b (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: \(1.92460583776\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 7x^{6} + 6x^{5} - 11x^{4} - 73x^{3} + 223x^{2} - 768x + 912 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{18}\cdot 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.7
Root \(0.410606 - 2.17330i\) of defining polynomial
Character \(\chi\) \(=\) 12.11
Dual form 12.6.b.a.11.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.41443 - 1.63829i) q^{2} +(-4.17995 - 15.0176i) q^{3} +(26.6320 - 17.7408i) q^{4} +73.1202i q^{5} +(-47.2352 - 74.4637i) q^{6} +51.8209i q^{7} +(115.132 - 139.687i) q^{8} +(-208.056 + 125.545i) q^{9} +O(q^{10})\) \(q+(5.41443 - 1.63829i) q^{2} +(-4.17995 - 15.0176i) q^{3} +(26.6320 - 17.7408i) q^{4} +73.1202i q^{5} +(-47.2352 - 74.4637i) q^{6} +51.8209i q^{7} +(115.132 - 139.687i) q^{8} +(-208.056 + 125.545i) q^{9} +(119.792 + 395.904i) q^{10} -371.603 q^{11} +(-377.744 - 325.793i) q^{12} +424.112 q^{13} +(84.8976 + 280.580i) q^{14} +(1098.09 - 305.638i) q^{15} +(394.528 - 944.946i) q^{16} -1401.69i q^{17} +(-920.824 + 1020.61i) q^{18} +319.814i q^{19} +(1297.21 + 1947.34i) q^{20} +(778.224 - 216.608i) q^{21} +(-2012.02 + 608.793i) q^{22} -2421.07 q^{23} +(-2579.01 - 1145.13i) q^{24} -2221.56 q^{25} +(2296.32 - 694.819i) q^{26} +(2755.05 + 2599.73i) q^{27} +(919.343 + 1380.09i) q^{28} +3392.51i q^{29} +(5444.80 - 3453.85i) q^{30} -4656.09i q^{31} +(588.047 - 5762.69i) q^{32} +(1553.28 + 5580.58i) q^{33} +(-2296.38 - 7589.37i) q^{34} -3789.15 q^{35} +(-3313.68 + 7034.61i) q^{36} +395.888 q^{37} +(523.948 + 1731.61i) q^{38} +(-1772.77 - 6369.14i) q^{39} +(10214.0 + 8418.51i) q^{40} -5780.65i q^{41} +(3858.77 - 2447.77i) q^{42} +16385.7i q^{43} +(-9896.53 + 6592.53i) q^{44} +(-9179.91 - 15213.1i) q^{45} +(-13108.7 + 3966.42i) q^{46} +23646.2 q^{47} +(-15839.9 - 1975.04i) q^{48} +14121.6 q^{49} +(-12028.5 + 3639.56i) q^{50} +(-21050.1 + 5859.01i) q^{51} +(11295.0 - 7524.09i) q^{52} +1965.93i q^{53} +(19176.1 + 9562.46i) q^{54} -27171.7i q^{55} +(7238.71 + 5966.26i) q^{56} +(4802.83 - 1336.80i) q^{57} +(5557.91 + 18368.5i) q^{58} +7861.94 q^{59} +(23822.0 - 27620.7i) q^{60} -9360.60 q^{61} +(-7628.03 - 25210.1i) q^{62} +(-6505.87 - 10781.6i) q^{63} +(-6257.03 - 32165.1i) q^{64} +31011.2i q^{65} +(17552.7 + 27670.9i) q^{66} +37881.9i q^{67} +(-24867.2 - 37330.0i) q^{68} +(10119.9 + 36358.6i) q^{69} +(-20516.1 + 6207.73i) q^{70} -20357.6 q^{71} +(-6416.92 + 43517.1i) q^{72} -62082.6 q^{73} +(2143.51 - 648.579i) q^{74} +(9286.01 + 33362.5i) q^{75} +(5673.75 + 8517.28i) q^{76} -19256.8i q^{77} +(-20033.0 - 31580.9i) q^{78} -64254.3i q^{79} +(69094.6 + 28848.0i) q^{80} +(27525.7 - 52241.0i) q^{81} +(-9470.38 - 31298.9i) q^{82} -10042.5 q^{83} +(16882.9 - 19575.0i) q^{84} +102492. q^{85} +(26844.5 + 88719.0i) q^{86} +(50947.3 - 14180.5i) q^{87} +(-42783.6 + 51908.2i) q^{88} -56638.8i q^{89} +(-74627.4 - 67330.8i) q^{90} +21977.9i q^{91} +(-64478.0 + 42951.7i) q^{92} +(-69923.3 + 19462.2i) q^{93} +(128031. - 38739.4i) q^{94} -23384.8 q^{95} +(-88999.8 + 15256.7i) q^{96} -22348.7 q^{97} +(76460.4 - 23135.3i) q^{98} +(77314.3 - 46653.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 24 q^{6} - 24 q^{9} - 272 q^{10} - 696 q^{12} + 112 q^{13} + 2336 q^{16} + 3696 q^{18} - 336 q^{21} - 8304 q^{22} - 11232 q^{24} - 1368 q^{25} + 19248 q^{28} + 25008 q^{30} + 4224 q^{33} - 36416 q^{34} - 42072 q^{36} + 6448 q^{37} + 53824 q^{40} + 59088 q^{42} - 17664 q^{45} - 69600 q^{46} - 74976 q^{48} - 21544 q^{49} + 84208 q^{52} + 78120 q^{54} + 43344 q^{57} - 62576 q^{58} - 64704 q^{60} + 59632 q^{61} + 38528 q^{64} + 33360 q^{66} - 92928 q^{69} - 30432 q^{70} + 20544 q^{72} - 129200 q^{73} - 86256 q^{76} - 83760 q^{78} + 200520 q^{81} + 154720 q^{82} + 167856 q^{84} + 229376 q^{85} - 150336 q^{88} - 251472 q^{90} - 346128 q^{93} + 386112 q^{94} + 331392 q^{96} - 392048 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.41443 1.63829i 0.957144 0.289612i
\(3\) −4.17995 15.0176i −0.268144 0.963379i
\(4\) 26.6320 17.7408i 0.832250 0.554400i
\(5\) 73.1202i 1.30801i 0.756489 + 0.654007i \(0.226913\pi\)
−0.756489 + 0.654007i \(0.773087\pi\)
\(6\) −47.2352 74.4637i −0.535658 0.844435i
\(7\) 51.8209i 0.399723i 0.979824 + 0.199862i \(0.0640493\pi\)
−0.979824 + 0.199862i \(0.935951\pi\)
\(8\) 115.132 139.687i 0.636023 0.771670i
\(9\) −208.056 + 125.545i −0.856198 + 0.516648i
\(10\) 119.792 + 395.904i 0.378816 + 1.25196i
\(11\) −371.603 −0.925971 −0.462986 0.886366i \(-0.653222\pi\)
−0.462986 + 0.886366i \(0.653222\pi\)
\(12\) −377.744 325.793i −0.757260 0.653114i
\(13\) 424.112 0.696021 0.348011 0.937491i \(-0.386857\pi\)
0.348011 + 0.937491i \(0.386857\pi\)
\(14\) 84.8976 + 280.580i 0.115764 + 0.382593i
\(15\) 1098.09 305.638i 1.26011 0.350736i
\(16\) 394.528 944.946i 0.385281 0.922799i
\(17\) 1401.69i 1.17634i −0.808739 0.588168i \(-0.799849\pi\)
0.808739 0.588168i \(-0.200151\pi\)
\(18\) −920.824 + 1020.61i −0.669878 + 0.742471i
\(19\) 319.814i 0.203242i 0.994823 + 0.101621i \(0.0324029\pi\)
−0.994823 + 0.101621i \(0.967597\pi\)
\(20\) 1297.21 + 1947.34i 0.725163 + 1.08859i
\(21\) 778.224 216.608i 0.385085 0.107183i
\(22\) −2012.02 + 608.793i −0.886288 + 0.268172i
\(23\) −2421.07 −0.954306 −0.477153 0.878820i \(-0.658331\pi\)
−0.477153 + 0.878820i \(0.658331\pi\)
\(24\) −2579.01 1145.13i −0.913956 0.405813i
\(25\) −2221.56 −0.710899
\(26\) 2296.32 694.819i 0.666193 0.201576i
\(27\) 2755.05 + 2599.73i 0.727312 + 0.686307i
\(28\) 919.343 + 1380.09i 0.221607 + 0.332670i
\(29\) 3392.51i 0.749076i 0.927212 + 0.374538i \(0.122199\pi\)
−0.927212 + 0.374538i \(0.877801\pi\)
\(30\) 5444.80 3453.85i 1.10453 0.700648i
\(31\) 4656.09i 0.870197i −0.900383 0.435098i \(-0.856714\pi\)
0.900383 0.435098i \(-0.143286\pi\)
\(32\) 588.047 5762.69i 0.101517 0.994834i
\(33\) 1553.28 + 5580.58i 0.248293 + 0.892061i
\(34\) −2296.38 7589.37i −0.340680 1.12592i
\(35\) −3789.15 −0.522843
\(36\) −3313.68 + 7034.61i −0.426141 + 0.904657i
\(37\) 395.888 0.0475409 0.0237705 0.999717i \(-0.492433\pi\)
0.0237705 + 0.999717i \(0.492433\pi\)
\(38\) 523.948 + 1731.61i 0.0588612 + 0.194532i
\(39\) −1772.77 6369.14i −0.186634 0.670532i
\(40\) 10214.0 + 8418.51i 1.00935 + 0.831927i
\(41\) 5780.65i 0.537053i −0.963272 0.268526i \(-0.913463\pi\)
0.963272 0.268526i \(-0.0865367\pi\)
\(42\) 3858.77 2447.77i 0.337540 0.214115i
\(43\) 16385.7i 1.35143i 0.737164 + 0.675714i \(0.236165\pi\)
−0.737164 + 0.675714i \(0.763835\pi\)
\(44\) −9896.53 + 6592.53i −0.770640 + 0.513358i
\(45\) −9179.91 15213.1i −0.675783 1.11992i
\(46\) −13108.7 + 3966.42i −0.913409 + 0.276378i
\(47\) 23646.2 1.56141 0.780706 0.624899i \(-0.214860\pi\)
0.780706 + 0.624899i \(0.214860\pi\)
\(48\) −15839.9 1975.04i −0.992316 0.123729i
\(49\) 14121.6 0.840221
\(50\) −12028.5 + 3639.56i −0.680433 + 0.205885i
\(51\) −21050.1 + 5859.01i −1.13326 + 0.315427i
\(52\) 11295.0 7524.09i 0.579264 0.385874i
\(53\) 1965.93i 0.0961345i 0.998844 + 0.0480673i \(0.0153062\pi\)
−0.998844 + 0.0480673i \(0.984694\pi\)
\(54\) 19176.1 + 9562.46i 0.894905 + 0.446257i
\(55\) 27171.7i 1.21118i
\(56\) 7238.71 + 5966.26i 0.308454 + 0.254233i
\(57\) 4802.83 1336.80i 0.195799 0.0544980i
\(58\) 5557.91 + 18368.5i 0.216941 + 0.716974i
\(59\) 7861.94 0.294035 0.147018 0.989134i \(-0.453033\pi\)
0.147018 + 0.989134i \(0.453033\pi\)
\(60\) 23822.0 27620.7i 0.854281 0.990506i
\(61\) −9360.60 −0.322091 −0.161046 0.986947i \(-0.551487\pi\)
−0.161046 + 0.986947i \(0.551487\pi\)
\(62\) −7628.03 25210.1i −0.252019 0.832904i
\(63\) −6505.87 10781.6i −0.206516 0.342242i
\(64\) −6257.03 32165.1i −0.190949 0.981600i
\(65\) 31011.2i 0.910405i
\(66\) 17552.7 + 27670.9i 0.496004 + 0.781922i
\(67\) 37881.9i 1.03097i 0.856899 + 0.515484i \(0.172388\pi\)
−0.856899 + 0.515484i \(0.827612\pi\)
\(68\) −24867.2 37330.0i −0.652160 0.979006i
\(69\) 10119.9 + 36358.6i 0.255891 + 0.919359i
\(70\) −20516.1 + 6207.73i −0.500437 + 0.151421i
\(71\) −20357.6 −0.479271 −0.239635 0.970863i \(-0.577028\pi\)
−0.239635 + 0.970863i \(0.577028\pi\)
\(72\) −6416.92 + 43517.1i −0.145880 + 0.989302i
\(73\) −62082.6 −1.36352 −0.681762 0.731574i \(-0.738786\pi\)
−0.681762 + 0.731574i \(0.738786\pi\)
\(74\) 2143.51 648.579i 0.0455035 0.0137684i
\(75\) 9286.01 + 33362.5i 0.190623 + 0.684866i
\(76\) 5673.75 + 8517.28i 0.112677 + 0.169148i
\(77\) 19256.8i 0.370132i
\(78\) −20033.0 31580.9i −0.372829 0.587745i
\(79\) 64254.3i 1.15834i −0.815209 0.579168i \(-0.803378\pi\)
0.815209 0.579168i \(-0.196622\pi\)
\(80\) 69094.6 + 28848.0i 1.20703 + 0.503953i
\(81\) 27525.7 52241.0i 0.466150 0.884706i
\(82\) −9470.38 31298.9i −0.155537 0.514037i
\(83\) −10042.5 −0.160009 −0.0800046 0.996794i \(-0.525494\pi\)
−0.0800046 + 0.996794i \(0.525494\pi\)
\(84\) 16882.9 19575.0i 0.261065 0.302694i
\(85\) 102492. 1.53866
\(86\) 26844.5 + 88719.0i 0.391389 + 1.29351i
\(87\) 50947.3 14180.5i 0.721644 0.200860i
\(88\) −42783.6 + 51908.2i −0.588939 + 0.714544i
\(89\) 56638.8i 0.757947i −0.925407 0.378974i \(-0.876277\pi\)
0.925407 0.378974i \(-0.123723\pi\)
\(90\) −74627.4 67330.8i −0.971163 0.876209i
\(91\) 21977.9i 0.278216i
\(92\) −64478.0 + 42951.7i −0.794222 + 0.529067i
\(93\) −69923.3 + 19462.2i −0.838329 + 0.233338i
\(94\) 128031. 38739.4i 1.49450 0.452203i
\(95\) −23384.8 −0.265843
\(96\) −88999.8 + 15256.7i −0.985623 + 0.168960i
\(97\) −22348.7 −0.241170 −0.120585 0.992703i \(-0.538477\pi\)
−0.120585 + 0.992703i \(0.538477\pi\)
\(98\) 76460.4 23135.3i 0.804213 0.243338i
\(99\) 77314.3 46653.1i 0.792814 0.478401i
\(100\) −59164.6 + 39412.3i −0.591646 + 0.394123i
\(101\) 48423.5i 0.472338i −0.971712 0.236169i \(-0.924108\pi\)
0.971712 0.236169i \(-0.0758919\pi\)
\(102\) −104375. + 66209.3i −0.993339 + 0.630113i
\(103\) 152205.i 1.41363i 0.707400 + 0.706813i \(0.249868\pi\)
−0.707400 + 0.706813i \(0.750132\pi\)
\(104\) 48829.1 59243.0i 0.442685 0.537099i
\(105\) 15838.4 + 56903.9i 0.140197 + 0.503696i
\(106\) 3220.77 + 10644.4i 0.0278417 + 0.0920146i
\(107\) −161378. −1.36265 −0.681325 0.731981i \(-0.738596\pi\)
−0.681325 + 0.731981i \(0.738596\pi\)
\(108\) 119494. + 20359.1i 0.985794 + 0.167958i
\(109\) 1239.70 0.00999422 0.00499711 0.999988i \(-0.498409\pi\)
0.00499711 + 0.999988i \(0.498409\pi\)
\(110\) −44515.1 147119.i −0.350772 1.15928i
\(111\) −1654.79 5945.28i −0.0127478 0.0457999i
\(112\) 48967.9 + 20444.8i 0.368864 + 0.154006i
\(113\) 156709.i 1.15451i 0.816565 + 0.577254i \(0.195876\pi\)
−0.816565 + 0.577254i \(0.804124\pi\)
\(114\) 23814.5 15106.5i 0.171625 0.108868i
\(115\) 177029.i 1.24825i
\(116\) 60185.8 + 90349.3i 0.415288 + 0.623419i
\(117\) −88239.1 + 53245.4i −0.595932 + 0.359598i
\(118\) 42567.9 12880.1i 0.281434 0.0851560i
\(119\) 72637.0 0.470209
\(120\) 83731.9 188578.i 0.530809 1.19547i
\(121\) −22962.3 −0.142578
\(122\) −50682.3 + 15335.4i −0.308288 + 0.0932814i
\(123\) −86811.4 + 24162.8i −0.517385 + 0.144007i
\(124\) −82602.8 124001.i −0.482437 0.724221i
\(125\) 66059.6i 0.378147i
\(126\) −52889.0 47717.9i −0.296783 0.267766i
\(127\) 23830.0i 0.131104i −0.997849 0.0655519i \(-0.979119\pi\)
0.997849 0.0655519i \(-0.0208808\pi\)
\(128\) −86573.9 163905.i −0.467049 0.884232i
\(129\) 246073. 68491.2i 1.30194 0.362377i
\(130\) 50805.3 + 167908.i 0.263664 + 0.871389i
\(131\) 346584. 1.76454 0.882269 0.470746i \(-0.156015\pi\)
0.882269 + 0.470746i \(0.156015\pi\)
\(132\) 140371. + 121066.i 0.701201 + 0.604764i
\(133\) −16573.0 −0.0812405
\(134\) 62061.6 + 205109.i 0.298580 + 0.986785i
\(135\) −190093. + 201450.i −0.897699 + 0.951334i
\(136\) −195799. 161381.i −0.907743 0.748177i
\(137\) 182307.i 0.829856i −0.909854 0.414928i \(-0.863807\pi\)
0.909854 0.414928i \(-0.136193\pi\)
\(138\) 114360. + 180282.i 0.511182 + 0.805850i
\(139\) 64467.5i 0.283011i −0.989937 0.141506i \(-0.954806\pi\)
0.989937 0.141506i \(-0.0451944\pi\)
\(140\) −100913. + 67222.6i −0.435137 + 0.289864i
\(141\) −98840.0 355110.i −0.418683 1.50423i
\(142\) −110225. + 33351.7i −0.458731 + 0.138802i
\(143\) −157601. −0.644495
\(144\) 36549.8 + 246133.i 0.146885 + 0.989154i
\(145\) −248061. −0.979801
\(146\) −336141. + 101709.i −1.30509 + 0.394892i
\(147\) −59027.5 212072.i −0.225300 0.809451i
\(148\) 10543.3 7023.37i 0.0395660 0.0263567i
\(149\) 25638.2i 0.0946067i −0.998881 0.0473033i \(-0.984937\pi\)
0.998881 0.0473033i \(-0.0150627\pi\)
\(150\) 104936. + 165426.i 0.380799 + 0.600308i
\(151\) 393481.i 1.40437i 0.711995 + 0.702185i \(0.247792\pi\)
−0.711995 + 0.702185i \(0.752208\pi\)
\(152\) 44673.9 + 36820.9i 0.156836 + 0.129266i
\(153\) 175976. + 291631.i 0.607751 + 1.00718i
\(154\) −31548.2 104264.i −0.107195 0.354270i
\(155\) 340454. 1.13823
\(156\) −160206. 138173.i −0.527069 0.454581i
\(157\) 463686. 1.50133 0.750663 0.660686i \(-0.229734\pi\)
0.750663 + 0.660686i \(0.229734\pi\)
\(158\) −105267. 347900.i −0.335467 1.10869i
\(159\) 29523.6 8217.50i 0.0926140 0.0257779i
\(160\) 421369. + 42998.1i 1.30126 + 0.132785i
\(161\) 125462.i 0.381458i
\(162\) 63449.8 327950.i 0.189952 0.981793i
\(163\) 369066.i 1.08801i −0.839081 0.544007i \(-0.816906\pi\)
0.839081 0.544007i \(-0.183094\pi\)
\(164\) −102553. 153950.i −0.297742 0.446962i
\(165\) −408053. + 113576.i −1.16683 + 0.324771i
\(166\) −54374.2 + 16452.5i −0.153152 + 0.0463405i
\(167\) −17762.9 −0.0492858 −0.0246429 0.999696i \(-0.507845\pi\)
−0.0246429 + 0.999696i \(0.507845\pi\)
\(168\) 59341.5 133647.i 0.162213 0.365330i
\(169\) −191422. −0.515555
\(170\) 554936. 167912.i 1.47272 0.445614i
\(171\) −40151.2 66539.2i −0.105004 0.174015i
\(172\) 290695. + 436383.i 0.749232 + 1.12473i
\(173\) 720659.i 1.83069i 0.402672 + 0.915344i \(0.368081\pi\)
−0.402672 + 0.915344i \(0.631919\pi\)
\(174\) 252618. 160246.i 0.632546 0.401248i
\(175\) 115123.i 0.284163i
\(176\) −146608. + 351145.i −0.356759 + 0.854485i
\(177\) −32862.5 118067.i −0.0788437 0.283267i
\(178\) −92790.8 306666.i −0.219510 0.725465i
\(179\) −817432. −1.90686 −0.953431 0.301613i \(-0.902475\pi\)
−0.953431 + 0.301613i \(0.902475\pi\)
\(180\) −514372. 242297.i −1.18330 0.557399i
\(181\) 389376. 0.883431 0.441716 0.897155i \(-0.354370\pi\)
0.441716 + 0.897155i \(0.354370\pi\)
\(182\) 36006.1 + 118997.i 0.0805745 + 0.266293i
\(183\) 39126.8 + 140574.i 0.0863668 + 0.310296i
\(184\) −278744. + 338193.i −0.606961 + 0.736410i
\(185\) 28947.4i 0.0621842i
\(186\) −346710. + 219931.i −0.734825 + 0.466128i
\(187\) 520874.i 1.08925i
\(188\) 629747. 419503.i 1.29949 0.865647i
\(189\) −134720. + 142769.i −0.274333 + 0.290723i
\(190\) −126615. + 38311.1i −0.254450 + 0.0769912i
\(191\) 477051. 0.946197 0.473099 0.881009i \(-0.343135\pi\)
0.473099 + 0.881009i \(0.343135\pi\)
\(192\) −456888. + 228414.i −0.894451 + 0.447166i
\(193\) −757371. −1.46358 −0.731788 0.681533i \(-0.761314\pi\)
−0.731788 + 0.681533i \(0.761314\pi\)
\(194\) −121005. + 36613.7i −0.230834 + 0.0698456i
\(195\) 465713. 129625.i 0.877065 0.244119i
\(196\) 376087. 250528.i 0.699274 0.465819i
\(197\) 948808.i 1.74186i −0.491409 0.870929i \(-0.663518\pi\)
0.491409 0.870929i \(-0.336482\pi\)
\(198\) 342181. 379263.i 0.620287 0.687507i
\(199\) 221239.i 0.396030i 0.980199 + 0.198015i \(0.0634495\pi\)
−0.980199 + 0.198015i \(0.936551\pi\)
\(200\) −255774. + 310324.i −0.452148 + 0.548580i
\(201\) 568895. 158344.i 0.993212 0.276447i
\(202\) −79331.8 262186.i −0.136795 0.452096i
\(203\) −175803. −0.299423
\(204\) −456663. + 529483.i −0.768281 + 0.890792i
\(205\) 422682. 0.702472
\(206\) 249355. + 824100.i 0.409403 + 1.35304i
\(207\) 503718. 303954.i 0.817075 0.493040i
\(208\) 167324. 400763.i 0.268164 0.642288i
\(209\) 118844.i 0.188196i
\(210\) 178981. + 282154.i 0.280065 + 0.441507i
\(211\) 670682.i 1.03708i −0.855055 0.518538i \(-0.826476\pi\)
0.855055 0.518538i \(-0.173524\pi\)
\(212\) 34877.3 + 52356.8i 0.0532970 + 0.0800080i
\(213\) 85093.8 + 305722.i 0.128513 + 0.461720i
\(214\) −873768. + 264384.i −1.30425 + 0.394639i
\(215\) −1.19812e6 −1.76769
\(216\) 680345. 85532.7i 0.992190 0.124738i
\(217\) 241283. 0.347838
\(218\) 6712.24 2030.98i 0.00956591 0.00289444i
\(219\) 259502. + 932331.i 0.365620 + 1.31359i
\(220\) −482047. 723636.i −0.671480 1.00801i
\(221\) 594476.i 0.818754i
\(222\) −18699.8 29479.3i −0.0254657 0.0401452i
\(223\) 1.21387e6i 1.63459i −0.576216 0.817297i \(-0.695471\pi\)
0.576216 0.817297i \(-0.304529\pi\)
\(224\) 298628. + 30473.1i 0.397658 + 0.0405785i
\(225\) 462209. 278907.i 0.608671 0.367285i
\(226\) 256734. + 848488.i 0.334359 + 1.10503i
\(227\) 800234. 1.03075 0.515374 0.856965i \(-0.327653\pi\)
0.515374 + 0.856965i \(0.327653\pi\)
\(228\) 104193. 120808.i 0.132740 0.153907i
\(229\) −937980. −1.18197 −0.590983 0.806684i \(-0.701260\pi\)
−0.590983 + 0.806684i \(0.701260\pi\)
\(230\) −290025. 958511.i −0.361506 1.19475i
\(231\) −289190. + 80492.3i −0.356578 + 0.0992486i
\(232\) 473890. + 390588.i 0.578039 + 0.476429i
\(233\) 925881.i 1.11729i 0.829407 + 0.558645i \(0.188678\pi\)
−0.829407 + 0.558645i \(0.811322\pi\)
\(234\) −390533. + 432854.i −0.466249 + 0.516776i
\(235\) 1.72902e6i 2.04235i
\(236\) 209379. 139477.i 0.244711 0.163013i
\(237\) −964944. + 268579.i −1.11592 + 0.310600i
\(238\) 393288. 119001.i 0.450058 0.136178i
\(239\) 619662. 0.701714 0.350857 0.936429i \(-0.385890\pi\)
0.350857 + 0.936429i \(0.385890\pi\)
\(240\) 144415. 1.15822e6i 0.161839 1.29796i
\(241\) 39339.5 0.0436301 0.0218151 0.999762i \(-0.493055\pi\)
0.0218151 + 0.999762i \(0.493055\pi\)
\(242\) −124327. + 37618.9i −0.136467 + 0.0412921i
\(243\) −899590. 195005.i −0.977302 0.211850i
\(244\) −249292. + 166065.i −0.268061 + 0.178567i
\(245\) 1.03257e6i 1.09902i
\(246\) −430448. + 273050.i −0.453506 + 0.287677i
\(247\) 135637.i 0.141461i
\(248\) −650397. 536067.i −0.671505 0.553465i
\(249\) 41977.0 + 150814.i 0.0429055 + 0.154150i
\(250\) 108225. + 357675.i 0.109516 + 0.361942i
\(251\) −699759. −0.701074 −0.350537 0.936549i \(-0.614001\pi\)
−0.350537 + 0.936549i \(0.614001\pi\)
\(252\) −364539. 171717.i −0.361612 0.170339i
\(253\) 899677. 0.883660
\(254\) −39040.5 129026.i −0.0379692 0.125485i
\(255\) −428412. 1.53919e6i −0.412583 1.48232i
\(256\) −737271. 745616.i −0.703117 0.711075i
\(257\) 762091.i 0.719738i 0.933003 + 0.359869i \(0.117179\pi\)
−0.933003 + 0.359869i \(0.882821\pi\)
\(258\) 1.22014e6 773980.i 1.14119 0.723903i
\(259\) 20515.2i 0.0190032i
\(260\) 550163. + 825890.i 0.504729 + 0.757685i
\(261\) −425914. 705832.i −0.387008 0.641357i
\(262\) 1.87656e6 567806.i 1.68892 0.511030i
\(263\) 1.39808e6 1.24636 0.623180 0.782079i \(-0.285841\pi\)
0.623180 + 0.782079i \(0.285841\pi\)
\(264\) 958369. + 425533.i 0.846297 + 0.375771i
\(265\) −143749. −0.125745
\(266\) −89733.4 + 27151.4i −0.0777589 + 0.0235282i
\(267\) −850578. + 236747.i −0.730190 + 0.203239i
\(268\) 672055. + 1.00887e6i 0.571568 + 0.858023i
\(269\) 1.01587e6i 0.855966i −0.903787 0.427983i \(-0.859224\pi\)
0.903787 0.427983i \(-0.140776\pi\)
\(270\) −699209. + 1.40216e6i −0.583710 + 1.17055i
\(271\) 1.06520e6i 0.881068i −0.897736 0.440534i \(-0.854789\pi\)
0.897736 0.440534i \(-0.145211\pi\)
\(272\) −1.32453e6 553008.i −1.08552 0.453220i
\(273\) 330054. 91866.3i 0.268027 0.0746018i
\(274\) −298672. 987090.i −0.240336 0.794292i
\(275\) 825539. 0.658272
\(276\) 914546. + 788768.i 0.722658 + 0.623270i
\(277\) 1.09974e6 0.861172 0.430586 0.902550i \(-0.358307\pi\)
0.430586 + 0.902550i \(0.358307\pi\)
\(278\) −105617. 349055.i −0.0819634 0.270883i
\(279\) 584551. + 968728.i 0.449585 + 0.745060i
\(280\) −436254. + 529296.i −0.332540 + 0.403463i
\(281\) 1.73035e6i 1.30728i −0.756807 0.653639i \(-0.773242\pi\)
0.756807 0.653639i \(-0.226758\pi\)
\(282\) −1.11693e6 1.76079e6i −0.836383 1.31851i
\(283\) 787037.i 0.584156i 0.956394 + 0.292078i \(0.0943468\pi\)
−0.956394 + 0.292078i \(0.905653\pi\)
\(284\) −542164. + 361160.i −0.398873 + 0.265708i
\(285\) 97747.4 + 351184.i 0.0712841 + 0.256108i
\(286\) −853321. + 258197.i −0.616875 + 0.186653i
\(287\) 299558. 0.214673
\(288\) 601133. + 1.27279e6i 0.427061 + 0.904223i
\(289\) −544892. −0.383765
\(290\) −1.34311e6 + 406395.i −0.937811 + 0.283762i
\(291\) 93416.4 + 335624.i 0.0646682 + 0.232338i
\(292\) −1.65338e6 + 1.10139e6i −1.13479 + 0.755937i
\(293\) 618982.i 0.421220i 0.977570 + 0.210610i \(0.0675450\pi\)
−0.977570 + 0.210610i \(0.932455\pi\)
\(294\) −667036. 1.05155e6i −0.450071 0.709512i
\(295\) 574866.i 0.384602i
\(296\) 45579.5 55300.5i 0.0302371 0.0366859i
\(297\) −1.02379e6 966067.i −0.673470 0.635501i
\(298\) −42002.8 138816.i −0.0273992 0.0905523i
\(299\) −1.02681e6 −0.664217
\(300\) 839182. + 723769.i 0.538336 + 0.464298i
\(301\) −849120. −0.540198
\(302\) 644636. + 2.13047e6i 0.406721 + 1.34418i
\(303\) −727205. + 202408.i −0.455041 + 0.126654i
\(304\) 302207. + 126175.i 0.187551 + 0.0783053i
\(305\) 684449.i 0.421300i
\(306\) 1.43059e6 + 1.29071e6i 0.873396 + 0.788001i
\(307\) 744212.i 0.450662i −0.974282 0.225331i \(-0.927654\pi\)
0.974282 0.225331i \(-0.0723463\pi\)
\(308\) −341631. 512847.i −0.205201 0.308043i
\(309\) 2.28575e6 636207.i 1.36186 0.379055i
\(310\) 1.84336e6 557763.i 1.08945 0.329644i
\(311\) −170581. −0.100007 −0.0500035 0.998749i \(-0.515923\pi\)
−0.0500035 + 0.998749i \(0.515923\pi\)
\(312\) −1.09379e6 485662.i −0.636133 0.282454i
\(313\) −772718. −0.445821 −0.222910 0.974839i \(-0.571556\pi\)
−0.222910 + 0.974839i \(0.571556\pi\)
\(314\) 2.51059e6 759652.i 1.43699 0.434801i
\(315\) 788356. 475711.i 0.447657 0.270126i
\(316\) −1.13992e6 1.71122e6i −0.642181 0.964025i
\(317\) 1.69947e6i 0.949874i 0.880020 + 0.474937i \(0.157529\pi\)
−0.880020 + 0.474937i \(0.842471\pi\)
\(318\) 146391. 92861.3i 0.0811794 0.0514952i
\(319\) 1.26067e6i 0.693622i
\(320\) 2.35192e6 457515.i 1.28395 0.249764i
\(321\) 674550. + 2.42351e6i 0.365386 + 1.31275i
\(322\) −205543. 679304.i −0.110475 0.365111i
\(323\) 448281. 0.239081
\(324\) −193733. 1.87961e6i −0.102528 0.994730i
\(325\) −942191. −0.494801
\(326\) −604636. 1.99828e6i −0.315101 1.04139i
\(327\) −5181.86 18617.2i −0.00267989 0.00962822i
\(328\) −807483. 665540.i −0.414428 0.341578i
\(329\) 1.22537e6i 0.624133i
\(330\) −2.02330e6 + 1.28346e6i −1.02277 + 0.648780i
\(331\) 23171.2i 0.0116246i −0.999983 0.00581231i \(-0.998150\pi\)
0.999983 0.00581231i \(-0.00185013\pi\)
\(332\) −267451. + 178161.i −0.133168 + 0.0887091i
\(333\) −82366.9 + 49701.9i −0.0407045 + 0.0245619i
\(334\) −96175.6 + 29100.7i −0.0471736 + 0.0142737i
\(335\) −2.76993e6 −1.34852
\(336\) 102348. 820838.i 0.0494574 0.396652i
\(337\) 1.55319e6 0.744991 0.372495 0.928034i \(-0.378502\pi\)
0.372495 + 0.928034i \(0.378502\pi\)
\(338\) −1.03644e6 + 313605.i −0.493460 + 0.149311i
\(339\) 2.35339e6 655034.i 1.11223 0.309574i
\(340\) 2.72957e6 1.81829e6i 1.28055 0.853035i
\(341\) 1.73022e6i 0.805777i
\(342\) −326406. 294492.i −0.150901 0.136147i
\(343\) 1.60275e6i 0.735579i
\(344\) 2.28887e6 + 1.88652e6i 1.04286 + 0.859540i
\(345\) −2.65855e6 + 739972.i −1.20253 + 0.334709i
\(346\) 1.18065e6 + 3.90195e6i 0.530188 + 1.75223i
\(347\) −976969. −0.435569 −0.217784 0.975997i \(-0.569883\pi\)
−0.217784 + 0.975997i \(0.569883\pi\)
\(348\) 1.10526e6 1.28150e6i 0.489232 0.567245i
\(349\) −1.06380e6 −0.467515 −0.233758 0.972295i \(-0.575102\pi\)
−0.233758 + 0.972295i \(0.575102\pi\)
\(350\) −188605. 623326.i −0.0822969 0.271985i
\(351\) 1.16845e6 + 1.10258e6i 0.506224 + 0.477684i
\(352\) −218520. + 2.14143e6i −0.0940014 + 0.921187i
\(353\) 3.56017e6i 1.52067i −0.649532 0.760334i \(-0.725035\pi\)
0.649532 0.760334i \(-0.274965\pi\)
\(354\) −371360. 585429.i −0.157502 0.248294i
\(355\) 1.48855e6i 0.626893i
\(356\) −1.00482e6 1.50840e6i −0.420206 0.630802i
\(357\) −303619. 1.09083e6i −0.126084 0.452989i
\(358\) −4.42592e6 + 1.33919e6i −1.82514 + 0.552249i
\(359\) −1.37771e6 −0.564184 −0.282092 0.959387i \(-0.591028\pi\)
−0.282092 + 0.959387i \(0.591028\pi\)
\(360\) −3.18198e6 469206.i −1.29402 0.190813i
\(361\) 2.37382e6 0.958693
\(362\) 2.10825e6 637911.i 0.845571 0.255852i
\(363\) 95981.0 + 344838.i 0.0382313 + 0.137356i
\(364\) 389905. + 585314.i 0.154243 + 0.231545i
\(365\) 4.53949e6i 1.78351i
\(366\) 442150. + 697025.i 0.172531 + 0.271985i
\(367\) 3.26242e6i 1.26437i 0.774817 + 0.632186i \(0.217842\pi\)
−0.774817 + 0.632186i \(0.782158\pi\)
\(368\) −955180. + 2.28778e6i −0.367676 + 0.880633i
\(369\) 725734. + 1.20270e6i 0.277467 + 0.459823i
\(370\) 47424.2 + 156733.i 0.0180093 + 0.0595193i
\(371\) −101876. −0.0384272
\(372\) −1.51692e6 + 1.75881e6i −0.568337 + 0.658965i
\(373\) 464538. 0.172882 0.0864409 0.996257i \(-0.472451\pi\)
0.0864409 + 0.996257i \(0.472451\pi\)
\(374\) 853343. + 2.82023e6i 0.315460 + 1.04257i
\(375\) 992057. 276126.i 0.364299 0.101398i
\(376\) 2.72245e6 3.30308e6i 0.993094 1.20489i
\(377\) 1.43880e6i 0.521372i
\(378\) −495535. + 993724.i −0.178379 + 0.357714i
\(379\) 2.81783e6i 1.00767i −0.863801 0.503834i \(-0.831922\pi\)
0.863801 0.503834i \(-0.168078\pi\)
\(380\) −622785. + 414866.i −0.221248 + 0.147383i
\(381\) −357870. + 99608.3i −0.126303 + 0.0351547i
\(382\) 2.58296e6 781549.i 0.905647 0.274030i
\(383\) 1.82945e6 0.637270 0.318635 0.947878i \(-0.396776\pi\)
0.318635 + 0.947878i \(0.396776\pi\)
\(384\) −2.09958e6 + 1.98524e6i −0.726614 + 0.687046i
\(385\) 1.40806e6 0.484138
\(386\) −4.10073e6 + 1.24079e6i −1.40085 + 0.423868i
\(387\) −2.05715e6 3.40914e6i −0.698213 1.15709i
\(388\) −595191. + 396484.i −0.200714 + 0.133705i
\(389\) 4035.50i 0.00135215i 1.00000 0.000676073i \(0.000215201\pi\)
−1.00000 0.000676073i \(0.999785\pi\)
\(390\) 2.30920e6 1.46482e6i 0.768778 0.487666i
\(391\) 3.39360e6i 1.12258i
\(392\) 1.62585e6 1.97261e6i 0.534400 0.648374i
\(393\) −1.44870e6 5.20486e6i −0.473150 1.69992i
\(394\) −1.55442e6 5.13725e6i −0.504462 1.66721i
\(395\) 4.69828e6 1.51512
\(396\) 1.23137e6 2.61408e6i 0.394595 0.837686i
\(397\) −2.37250e6 −0.755493 −0.377746 0.925909i \(-0.623301\pi\)
−0.377746 + 0.925909i \(0.623301\pi\)
\(398\) 362453. + 1.19788e6i 0.114695 + 0.379058i
\(399\) 69274.3 + 248887.i 0.0217841 + 0.0782654i
\(400\) −876468. + 2.09926e6i −0.273896 + 0.656017i
\(401\) 4.05826e6i 1.26031i 0.776468 + 0.630157i \(0.217009\pi\)
−0.776468 + 0.630157i \(0.782991\pi\)
\(402\) 2.82083e6 1.78936e6i 0.870585 0.552246i
\(403\) 1.97471e6i 0.605675i
\(404\) −859072. 1.28962e6i −0.261864 0.393104i
\(405\) 3.81987e6 + 2.01268e6i 1.15721 + 0.609730i
\(406\) −951870. + 288016.i −0.286591 + 0.0867163i
\(407\) −147113. −0.0440215
\(408\) −1.60512e6 + 3.61499e6i −0.477372 + 1.07512i
\(409\) 3.68529e6 1.08934 0.544670 0.838650i \(-0.316655\pi\)
0.544670 + 0.838650i \(0.316655\pi\)
\(410\) 2.28858e6 692476.i 0.672367 0.203444i
\(411\) −2.73782e6 + 762035.i −0.799466 + 0.222521i
\(412\) 2.70023e6 + 4.05351e6i 0.783715 + 1.17649i
\(413\) 407412.i 0.117533i
\(414\) 2.22938e6 2.47098e6i 0.639269 0.708545i
\(415\) 734307.i 0.209294i
\(416\) 249398. 2.44403e6i 0.0706576 0.692425i
\(417\) −968147. + 269471.i −0.272647 + 0.0758877i
\(418\) −194700. 643470.i −0.0545037 0.180131i
\(419\) −3.99766e6 −1.11242 −0.556212 0.831040i \(-0.687746\pi\)
−0.556212 + 0.831040i \(0.687746\pi\)
\(420\) 1.43133e6 + 1.23448e6i 0.395928 + 0.341476i
\(421\) −6.97378e6 −1.91762 −0.958811 0.284044i \(-0.908324\pi\)
−0.958811 + 0.284044i \(0.908324\pi\)
\(422\) −1.09877e6 3.63136e6i −0.300349 0.992632i
\(423\) −4.91974e6 + 2.96868e6i −1.33688 + 0.806700i
\(424\) 274616. + 226343.i 0.0741841 + 0.0611438i
\(425\) 3.11395e6i 0.836256i
\(426\) 961596. + 1.51590e6i 0.256725 + 0.404713i
\(427\) 485074.i 0.128747i
\(428\) −4.29781e6 + 2.86297e6i −1.13407 + 0.755453i
\(429\) 658765. + 2.36679e6i 0.172817 + 0.620893i
\(430\) −6.48715e6 + 1.96287e6i −1.69193 + 0.511943i
\(431\) 3.92239e6 1.01709 0.508543 0.861037i \(-0.330184\pi\)
0.508543 + 0.861037i \(0.330184\pi\)
\(432\) 3.54355e6 1.57771e6i 0.913543 0.406742i
\(433\) −4.53851e6 −1.16331 −0.581653 0.813437i \(-0.697594\pi\)
−0.581653 + 0.813437i \(0.697594\pi\)
\(434\) 1.30641e6 395291.i 0.332931 0.100738i
\(435\) 1.03688e6 + 3.72527e6i 0.262728 + 0.943920i
\(436\) 33015.6 21993.2i 0.00831769 0.00554079i
\(437\) 774292.i 0.193955i
\(438\) 2.93248e6 + 4.62290e6i 0.730382 + 1.15141i
\(439\) 4.33755e6i 1.07419i −0.843520 0.537097i \(-0.819521\pi\)
0.843520 0.537097i \(-0.180479\pi\)
\(440\) −3.79554e6 3.12834e6i −0.934633 0.770340i
\(441\) −2.93808e6 + 1.77290e6i −0.719396 + 0.434099i
\(442\) −973924. 3.21875e6i −0.237121 0.783666i
\(443\) 2.55182e6 0.617791 0.308895 0.951096i \(-0.400041\pi\)
0.308895 + 0.951096i \(0.400041\pi\)
\(444\) −149544. 128978.i −0.0360009 0.0310496i
\(445\) 4.14144e6 0.991405
\(446\) −1.98867e6 6.57241e6i −0.473397 1.56454i
\(447\) −385024. + 107166.i −0.0911421 + 0.0253682i
\(448\) 1.66682e6 324245.i 0.392368 0.0763269i
\(449\) 1.60272e6i 0.375182i −0.982247 0.187591i \(-0.939932\pi\)
0.982247 0.187591i \(-0.0600680\pi\)
\(450\) 2.04567e6 2.26735e6i 0.476216 0.527823i
\(451\) 2.14811e6i 0.497295i
\(452\) 2.78014e6 + 4.17347e6i 0.640059 + 0.960840i
\(453\) 5.90913e6 1.64473e6i 1.35294 0.376573i
\(454\) 4.33281e6 1.31102e6i 0.986574 0.298516i
\(455\) −1.60702e6 −0.363910
\(456\) 366227. 824804.i 0.0824781 0.185754i
\(457\) 4.62120e6 1.03506 0.517528 0.855666i \(-0.326852\pi\)
0.517528 + 0.855666i \(0.326852\pi\)
\(458\) −5.07862e6 + 1.53668e6i −1.13131 + 0.342311i
\(459\) 3.64403e6 3.86175e6i 0.807327 0.855563i
\(460\) −3.14064e6 4.71464e6i −0.692027 1.03885i
\(461\) 1.81893e6i 0.398625i 0.979936 + 0.199313i \(0.0638709\pi\)
−0.979936 + 0.199313i \(0.936129\pi\)
\(462\) −1.43393e6 + 909598.i −0.312553 + 0.198264i
\(463\) 4.06917e6i 0.882171i 0.897465 + 0.441086i \(0.145406\pi\)
−0.897465 + 0.441086i \(0.854594\pi\)
\(464\) 3.20574e6 + 1.33844e6i 0.691246 + 0.288605i
\(465\) −1.42308e6 5.11280e6i −0.305209 1.09655i
\(466\) 1.51686e6 + 5.01312e6i 0.323580 + 1.06941i
\(467\) 4.47865e6 0.950287 0.475143 0.879908i \(-0.342396\pi\)
0.475143 + 0.879908i \(0.342396\pi\)
\(468\) −1.40537e6 + 2.98346e6i −0.296603 + 0.629660i
\(469\) −1.96307e6 −0.412102
\(470\) 2.83263e6 + 9.36164e6i 0.591487 + 1.95482i
\(471\) −1.93818e6 6.96345e6i −0.402571 1.44635i
\(472\) 905164. 1.09821e6i 0.187013 0.226898i
\(473\) 6.08896e6i 1.25138i
\(474\) −4.78461e6 + 3.03506e6i −0.978139 + 0.620471i
\(475\) 710486.i 0.144485i
\(476\) 1.93447e6 1.28864e6i 0.391331 0.260684i
\(477\) −246814. 409025.i −0.0496677 0.0823102i
\(478\) 3.35512e6 1.01519e6i 0.671642 0.203225i
\(479\) −4.95004e6 −0.985757 −0.492879 0.870098i \(-0.664055\pi\)
−0.492879 + 0.870098i \(0.664055\pi\)
\(480\) −1.11557e6 6.50768e6i −0.221001 1.28921i
\(481\) 167901. 0.0330895
\(482\) 213001. 64449.6i 0.0417603 0.0126358i
\(483\) −1.88414e6 + 524424.i −0.367489 + 0.102286i
\(484\) −611531. + 407369.i −0.118660 + 0.0790450i
\(485\) 1.63414e6i 0.315453i
\(486\) −5.19024e6 + 417950.i −0.996773 + 0.0802665i
\(487\) 3.60548e6i 0.688875i −0.938809 0.344438i \(-0.888070\pi\)
0.938809 0.344438i \(-0.111930\pi\)
\(488\) −1.07771e6 + 1.30756e6i −0.204858 + 0.248548i
\(489\) −5.54248e6 + 1.54267e6i −1.04817 + 0.291744i
\(490\) 1.69166e6 + 5.59079e6i 0.318289 + 1.05192i
\(491\) −2.76149e6 −0.516939 −0.258469 0.966019i \(-0.583218\pi\)
−0.258469 + 0.966019i \(0.583218\pi\)
\(492\) −1.88330e6 + 2.18361e6i −0.350756 + 0.406689i
\(493\) 4.75526e6 0.881164
\(494\) 222213. + 734396.i 0.0409686 + 0.135398i
\(495\) 3.41128e6 + 5.65323e6i 0.625755 + 1.03701i
\(496\) −4.39976e6 1.83696e6i −0.803017 0.335270i
\(497\) 1.05495e6i 0.191576i
\(498\) 474358. + 747799.i 0.0857102 + 0.135117i
\(499\) 1.08070e7i 1.94292i 0.237211 + 0.971458i \(0.423767\pi\)
−0.237211 + 0.971458i \(0.576233\pi\)
\(500\) 1.17195e6 + 1.75930e6i 0.209645 + 0.314713i
\(501\) 74247.8 + 266755.i 0.0132157 + 0.0474809i
\(502\) −3.78879e6 + 1.14641e6i −0.671029 + 0.203039i
\(503\) 8.16383e6 1.43871 0.719356 0.694641i \(-0.244437\pi\)
0.719356 + 0.694641i \(0.244437\pi\)
\(504\) −2.25509e6 332530.i −0.395447 0.0583116i
\(505\) 3.54074e6 0.617825
\(506\) 4.87123e6 1.47393e6i 0.845790 0.255918i
\(507\) 800133. + 2.87470e6i 0.138243 + 0.496675i
\(508\) −422764. 634642.i −0.0726840 0.109111i
\(509\) 2.33136e6i 0.398855i 0.979913 + 0.199428i \(0.0639083\pi\)
−0.979913 + 0.199428i \(0.936092\pi\)
\(510\) −4.84124e6 7.63194e6i −0.824197 1.29930i
\(511\) 3.21717e6i 0.545032i
\(512\) −5.21344e6 2.82922e6i −0.878919 0.476970i
\(513\) −831429. + 881104.i −0.139486 + 0.147820i
\(514\) 1.24853e6 + 4.12629e6i 0.208444 + 0.688893i
\(515\) −1.11292e7 −1.84904
\(516\) 5.33834e6 6.18960e6i 0.882636 1.02338i
\(517\) −8.78701e6 −1.44582
\(518\) 33609.9 + 111078.i 0.00550355 + 0.0181888i
\(519\) 1.08226e7 3.01232e6i 1.76365 0.490888i
\(520\) 4.33186e6 + 3.57039e6i 0.702532 + 0.579039i
\(521\) 6.09574e6i 0.983857i 0.870636 + 0.491928i \(0.163708\pi\)
−0.870636 + 0.491928i \(0.836292\pi\)
\(522\) −3.46244e6 3.12390e6i −0.556167 0.501789i
\(523\) 1.98277e6i 0.316970i −0.987361 0.158485i \(-0.949339\pi\)
0.987361 0.158485i \(-0.0506610\pi\)
\(524\) 9.23024e6 6.14868e6i 1.46854 0.978259i
\(525\) −1.72887e6 + 481209.i −0.273757 + 0.0761965i
\(526\) 7.56981e6 2.29046e6i 1.19295 0.360960i
\(527\) −6.52642e6 −1.02364
\(528\) 5.88616e6 + 733929.i 0.918856 + 0.114570i
\(529\) −574761. −0.0892993
\(530\) −778321. + 235503.i −0.120356 + 0.0364173i
\(531\) −1.63572e6 + 987031.i −0.251752 + 0.151913i
\(532\) −441373. + 294019.i −0.0676124 + 0.0450397i
\(533\) 2.45164e6i 0.373800i
\(534\) −4.21753e6 + 2.67534e6i −0.640037 + 0.406000i
\(535\) 1.18000e7i 1.78236i
\(536\) 5.29162e6 + 4.36144e6i 0.795567 + 0.655719i
\(537\) 3.41682e6 + 1.22759e7i 0.511313 + 1.83703i
\(538\) −1.66429e6 5.50034e6i −0.247897 0.819283i
\(539\) −5.24763e6 −0.778021
\(540\) −1.48866e6 + 8.73741e6i −0.219691 + 1.28943i
\(541\) 3.04420e6 0.447178 0.223589 0.974684i \(-0.428223\pi\)
0.223589 + 0.974684i \(0.428223\pi\)
\(542\) −1.74511e6 5.76747e6i −0.255168 0.843310i
\(543\) −1.62757e6 5.84749e6i −0.236887 0.851079i
\(544\) −8.07754e6 824262.i −1.17026 0.119417i
\(545\) 90646.8i 0.0130726i
\(546\) 1.63655e6 1.03813e6i 0.234935 0.149028i
\(547\) 6.16452e6i 0.880909i 0.897775 + 0.440454i \(0.145183\pi\)
−0.897775 + 0.440454i \(0.854817\pi\)
\(548\) −3.23428e6 4.85521e6i −0.460072 0.690648i
\(549\) 1.94753e6 1.17518e6i 0.275774 0.166408i
\(550\) 4.46982e6 1.35247e6i 0.630062 0.190643i
\(551\) −1.08497e6 −0.152244
\(552\) 6.24397e6 + 2.77243e6i 0.872194 + 0.387270i
\(553\) 3.32971e6 0.463013
\(554\) 5.95445e6 1.80169e6i 0.824266 0.249405i
\(555\) 434720. 120999.i 0.0599070 0.0166743i
\(556\) −1.14371e6 1.71690e6i −0.156902 0.235536i
\(557\) 4.80670e6i 0.656461i 0.944598 + 0.328230i \(0.106452\pi\)
−0.944598 + 0.328230i \(0.893548\pi\)
\(558\) 4.75207e6 + 4.28744e6i 0.646096 + 0.582925i
\(559\) 6.94936e6i 0.940623i
\(560\) −1.49493e6 + 3.58054e6i −0.201442 + 0.482480i
\(561\) 7.82227e6 2.17723e6i 1.04936 0.292076i
\(562\) −2.83481e6 9.36884e6i −0.378603 1.25125i
\(563\) 8.63483e6 1.14811 0.574054 0.818818i \(-0.305370\pi\)
0.574054 + 0.818818i \(0.305370\pi\)
\(564\) −8.93224e6 7.70378e6i −1.18239 1.01978i
\(565\) −1.14586e7 −1.51011
\(566\) 1.28940e6 + 4.26135e6i 0.169178 + 0.559122i
\(567\) 2.70717e6 + 1.42640e6i 0.353638 + 0.186331i
\(568\) −2.34382e6 + 2.84370e6i −0.304827 + 0.369839i
\(569\) 1.07164e7i 1.38761i −0.720161 0.693807i \(-0.755932\pi\)
0.720161 0.693807i \(-0.244068\pi\)
\(570\) 1.10459e6 + 1.74132e6i 0.142401 + 0.224487i
\(571\) 5.59442e6i 0.718066i −0.933325 0.359033i \(-0.883107\pi\)
0.933325 0.359033i \(-0.116893\pi\)
\(572\) −4.19724e6 + 2.79597e6i −0.536381 + 0.357308i
\(573\) −1.99405e6 7.16416e6i −0.253717 0.911547i
\(574\) 1.62194e6 490763.i 0.205473 0.0621716i
\(575\) 5.37856e6 0.678416
\(576\) 5.33999e6 + 5.90660e6i 0.670632 + 0.741790i
\(577\) −5.26236e6 −0.658023 −0.329012 0.944326i \(-0.606716\pi\)
−0.329012 + 0.944326i \(0.606716\pi\)
\(578\) −2.95028e6 + 892691.i −0.367319 + 0.111143i
\(579\) 3.16577e6 + 1.13739e7i 0.392449 + 1.40998i
\(580\) −6.60636e6 + 4.40080e6i −0.815440 + 0.543202i
\(581\) 520409.i 0.0639594i
\(582\) 1.05565e6 + 1.66417e6i 0.129185 + 0.203652i
\(583\) 730547.i 0.0890178i
\(584\) −7.14772e6 + 8.67214e6i −0.867232 + 1.05219i
\(585\) −3.89331e6 6.45206e6i −0.470359 0.779487i
\(586\) 1.01407e6 + 3.35143e6i 0.121990 + 0.403168i
\(587\) 1.09294e6 0.130919 0.0654594 0.997855i \(-0.479149\pi\)
0.0654594 + 0.997855i \(0.479149\pi\)
\(588\) −5.33436e6 4.60072e6i −0.636266 0.548760i
\(589\) 1.48908e6 0.176860
\(590\) 941798. + 3.11257e6i 0.111385 + 0.368120i
\(591\) −1.42488e7 + 3.96597e6i −1.67807 + 0.467068i
\(592\) 156189. 374093.i 0.0183166 0.0438707i
\(593\) 2.21385e6i 0.258530i 0.991610 + 0.129265i \(0.0412618\pi\)
−0.991610 + 0.129265i \(0.958738\pi\)
\(594\) −7.12591e6 3.55344e6i −0.828656 0.413221i
\(595\) 5.31123e6i 0.615039i
\(596\) −454842. 682797.i −0.0524500 0.0787365i
\(597\) 3.32247e6 924766.i 0.381527 0.106193i
\(598\) −5.55956e6 + 1.68221e6i −0.635752 + 0.192365i
\(599\) −674331. −0.0767902 −0.0383951 0.999263i \(-0.512225\pi\)
−0.0383951 + 0.999263i \(0.512225\pi\)
\(600\) 5.72943e6 + 2.54397e6i 0.649731 + 0.288492i
\(601\) 9.18665e6 1.03746 0.518730 0.854938i \(-0.326405\pi\)
0.518730 + 0.854938i \(0.326405\pi\)
\(602\) −4.59749e6 + 1.39110e6i −0.517047 + 0.156447i
\(603\) −4.75590e6 7.88156e6i −0.532647 0.882712i
\(604\) 6.98067e6 + 1.04792e7i 0.778582 + 1.16879i
\(605\) 1.67901e6i 0.186493i
\(606\) −3.60579e6 + 2.28729e6i −0.398859 + 0.253012i
\(607\) 7.32920e6i 0.807393i −0.914893 0.403696i \(-0.867725\pi\)
0.914893 0.403696i \(-0.132275\pi\)
\(608\) 1.84299e6 + 188065.i 0.202192 + 0.0206324i
\(609\) 734845. + 2.64013e6i 0.0802884 + 0.288458i
\(610\) −1.12133e6 3.70590e6i −0.122013 0.403245i
\(611\) 1.00287e7 1.08678
\(612\) 9.86038e6 + 4.64476e6i 1.06418 + 0.501285i
\(613\) 1.45783e7 1.56696 0.783478 0.621420i \(-0.213444\pi\)
0.783478 + 0.621420i \(0.213444\pi\)
\(614\) −1.21923e6 4.02948e6i −0.130517 0.431348i
\(615\) −1.76679e6 6.34767e6i −0.188364 0.676747i
\(616\) −2.68993e6 2.21708e6i −0.285620 0.235413i
\(617\) 475062.i 0.0502386i −0.999684 0.0251193i \(-0.992003\pi\)
0.999684 0.0251193i \(-0.00799656\pi\)
\(618\) 1.13337e7 7.18941e6i 1.19372 0.757220i
\(619\) 737236.i 0.0773357i 0.999252 + 0.0386678i \(0.0123114\pi\)
−0.999252 + 0.0386678i \(0.987689\pi\)
\(620\) 9.06698e6 6.03993e6i 0.947291 0.631034i
\(621\) −6.67018e6 6.29412e6i −0.694078 0.654947i
\(622\) −923601. + 279462.i −0.0957212 + 0.0289632i
\(623\) 2.93507e6 0.302969
\(624\) −6.71790e6 837637.i −0.690673 0.0861180i
\(625\) −1.17727e7 −1.20552
\(626\) −4.18383e6 + 1.26594e6i −0.426715 + 0.129115i
\(627\) −1.78475e6 + 496760.i −0.181304 + 0.0504636i
\(628\) 1.23489e7 8.22616e6i 1.24948 0.832335i
\(629\) 554914.i 0.0559241i
\(630\) 3.48914e6 3.86726e6i 0.350241 0.388196i
\(631\) 153956.i 0.0153930i −0.999970 0.00769648i \(-0.997550\pi\)
0.999970 0.00769648i \(-0.00244989\pi\)
\(632\) −8.97550e6 7.39775e6i −0.893852 0.736728i
\(633\) −1.00720e7 + 2.80342e6i −0.999097 + 0.278085i
\(634\) 2.78423e6 + 9.20167e6i 0.275094 + 0.909166i
\(635\) 1.74246e6 0.171486
\(636\) 640488. 742621.i 0.0627868 0.0727988i
\(637\) 5.98914e6 0.584812
\(638\) −2.06534e6 6.82578e6i −0.200881 0.663897i
\(639\) 4.23553e6 2.55581e6i 0.410351 0.247614i
\(640\) 1.19847e7 6.33030e6i 1.15659 0.610906i
\(641\) 1.07313e7i 1.03159i 0.856713 + 0.515794i \(0.172503\pi\)
−0.856713 + 0.515794i \(0.827497\pi\)
\(642\) 7.62271e6 + 1.20168e7i 0.729914 + 1.15067i
\(643\) 2.61064e6i 0.249011i −0.992219 0.124506i \(-0.960266\pi\)
0.992219 0.124506i \(-0.0397345\pi\)
\(644\) −2.22579e6 3.34130e6i −0.211481 0.317469i
\(645\) 5.00809e6 + 1.79929e7i 0.473994 + 1.70295i
\(646\) 2.42719e6 734415.i 0.228835 0.0692405i
\(647\) 2.10997e6 0.198160 0.0990800 0.995079i \(-0.468410\pi\)
0.0990800 + 0.995079i \(0.468410\pi\)
\(648\) −4.12830e6 9.85962e6i −0.386219 0.922407i
\(649\) −2.92152e6 −0.272268
\(650\) −5.10142e6 + 1.54358e6i −0.473596 + 0.143300i
\(651\) −1.00855e6 3.62348e6i −0.0932705 0.335100i
\(652\) −6.54752e6 9.82896e6i −0.603195 0.905500i
\(653\) 1.32077e7i 1.21211i 0.795421 + 0.606057i \(0.207250\pi\)
−0.795421 + 0.606057i \(0.792750\pi\)
\(654\) −58557.2 92312.3i −0.00535348 0.00843947i
\(655\) 2.53423e7i 2.30804i
\(656\) −5.46240e6 2.28063e6i −0.495592 0.206916i
\(657\) 1.29167e7 7.79418e6i 1.16745 0.704461i
\(658\) 2.00751e6 + 6.63467e6i 0.180756 + 0.597385i
\(659\) −1.28753e7 −1.15490 −0.577449 0.816427i \(-0.695952\pi\)
−0.577449 + 0.816427i \(0.695952\pi\)
\(660\) −8.85234e6 + 1.02639e7i −0.791040 + 0.917180i
\(661\) −3.96909e6 −0.353335 −0.176668 0.984271i \(-0.556532\pi\)
−0.176668 + 0.984271i \(0.556532\pi\)
\(662\) −37961.2 125459.i −0.00336663 0.0111264i
\(663\) −8.92760e6 + 2.48488e6i −0.788771 + 0.219544i
\(664\) −1.15621e6 + 1.40280e6i −0.101770 + 0.123474i
\(665\) 1.21182e6i 0.106264i
\(666\) −364543. + 404048.i −0.0318466 + 0.0352978i
\(667\) 8.21350e6i 0.714848i
\(668\) −473060. + 315127.i −0.0410181 + 0.0273240i
\(669\) −1.82294e7 + 5.07391e6i −1.57473 + 0.438306i
\(670\) −1.49976e7 + 4.53795e6i −1.29073 + 0.390547i
\(671\) 3.47843e6 0.298247
\(672\) −790616. 4.61204e6i −0.0675371 0.393976i
\(673\) −8.93046e6 −0.760040 −0.380020 0.924978i \(-0.624083\pi\)
−0.380020 + 0.924978i \(0.624083\pi\)
\(674\) 8.40965e6 2.54458e6i 0.713064 0.215758i
\(675\) −6.12052e6 5.77545e6i −0.517046 0.487895i
\(676\) −5.09795e6 + 3.39598e6i −0.429071 + 0.285824i
\(677\) 9.17967e6i 0.769760i −0.922967 0.384880i \(-0.874243\pi\)
0.922967 0.384880i \(-0.125757\pi\)
\(678\) 1.16691e7 7.40216e6i 0.974907 0.618421i
\(679\) 1.15813e6i 0.0964012i
\(680\) 1.18002e7 1.43168e7i 0.978625 1.18734i
\(681\) −3.34494e6 1.20176e7i −0.276389 0.993001i
\(682\) 2.83460e6 + 9.36813e6i 0.233362 + 0.771245i
\(683\) −498838. −0.0409173 −0.0204587 0.999791i \(-0.506513\pi\)
−0.0204587 + 0.999791i \(0.506513\pi\)
\(684\) −2.24976e6 1.05976e6i −0.183864 0.0866097i
\(685\) 1.33304e7 1.08546
\(686\) 2.62576e6 + 8.67795e6i 0.213032 + 0.704056i
\(687\) 3.92071e6 + 1.40862e7i 0.316937 + 1.13868i
\(688\) 1.54836e7 + 6.46461e6i 1.24710 + 0.520680i
\(689\) 833777.i 0.0669117i
\(690\) −1.31822e7 + 8.36200e6i −1.05406 + 0.668633i
\(691\) 1.14456e7i 0.911894i −0.890007 0.455947i \(-0.849301\pi\)
0.890007 0.455947i \(-0.150699\pi\)
\(692\) 1.27851e7 + 1.91926e7i 1.01493 + 1.52359i
\(693\) 2.41760e6 + 4.00649e6i 0.191228 + 0.316906i
\(694\) −5.28972e6 + 1.60056e6i −0.416902 + 0.126146i
\(695\) 4.71388e6 0.370183
\(696\) 3.88485e6 8.74932e6i 0.303984 0.684622i
\(697\) −8.10271e6 −0.631754
\(698\) −5.75986e6 + 1.74281e6i −0.447480 + 0.135398i
\(699\) 1.39045e7 3.87014e6i 1.07637 0.299594i
\(700\) −2.04238e6 3.06596e6i −0.157540 0.236495i
\(701\) 1.50903e7i 1.15985i −0.814670 0.579925i \(-0.803082\pi\)
0.814670 0.579925i \(-0.196918\pi\)
\(702\) 8.13284e6 + 4.05555e6i 0.622873 + 0.310604i
\(703\) 126610.i 0.00966231i
\(704\) 2.32513e6 + 1.19526e7i 0.176814 + 0.908933i
\(705\) 2.59657e7 7.22720e6i 1.96755 0.547643i
\(706\) −5.83260e6 1.92763e7i −0.440403 1.45550i
\(707\) 2.50935e6 0.188805
\(708\) −2.96980e6 2.56136e6i −0.222661 0.192038i
\(709\) 9.48825e6 0.708876 0.354438 0.935080i \(-0.384672\pi\)
0.354438 + 0.935080i \(0.384672\pi\)
\(710\) −2.43868e6 8.05966e6i −0.181555 0.600027i
\(711\) 8.06683e6 + 1.33685e7i 0.598451 + 0.991764i
\(712\) −7.91171e6 6.52096e6i −0.584885 0.482072i
\(713\) 1.12727e7i 0.830434i
\(714\) −3.43102e6 5.40882e6i −0.251871 0.397061i
\(715\) 1.15238e7i 0.843009i
\(716\) −2.17699e7 + 1.45019e7i −1.58699 + 1.05716i
\(717\) −2.59016e6 9.30583e6i −0.188160 0.676017i
\(718\) −7.45950e6 + 2.25708e6i −0.540006 + 0.163394i
\(719\) −2.38849e7 −1.72306 −0.861532 0.507703i \(-0.830495\pi\)
−0.861532 + 0.507703i \(0.830495\pi\)
\(720\) −1.79973e7 + 2.67253e6i −1.29383 + 0.192128i
\(721\) −7.88737e6 −0.565059
\(722\) 1.28529e7 3.88900e6i 0.917607 0.277648i
\(723\) −164437. 590785.i −0.0116991 0.0420323i
\(724\) 1.03699e7 6.90784e6i 0.735236 0.489774i
\(725\) 7.53666e6i 0.532518i
\(726\) 1.08463e6 + 1.70985e6i 0.0763728 + 0.120398i
\(727\) 8.95331e6i 0.628272i −0.949378 0.314136i \(-0.898285\pi\)
0.949378 0.314136i \(-0.101715\pi\)
\(728\) 3.07002e6 + 2.53036e6i 0.214691 + 0.176952i
\(729\) 831736. + 1.43248e7i 0.0579651 + 0.998319i
\(730\) −7.43700e6 2.45787e7i −0.516524 1.70707i
\(731\) 2.29677e7 1.58973
\(732\) 3.53591e6 + 3.04962e6i 0.243907 + 0.210362i
\(733\) −5.08443e6 −0.349529 −0.174764 0.984610i \(-0.555916\pi\)
−0.174764 + 0.984610i \(0.555916\pi\)
\(734\) 5.34479e6 + 1.76641e7i 0.366177 + 1.21019i
\(735\) 1.55068e7 4.31610e6i 1.05877 0.294696i
\(736\) −1.42370e6 + 1.39519e7i −0.0968779 + 0.949376i
\(737\) 1.40770e7i 0.954646i
\(738\) 5.89980e6 + 5.32296e6i 0.398746 + 0.359760i
\(739\) 5.96874e6i 0.402042i 0.979587 + 0.201021i \(0.0644260\pi\)
−0.979587 + 0.201021i \(0.935574\pi\)
\(740\) 513550. + 770927.i 0.0344749 + 0.0517528i
\(741\) 2.03694e6 566955.i 0.136280 0.0379318i
\(742\) −551602. + 166903.i −0.0367804 + 0.0111290i
\(743\) −1.80015e7 −1.19629 −0.598145 0.801388i \(-0.704095\pi\)
−0.598145 + 0.801388i \(0.704095\pi\)
\(744\) −5.33182e6 + 1.20081e7i −0.353137 + 0.795322i
\(745\) 1.87467e6 0.123747
\(746\) 2.51521e6 761048.i 0.165473 0.0500686i
\(747\) 2.08940e6 1.26079e6i 0.137000 0.0826684i
\(748\) 9.24072e6 + 1.38719e7i 0.603882 + 0.906531i
\(749\) 8.36273e6i 0.544683i
\(750\) 4.91904e6 3.12034e6i 0.319321 0.202558i
\(751\) 2.58444e7i 1.67212i 0.548640 + 0.836059i \(0.315146\pi\)
−0.548640 + 0.836059i \(0.684854\pi\)
\(752\) 9.32911e6 2.23444e7i 0.601583 1.44087i
\(753\) 2.92496e6 + 1.05087e7i 0.187989 + 0.675400i
\(754\) 2.35718e6 + 7.79029e6i 0.150995 + 0.499029i
\(755\) −2.87714e7 −1.83693
\(756\) −1.05503e6 + 6.19227e6i −0.0671366 + 0.394045i
\(757\) −1.03124e7 −0.654064 −0.327032 0.945013i \(-0.606049\pi\)
−0.327032 + 0.945013i \(0.606049\pi\)
\(758\) −4.61643e6 1.52569e7i −0.291832 0.964483i
\(759\) −3.76060e6 1.35110e7i −0.236948 0.851300i
\(760\) −2.69235e6 + 3.26656e6i −0.169082 + 0.205143i
\(761\) 1.62986e7i 1.02021i −0.860112 0.510104i \(-0.829607\pi\)
0.860112 0.510104i \(-0.170393\pi\)
\(762\) −1.77447e6 + 1.12562e6i −0.110709 + 0.0702268i
\(763\) 64242.1i 0.00399492i
\(764\) 1.27048e7 8.46327e6i 0.787473 0.524572i
\(765\) −2.13241e7 + 1.28674e7i −1.31740 + 0.794947i
\(766\) 9.90541e6 2.99717e6i 0.609959 0.184561i
\(767\) 3.33434e6 0.204655
\(768\) −8.11560e6 + 1.41887e7i −0.496498 + 0.868038i
\(769\) 7.98701e6 0.487044 0.243522 0.969895i \(-0.421697\pi\)
0.243522 + 0.969895i \(0.421697\pi\)
\(770\) 7.62383e6 2.30681e6i 0.463390 0.140212i
\(771\) 1.14448e7 3.18550e6i 0.693380 0.192993i
\(772\) −2.01703e7 + 1.34364e7i −1.21806 + 0.811406i
\(773\) 3.08377e7i 1.85624i 0.372283 + 0.928119i \(0.378575\pi\)
−0.372283 + 0.928119i \(0.621425\pi\)
\(774\) −1.67234e7 1.50883e7i −1.00340 0.905292i
\(775\) 1.03438e7i 0.618622i
\(776\) −2.57306e6 + 3.12183e6i −0.153390 + 0.186104i
\(777\) 308090. 85752.6i 0.0183073 0.00509559i
\(778\) 6611.33 + 21849.9i 0.000391597 + 0.00129420i
\(779\) 1.84873e6 0.109152
\(780\) 1.01032e7 1.17143e7i 0.594598 0.689413i
\(781\) 7.56495e6 0.443791
\(782\) 5.55970e6 + 1.83744e7i 0.325113 + 1.07448i
\(783\) −8.81959e6 + 9.34654e6i −0.514096 + 0.544812i
\(784\) 5.57137e6 1.33442e7i 0.323722 0.775356i
\(785\) 3.39048e7i 1.96375i
\(786\) −1.63710e7 2.58079e7i −0.945188 1.49004i
\(787\) 2.96941e6i 0.170897i −0.996343 0.0854483i \(-0.972768\pi\)
0.996343 0.0854483i \(-0.0272322\pi\)
\(788\) −1.68326e7 2.52687e7i −0.965686 1.44966i
\(789\) −5.84391e6 2.09958e7i −0.334203 1.20072i
\(790\) 2.54385e7 7.69715e6i 1.45019 0.438796i
\(791\) −8.12078e6 −0.461484
\(792\) 2.38455e6 1.61711e7i 0.135080 0.916065i
\(793\) −3.96994e6 −0.224182
\(794\) −1.28457e7 + 3.88685e6i −0.723115 + 0.218799i
\(795\) 600865. + 2.15877e6i 0.0337178 + 0.121140i
\(796\) 3.92495e6 + 5.89203e6i 0.219559 + 0.329596i
\(797\) 6.95811e6i 0.388012i 0.981000 + 0.194006i \(0.0621482\pi\)
−0.981000 + 0.194006i \(0.937852\pi\)
\(798\) 782830. + 1.23409e6i 0.0435171 + 0.0686023i
\(799\) 3.31448e7i 1.83674i
\(800\) −1.30638e6 + 1.28022e7i −0.0721680 + 0.707227i
\(801\) 7.11074e6 + 1.17840e7i 0.391592 + 0.648953i
\(802\) 6.64860e6 + 2.19731e7i 0.365001 + 1.20630i
\(803\) 2.30701e7 1.26258
\(804\) 1.23417e7 1.43097e7i 0.673339 0.780710i
\(805\) 9.17380e6 0.498953
\(806\) −3.23514e6 1.06919e7i −0.175410 0.579718i
\(807\) −1.52559e7 + 4.24627e6i −0.824619 + 0.229522i
\(808\) −6.76415e6 5.57512e6i −0.364489 0.300418i
\(809\) 6.18442e6i 0.332221i −0.986107 0.166111i \(-0.946879\pi\)
0.986107 0.166111i \(-0.0531209\pi\)
\(810\) 2.39798e7 + 4.63946e6i 1.28420 + 0.248459i
\(811\) 381738.i 0.0203804i −0.999948 0.0101902i \(-0.996756\pi\)
0.999948 0.0101902i \(-0.00324370\pi\)
\(812\) −4.68198e6 + 3.11888e6i −0.249195 + 0.166000i
\(813\) −1.59968e7 + 4.45250e6i −0.848803 + 0.236253i
\(814\) −796533. + 241014.i −0.0421350 + 0.0127491i
\(815\) 2.69861e7 1.42314
\(816\) −2.76840e6 + 2.22027e7i −0.145547 + 1.16730i
\(817\) −5.24036e6 −0.274667
\(818\) 1.99537e7 6.03758e6i 1.04266 0.315486i
\(819\) −2.75922e6 4.57263e6i −0.143740 0.238208i
\(820\) 1.12569e7 7.49872e6i 0.584633 0.389451i
\(821\) 7.63930e6i 0.395545i −0.980248 0.197772i \(-0.936629\pi\)
0.980248 0.197772i \(-0.0633707\pi\)
\(822\) −1.35753e7 + 8.61133e6i −0.700760 + 0.444519i
\(823\) 1.36924e7i 0.704661i 0.935876 + 0.352330i \(0.114611\pi\)
−0.935876 + 0.352330i \(0.885389\pi\)
\(824\) 2.12610e7 + 1.75237e7i 1.09085 + 0.899099i
\(825\) −3.45071e6 1.23976e7i −0.176512 0.634166i
\(826\) 667460. + 2.20590e6i 0.0340388 + 0.112496i
\(827\) −1.85056e7 −0.940891 −0.470445 0.882429i \(-0.655907\pi\)
−0.470445 + 0.882429i \(0.655907\pi\)
\(828\) 8.02264e6 1.70313e7i 0.406669 0.863320i
\(829\) 3.00466e7 1.51848 0.759241 0.650810i \(-0.225571\pi\)
0.759241 + 0.650810i \(0.225571\pi\)
\(830\) −1.20301e6 3.97585e6i −0.0606140 0.200325i
\(831\) −4.59685e6 1.65154e7i −0.230918 0.829635i
\(832\) −2.65368e6 1.36416e7i −0.132905 0.683214i
\(833\) 1.97942e7i 0.988382i
\(834\) −4.80049e6 + 3.04514e6i −0.238985 + 0.151597i
\(835\) 1.29882e6i 0.0644664i
\(836\) −2.10838e6 3.16505e6i −0.104336 0.156626i
\(837\) 1.21046e7 1.28278e7i 0.597222 0.632904i
\(838\) −2.16450e7 + 6.54933e6i −1.06475 + 0.322171i
\(839\) 2.67597e7 1.31243 0.656215 0.754574i \(-0.272157\pi\)
0.656215 + 0.754574i \(0.272157\pi\)
\(840\) 9.77227e6 + 4.33906e6i 0.477856 + 0.212177i
\(841\) 9.00205e6 0.438886
\(842\) −3.77590e7 + 1.14251e7i −1.83544 + 0.555366i
\(843\) −2.59857e7 + 7.23276e6i −1.25940 + 0.350538i
\(844\) −1.18984e7 1.78616e7i −0.574955 0.863107i
\(845\) 1.39968e7i 0.674353i
\(846\) −2.17740e7 + 2.41337e7i −1.04596 + 1.15930i
\(847\) 1.18992e6i 0.0569916i
\(848\) 1.85770e6 + 775616.i 0.0887129 + 0.0370388i
\(849\) 1.18194e7 3.28977e6i 0.562764 0.156638i
\(850\) 5.10155e6 + 1.68603e7i 0.242189 + 0.800418i
\(851\) −958472. −0.0453686
\(852\) 7.68998e6 + 6.63237e6i 0.362933 + 0.313018i
\(853\) −2.58364e7 −1.21579 −0.607896 0.794016i \(-0.707986\pi\)
−0.607896 + 0.794016i \(0.707986\pi\)
\(854\) −794692. 2.62640e6i −0.0372867 0.123230i
\(855\) 4.86536e6 2.93586e6i 0.227614 0.137347i
\(856\) −1.85798e7 + 2.25424e7i −0.866677 + 1.05152i
\(857\) 3.41755e6i 0.158951i 0.996837 + 0.0794755i \(0.0253245\pi\)
−0.996837 + 0.0794755i \(0.974675\pi\)
\(858\) 7.44433e6 + 1.17356e7i 0.345229 + 0.544234i
\(859\) 3.12572e7i 1.44533i 0.691199 + 0.722664i \(0.257083\pi\)
−0.691199 + 0.722664i \(0.742917\pi\)
\(860\) −3.19084e7 + 2.12557e7i −1.47116 + 0.980006i
\(861\) −1.25214e6 4.49864e6i −0.0575631 0.206811i
\(862\) 2.12375e7 6.42601e6i 0.973498 0.294560i
\(863\) −613502. −0.0280407 −0.0140204 0.999902i \(-0.504463\pi\)
−0.0140204 + 0.999902i \(0.504463\pi\)
\(864\) 1.66015e7 1.43478e7i 0.756596 0.653883i
\(865\) −5.26947e7 −2.39457
\(866\) −2.45735e7 + 7.43540e6i −1.11345 + 0.336907i
\(867\) 2.27762e6 + 8.18296e6i 0.102904 + 0.369711i
\(868\) 6.42584e6 4.28055e6i 0.289488 0.192841i
\(869\) 2.38771e7i 1.07258i
\(870\) 1.17172e7 + 1.84715e7i 0.524838 + 0.827379i
\(871\) 1.60662e7i 0.717575i
\(872\) 142729. 173170.i 0.00635655 0.00771224i
\(873\) 4.64978e6 2.80578e6i 0.206489 0.124600i
\(874\) −1.26851e6 4.19234e6i −0.0561716 0.185643i
\(875\) −3.42327e6 −0.151154
\(876\) 2.34513e7 + 2.02261e7i 1.03254 + 0.890535i
\(877\) 2.66479e7 1.16994 0.584971 0.811054i \(-0.301106\pi\)
0.584971 + 0.811054i \(0.301106\pi\)
\(878\) −7.10616e6 2.34853e7i −0.311099 1.02816i
\(879\) 9.29561e6 2.58731e6i 0.405794 0.112947i
\(880\) −2.56758e7 1.07200e7i −1.11768 0.466646i
\(881\) 4.32956e7i 1.87933i −0.342092 0.939667i \(-0.611135\pi\)
0.342092 0.939667i \(-0.388865\pi\)
\(882\) −1.30035e7 + 1.44127e7i −0.562846 + 0.623840i
\(883\) 1.40501e7i 0.606424i −0.952923 0.303212i \(-0.901941\pi\)
0.952923 0.303212i \(-0.0980590\pi\)
\(884\) −1.05465e7 1.58321e7i −0.453917 0.681409i
\(885\) 8.63311e6 2.40291e6i 0.370518 0.103129i
\(886\) 1.38167e7 4.18063e6i 0.591315 0.178919i
\(887\) 2.40151e7 1.02489 0.512444 0.858721i \(-0.328740\pi\)
0.512444 + 0.858721i \(0.328740\pi\)
\(888\) −1.02100e6 453342.i −0.0434503 0.0192927i
\(889\) 1.23489e6 0.0524053
\(890\) 2.24235e7 6.78488e6i 0.948918 0.287122i
\(891\) −1.02286e7 + 1.94129e7i −0.431641 + 0.819212i
\(892\) −2.15350e7 3.23278e7i −0.906219 1.36039i
\(893\) 7.56239e6i 0.317344i
\(894\) −1.90911e6 + 1.21103e6i −0.0798892 + 0.0506768i
\(895\) 5.97708e7i 2.49420i
\(896\) 8.49367e6 4.48633e6i 0.353448 0.186690i
\(897\) 4.29199e6 + 1.54201e7i 0.178106 + 0.639893i
\(898\) −2.62572e6 8.67782e6i −0.108657 0.359104i
\(899\) 1.57958e7 0.651843
\(900\) 7.36153e6 1.56278e7i 0.302944 0.643120i
\(901\) 2.75564e6 0.113086
\(902\) 3.51922e6 + 1.16308e7i 0.144022 + 0.475983i
\(903\) 3.54927e6 + 1.27517e7i 0.144851 + 0.520415i
\(904\) 2.18902e7 + 1.80423e7i 0.890899 + 0.734294i
\(905\) 2.84712e7i 1.15554i
\(906\) 2.93000e7 1.85861e7i 1.18590 0.752261i
\(907\) 1.74069e7i 0.702592i 0.936264 + 0.351296i \(0.114259\pi\)
−0.936264 + 0.351296i \(0.885741\pi\)
\(908\) 2.13118e7 1.41968e7i 0.857840 0.571447i
\(909\) 6.07935e6 + 1.00748e7i 0.244033 + 0.404415i
\(910\) −8.70112e6 + 2.63277e6i −0.348314 + 0.105393i
\(911\) −2.35129e7 −0.938666 −0.469333 0.883021i \(-0.655506\pi\)
−0.469333 + 0.883021i \(0.655506\pi\)
\(912\) 631643. 5.06583e6i 0.0251469 0.201680i
\(913\) 3.73181e6 0.148164
\(914\) 2.50211e7 7.57086e6i 0.990698 0.299764i
\(915\) −1.02788e7 + 2.86096e6i −0.405871 + 0.112969i
\(916\) −2.49803e7 + 1.66405e7i −0.983691 + 0.655282i
\(917\) 1.79603e7i 0.705327i
\(918\) 1.34036e7 2.68791e7i 0.524948 1.05271i
\(919\) 3.60463e7i 1.40790i −0.710249 0.703951i \(-0.751418\pi\)
0.710249 0.703951i \(-0.248582\pi\)
\(920\) −2.47287e7 2.03818e7i −0.963234 0.793913i
\(921\) −1.11763e7 + 3.11077e6i −0.434158 + 0.120842i
\(922\) 2.97994e6 + 9.84848e6i 0.115446 + 0.381542i
\(923\) −8.63391e6 −0.333583
\(924\) −6.27373e6 + 7.27414e6i −0.241738 + 0.280286i
\(925\) −879489. −0.0337968
\(926\) 6.66647e6 + 2.20322e7i 0.255487 + 0.844365i
\(927\) −1.91086e7 3.16671e7i −0.730347 1.21034i
\(928\) 1.95500e7 + 1.99495e6i 0.745206 + 0.0760436i
\(929\) 5.62572e6i 0.213865i 0.994266 + 0.106932i \(0.0341028\pi\)
−0.994266 + 0.106932i \(0.965897\pi\)
\(930\) −1.60814e7 2.53515e7i −0.609701 0.961160i
\(931\) 4.51628e6i 0.170768i
\(932\) 1.64259e7 + 2.46581e7i 0.619425 + 0.929864i
\(933\) 713021. + 2.56172e6i 0.0268163 + 0.0963447i
\(934\) 2.42493e7 7.33732e6i 0.909562 0.275214i
\(935\) −3.80864e7 −1.42476
\(936\) −2.72149e6 + 1.84561e7i −0.101535 + 0.688575i
\(937\) 3.98187e6 0.148162 0.0740812 0.997252i \(-0.476398\pi\)
0.0740812 + 0.997252i \(0.476398\pi\)
\(938\) −1.06289e7 + 3.21608e6i −0.394441 + 0.119349i
\(939\) 3.22992e6 + 1.16044e7i 0.119544 + 0.429494i
\(940\) 3.06742e7 + 4.60472e7i 1.13228 + 1.69974i
\(941\) 1.59581e7i 0.587499i 0.955882 + 0.293750i \(0.0949032\pi\)
−0.955882 + 0.293750i \(0.905097\pi\)
\(942\) −2.19023e7 3.45278e7i −0.804197 1.26777i
\(943\) 1.39954e7i 0.512513i
\(944\) 3.10176e6 7.42911e6i 0.113286 0.271336i
\(945\) −1.04393e7 9.85076e6i −0.380270 0.358831i
\(946\) −9.97549e6 3.29682e7i −0.362415 1.19775i
\(947\) 2.11747e7 0.767259 0.383629 0.923487i \(-0.374674\pi\)
0.383629 + 0.923487i \(0.374674\pi\)
\(948\) −2.09336e7 + 2.42717e7i −0.756524 + 0.877161i
\(949\) −2.63300e7 −0.949041
\(950\) −1.16398e6 3.84687e6i −0.0418444 0.138293i
\(951\) 2.55220e7 7.10370e6i 0.915088 0.254703i
\(952\) 8.36288e6 1.01465e7i 0.299064 0.362846i
\(953\) 3.38151e7i 1.20609i 0.797708 + 0.603044i \(0.206046\pi\)
−0.797708 + 0.603044i \(0.793954\pi\)
\(954\) −2.00646e6 1.81028e6i −0.0713771 0.0643984i
\(955\) 3.48821e7i 1.23764i
\(956\) 1.65029e7 1.09933e7i 0.584002 0.389030i
\(957\) −1.89322e7 + 5.26951e6i −0.668221 + 0.185990i
\(958\) −2.68016e7 + 8.10960e6i −0.943512 + 0.285487i
\(959\) 9.44733e6 0.331713
\(960\) −1.67017e7 3.34077e7i −0.584900 1.16995i
\(961\) 6.94995e6 0.242758
\(962\) 909087. 275070.i 0.0316714 0.00958310i
\(963\) 3.35756e7 2.02602e7i 1.16670 0.704010i
\(964\) 1.04769e6 697915.i 0.0363112 0.0241885i
\(965\) 5.53791e7i 1.91438i
\(966\) −9.34236e6 + 5.92622e6i −0.322117 + 0.204331i
\(967\) 4.65695e7i 1.60153i 0.598977 + 0.800766i \(0.295574\pi\)
−0.598977 + 0.800766i \(0.704426\pi\)
\(968\) −2.64370e6 + 3.20753e6i −0.0906826 + 0.110023i
\(969\) −1.87379e6 6.73211e6i −0.0641080 0.230325i
\(970\) −2.67720e6 8.84794e6i −0.0913590 0.301935i
\(971\) −2.54579e7 −0.866512 −0.433256 0.901271i \(-0.642635\pi\)
−0.433256 + 0.901271i \(0.642635\pi\)
\(972\) −2.74174e7 + 1.07661e7i −0.930810 + 0.365504i
\(973\) 3.34076e6 0.113126
\(974\) −5.90682e6 1.95216e7i −0.199506 0.659353i
\(975\) 3.93831e6 + 1.41494e7i 0.132678 + 0.476681i
\(976\) −3.69302e6 + 8.84526e6i −0.124096 + 0.297226i
\(977\) 1.14688e7i 0.384399i −0.981356 0.192200i \(-0.938438\pi\)
0.981356 0.192200i \(-0.0615621\pi\)
\(978\) −2.74820e7 + 1.74329e7i −0.918757 + 0.582803i
\(979\) 2.10471e7i 0.701837i
\(980\) 1.83187e7 + 2.74995e7i 0.609297 + 0.914660i
\(981\) −257926. + 155638.i −0.00855703 + 0.00516349i
\(982\) −1.49519e7 + 4.52411e6i −0.494785 + 0.149711i
\(983\) −1.13955e7 −0.376139 −0.188070 0.982156i \(-0.560223\pi\)
−0.188070 + 0.982156i \(0.560223\pi\)
\(984\) −6.61958e6 + 1.49084e7i −0.217943 + 0.490843i
\(985\) 6.93770e7 2.27837
\(986\) 2.57470e7 7.79049e6i 0.843401 0.255195i
\(987\) 1.84021e7 5.12197e6i 0.601276 0.167357i
\(988\) 2.40631e6 + 3.61228e6i 0.0784257 + 0.117731i
\(989\) 3.96709e7i 1.28968i
\(990\) 2.77318e7 + 2.50203e7i 0.899269 + 0.811344i
\(991\) 4.64763e7i 1.50331i −0.659558 0.751653i \(-0.729257\pi\)
0.659558 0.751653i \(-0.270743\pi\)
\(992\) −2.68316e7 2.73800e6i −0.865701 0.0883393i
\(993\) −347976. + 96854.5i −0.0111989 + 0.00311707i
\(994\) −1.72831e6 5.71194e6i −0.0554825 0.183366i
\(995\) −1.61770e7 −0.518013
\(996\) 3.79349e6 + 3.27176e6i 0.121169 + 0.104504i
\(997\) −2.78641e7 −0.887782 −0.443891 0.896081i \(-0.646402\pi\)
−0.443891 + 0.896081i \(0.646402\pi\)
\(998\) 1.77050e7 + 5.85137e7i 0.562691 + 1.85965i
\(999\) 1.09069e6 + 1.02920e6i 0.0345771 + 0.0326277i
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 12.6.b.a.11.7 yes 8
3.2 odd 2 inner 12.6.b.a.11.2 yes 8
4.3 odd 2 inner 12.6.b.a.11.1 8
8.3 odd 2 192.6.c.e.191.3 8
8.5 even 2 192.6.c.e.191.6 8
12.11 even 2 inner 12.6.b.a.11.8 yes 8
24.5 odd 2 192.6.c.e.191.4 8
24.11 even 2 192.6.c.e.191.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
12.6.b.a.11.1 8 4.3 odd 2 inner
12.6.b.a.11.2 yes 8 3.2 odd 2 inner
12.6.b.a.11.7 yes 8 1.1 even 1 trivial
12.6.b.a.11.8 yes 8 12.11 even 2 inner
192.6.c.e.191.3 8 8.3 odd 2
192.6.c.e.191.4 8 24.5 odd 2
192.6.c.e.191.5 8 24.11 even 2
192.6.c.e.191.6 8 8.5 even 2