Properties

Label 63.6.e.f.46.1
Level $63$
Weight $6$
Character 63.46
Analytic conductor $10.104$
Analytic rank $0$
Dimension $12$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,6,Mod(37,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.37");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.1041806482\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.1
Root \(-5.31117 - 9.19921i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.6.e.f.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.31117 - 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(33.7376 + 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} +518.731 q^{8} +O(q^{10})\) \(q+(-5.31117 - 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(33.7376 + 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} +518.731 q^{8} +(358.372 - 620.718i) q^{10} +(261.323 - 452.625i) q^{11} +76.6331 q^{13} +(193.887 + 1363.38i) q^{14} +(-1461.72 - 2531.78i) q^{16} +(634.801 - 1099.51i) q^{17} +(946.362 + 1639.15i) q^{19} -5454.28 q^{20} -5551.73 q^{22} +(-575.022 - 995.967i) q^{23} +(-713.945 + 1236.59i) q^{25} +(-407.011 - 704.964i) q^{26} +(8247.36 - 6465.31i) q^{28} +3850.03 q^{29} +(5206.86 - 9018.55i) q^{31} +(-7227.21 + 12517.9i) q^{32} -13486.1 q^{34} +(-1231.60 - 8660.46i) q^{35} +(2801.14 + 4851.71i) q^{37} +(10052.6 - 17411.6i) q^{38} +(17500.7 + 30312.1i) q^{40} +14232.7 q^{41} -14827.9 q^{43} +(21123.8 + 36587.5i) q^{44} +(-6108.08 + 10579.5i) q^{46} +(-5774.88 - 10002.4i) q^{47} +(12128.1 + 11635.5i) q^{49} +15167.5 q^{50} +(-3097.28 + 5364.64i) q^{52} +(-2338.86 + 4051.02i) q^{53} +35265.6 q^{55} +(-62393.5 - 25089.9i) q^{56} +(-20448.2 - 35417.3i) q^{58} +(14551.0 - 25203.0i) q^{59} +(-5921.45 - 10256.2i) q^{61} -110618. q^{62} +59989.5 q^{64} +(2585.41 + 4478.06i) q^{65} +(18106.3 - 31361.0i) q^{67} +(51313.5 + 88877.6i) q^{68} +(-73128.1 + 57326.9i) q^{70} +13477.6 q^{71} +(-1304.23 + 2258.98i) q^{73} +(29754.6 - 51536.5i) q^{74} -152996. q^{76} +(-53324.8 + 41802.6i) q^{77} +(39160.2 + 67827.4i) q^{79} +(98629.9 - 170832. i) q^{80} +(-75592.3 - 130930. i) q^{82} -16746.0 q^{83} +85666.5 q^{85} +(78753.5 + 136405. i) q^{86} +(135557. - 234791. i) q^{88} +(18384.2 + 31842.4i) q^{89} +(-9217.51 - 3706.58i) q^{91} +92962.7 q^{92} +(-61342.7 + 106249. i) q^{94} +(-63855.9 + 110602. i) q^{95} +36133.4 q^{97} +(42623.0 - 173367. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.31117 9.19921i −0.938891 1.62621i −0.767545 0.640995i \(-0.778522\pi\)
−0.171346 0.985211i \(-0.554811\pi\)
\(3\) 0 0
\(4\) −40.4170 + 70.0043i −1.26303 + 2.18763i
\(5\) 33.7376 + 58.4352i 0.603516 + 1.04532i 0.992284 + 0.123984i \(0.0395673\pi\)
−0.388769 + 0.921335i \(0.627099\pi\)
\(6\) 0 0
\(7\) −120.281 48.3679i −0.927796 0.373089i
\(8\) 518.731 2.86561
\(9\) 0 0
\(10\) 358.372 620.718i 1.13327 1.96288i
\(11\) 261.323 452.625i 0.651173 1.12787i −0.331665 0.943397i \(-0.607610\pi\)
0.982839 0.184468i \(-0.0590562\pi\)
\(12\) 0 0
\(13\) 76.6331 0.125764 0.0628822 0.998021i \(-0.479971\pi\)
0.0628822 + 0.998021i \(0.479971\pi\)
\(14\) 193.887 + 1363.38i 0.264379 + 1.85908i
\(15\) 0 0
\(16\) −1461.72 2531.78i −1.42746 2.47244i
\(17\) 634.801 1099.51i 0.532740 0.922733i −0.466529 0.884506i \(-0.654496\pi\)
0.999269 0.0382267i \(-0.0121709\pi\)
\(18\) 0 0
\(19\) 946.362 + 1639.15i 0.601414 + 1.04168i 0.992607 + 0.121371i \(0.0387290\pi\)
−0.391193 + 0.920309i \(0.627938\pi\)
\(20\) −5454.28 −3.04904
\(21\) 0 0
\(22\) −5551.73 −2.44552
\(23\) −575.022 995.967i −0.226655 0.392578i 0.730160 0.683276i \(-0.239446\pi\)
−0.956815 + 0.290699i \(0.906112\pi\)
\(24\) 0 0
\(25\) −713.945 + 1236.59i −0.228462 + 0.395708i
\(26\) −407.011 704.964i −0.118079 0.204519i
\(27\) 0 0
\(28\) 8247.36 6465.31i 1.98802 1.55845i
\(29\) 3850.03 0.850099 0.425049 0.905170i \(-0.360257\pi\)
0.425049 + 0.905170i \(0.360257\pi\)
\(30\) 0 0
\(31\) 5206.86 9018.55i 0.973132 1.68551i 0.287165 0.957881i \(-0.407287\pi\)
0.685967 0.727633i \(-0.259379\pi\)
\(32\) −7227.21 + 12517.9i −1.24766 + 2.16101i
\(33\) 0 0
\(34\) −13486.1 −2.00074
\(35\) −1231.60 8660.46i −0.169942 1.19501i
\(36\) 0 0
\(37\) 2801.14 + 4851.71i 0.336380 + 0.582627i 0.983749 0.179550i \(-0.0574641\pi\)
−0.647369 + 0.762177i \(0.724131\pi\)
\(38\) 10052.6 17411.6i 1.12932 1.95605i
\(39\) 0 0
\(40\) 17500.7 + 30312.1i 1.72944 + 2.99548i
\(41\) 14232.7 1.32229 0.661147 0.750256i \(-0.270070\pi\)
0.661147 + 0.750256i \(0.270070\pi\)
\(42\) 0 0
\(43\) −14827.9 −1.22295 −0.611475 0.791264i \(-0.709424\pi\)
−0.611475 + 0.791264i \(0.709424\pi\)
\(44\) 21123.8 + 36587.5i 1.64490 + 2.84906i
\(45\) 0 0
\(46\) −6108.08 + 10579.5i −0.425608 + 0.737175i
\(47\) −5774.88 10002.4i −0.381328 0.660479i 0.609925 0.792459i \(-0.291200\pi\)
−0.991252 + 0.131981i \(0.957866\pi\)
\(48\) 0 0
\(49\) 12128.1 + 11635.5i 0.721610 + 0.692300i
\(50\) 15167.5 0.858004
\(51\) 0 0
\(52\) −3097.28 + 5364.64i −0.158844 + 0.275127i
\(53\) −2338.86 + 4051.02i −0.114371 + 0.198096i −0.917528 0.397671i \(-0.869818\pi\)
0.803157 + 0.595767i \(0.203152\pi\)
\(54\) 0 0
\(55\) 35265.6 1.57197
\(56\) −62393.5 25089.9i −2.65870 1.06913i
\(57\) 0 0
\(58\) −20448.2 35417.3i −0.798150 1.38244i
\(59\) 14551.0 25203.0i 0.544205 0.942590i −0.454452 0.890771i \(-0.650165\pi\)
0.998656 0.0518189i \(-0.0165019\pi\)
\(60\) 0 0
\(61\) −5921.45 10256.2i −0.203753 0.352910i 0.745982 0.665966i \(-0.231980\pi\)
−0.949735 + 0.313056i \(0.898647\pi\)
\(62\) −110618. −3.65466
\(63\) 0 0
\(64\) 59989.5 1.83073
\(65\) 2585.41 + 4478.06i 0.0759008 + 0.131464i
\(66\) 0 0
\(67\) 18106.3 31361.0i 0.492768 0.853499i −0.507197 0.861830i \(-0.669319\pi\)
0.999965 + 0.00833093i \(0.00265185\pi\)
\(68\) 51313.5 + 88877.6i 1.34573 + 2.33088i
\(69\) 0 0
\(70\) −73128.1 + 57326.9i −1.78377 + 1.39834i
\(71\) 13477.6 0.317298 0.158649 0.987335i \(-0.449286\pi\)
0.158649 + 0.987335i \(0.449286\pi\)
\(72\) 0 0
\(73\) −1304.23 + 2258.98i −0.0286448 + 0.0496142i −0.879992 0.474988i \(-0.842452\pi\)
0.851348 + 0.524602i \(0.175786\pi\)
\(74\) 29754.6 51536.5i 0.631648 1.09405i
\(75\) 0 0
\(76\) −152996. −3.03842
\(77\) −53324.8 + 41802.6i −1.02495 + 0.803483i
\(78\) 0 0
\(79\) 39160.2 + 67827.4i 0.705955 + 1.22275i 0.966346 + 0.257246i \(0.0828151\pi\)
−0.260391 + 0.965503i \(0.583852\pi\)
\(80\) 98629.9 170832.i 1.72299 2.98431i
\(81\) 0 0
\(82\) −75592.3 130930.i −1.24149 2.15032i
\(83\) −16746.0 −0.266819 −0.133410 0.991061i \(-0.542593\pi\)
−0.133410 + 0.991061i \(0.542593\pi\)
\(84\) 0 0
\(85\) 85666.5 1.28607
\(86\) 78753.5 + 136405.i 1.14822 + 1.98877i
\(87\) 0 0
\(88\) 135557. 234791.i 1.86601 3.23202i
\(89\) 18384.2 + 31842.4i 0.246020 + 0.426119i 0.962418 0.271573i \(-0.0875437\pi\)
−0.716398 + 0.697692i \(0.754210\pi\)
\(90\) 0 0
\(91\) −9217.51 3706.58i −0.116684 0.0469213i
\(92\) 92962.7 1.14509
\(93\) 0 0
\(94\) −61342.7 + 106249.i −0.716050 + 1.24023i
\(95\) −63855.9 + 110602.i −0.725925 + 1.25734i
\(96\) 0 0
\(97\) 36133.4 0.389924 0.194962 0.980811i \(-0.437542\pi\)
0.194962 + 0.980811i \(0.437542\pi\)
\(98\) 42623.0 173367.i 0.448310 1.82348i
\(99\) 0 0
\(100\) −57711.0 99958.4i −0.577110 0.999584i
\(101\) −49337.6 + 85455.2i −0.481254 + 0.833557i −0.999769 0.0215120i \(-0.993152\pi\)
0.518514 + 0.855069i \(0.326485\pi\)
\(102\) 0 0
\(103\) −3636.75 6299.03i −0.0337769 0.0585034i 0.848643 0.528966i \(-0.177420\pi\)
−0.882420 + 0.470463i \(0.844087\pi\)
\(104\) 39751.9 0.360392
\(105\) 0 0
\(106\) 49688.3 0.429526
\(107\) −15476.8 26806.5i −0.130683 0.226350i 0.793257 0.608887i \(-0.208384\pi\)
−0.923940 + 0.382537i \(0.875050\pi\)
\(108\) 0 0
\(109\) −56915.6 + 98580.8i −0.458844 + 0.794742i −0.998900 0.0468875i \(-0.985070\pi\)
0.540056 + 0.841629i \(0.318403\pi\)
\(110\) −187302. 324416.i −1.47591 2.55635i
\(111\) 0 0
\(112\) 53360.9 + 375226.i 0.401955 + 2.82649i
\(113\) 894.559 0.00659041 0.00329521 0.999995i \(-0.498951\pi\)
0.00329521 + 0.999995i \(0.498951\pi\)
\(114\) 0 0
\(115\) 38799.7 67203.0i 0.273579 0.473854i
\(116\) −155607. + 269519.i −1.07370 + 1.85970i
\(117\) 0 0
\(118\) −309131. −2.04379
\(119\) −129535. + 101546.i −0.838535 + 0.657348i
\(120\) 0 0
\(121\) −56054.3 97088.9i −0.348053 0.602846i
\(122\) −62899.6 + 108945.i −0.382603 + 0.662687i
\(123\) 0 0
\(124\) 420891. + 729005.i 2.45819 + 4.25771i
\(125\) 114513. 0.655509
\(126\) 0 0
\(127\) 72325.9 0.397910 0.198955 0.980009i \(-0.436245\pi\)
0.198955 + 0.980009i \(0.436245\pi\)
\(128\) −87343.4 151283.i −0.471200 0.816142i
\(129\) 0 0
\(130\) 27463.1 47567.5i 0.142525 0.246861i
\(131\) −35084.0 60767.3i −0.178620 0.309380i 0.762788 0.646649i \(-0.223830\pi\)
−0.941408 + 0.337269i \(0.890497\pi\)
\(132\) 0 0
\(133\) −34547.4 242932.i −0.169350 1.19085i
\(134\) −384662. −1.85062
\(135\) 0 0
\(136\) 329291. 570348.i 1.52662 2.64419i
\(137\) 186004. 322169.i 0.846685 1.46650i −0.0374656 0.999298i \(-0.511928\pi\)
0.884150 0.467203i \(-0.154738\pi\)
\(138\) 0 0
\(139\) 5566.26 0.0244358 0.0122179 0.999925i \(-0.496111\pi\)
0.0122179 + 0.999925i \(0.496111\pi\)
\(140\) 656047. + 263812.i 2.82888 + 1.13756i
\(141\) 0 0
\(142\) −71581.9 123984.i −0.297908 0.515992i
\(143\) 20026.0 34686.1i 0.0818944 0.141845i
\(144\) 0 0
\(145\) 129891. + 224977.i 0.513048 + 0.888625i
\(146\) 27707.8 0.107577
\(147\) 0 0
\(148\) −452854. −1.69943
\(149\) −166957. 289178.i −0.616083 1.06709i −0.990193 0.139703i \(-0.955385\pi\)
0.374110 0.927384i \(-0.377948\pi\)
\(150\) 0 0
\(151\) −37578.6 + 65088.1i −0.134122 + 0.232305i −0.925262 0.379330i \(-0.876155\pi\)
0.791140 + 0.611635i \(0.209488\pi\)
\(152\) 490907. + 850277.i 1.72342 + 2.98505i
\(153\) 0 0
\(154\) 667768. + 268525.i 2.26894 + 0.912396i
\(155\) 702667. 2.34920
\(156\) 0 0
\(157\) −237792. + 411868.i −0.769926 + 1.33355i 0.167677 + 0.985842i \(0.446373\pi\)
−0.937603 + 0.347708i \(0.886960\pi\)
\(158\) 415972. 720485.i 1.32563 2.29606i
\(159\) 0 0
\(160\) −975314. −3.01193
\(161\) 20991.4 + 147609.i 0.0638231 + 0.448794i
\(162\) 0 0
\(163\) −119611. 207173.i −0.352617 0.610751i 0.634090 0.773259i \(-0.281375\pi\)
−0.986707 + 0.162508i \(0.948042\pi\)
\(164\) −575243. + 996351.i −1.67010 + 2.89270i
\(165\) 0 0
\(166\) 88941.0 + 154050.i 0.250514 + 0.433903i
\(167\) 111308. 0.308842 0.154421 0.988005i \(-0.450649\pi\)
0.154421 + 0.988005i \(0.450649\pi\)
\(168\) 0 0
\(169\) −365420. −0.984183
\(170\) −454989. 788064.i −1.20748 2.09141i
\(171\) 0 0
\(172\) 599299. 1.03802e6i 1.54462 2.67537i
\(173\) −349497. 605346.i −0.887826 1.53776i −0.842440 0.538791i \(-0.818881\pi\)
−0.0453864 0.998970i \(-0.514452\pi\)
\(174\) 0 0
\(175\) 145685. 114206.i 0.359601 0.281900i
\(176\) −1.52793e6 −3.71810
\(177\) 0 0
\(178\) 195284. 338241.i 0.461972 0.800159i
\(179\) 51954.4 89987.7i 0.121196 0.209918i −0.799043 0.601273i \(-0.794660\pi\)
0.920240 + 0.391355i \(0.127994\pi\)
\(180\) 0 0
\(181\) −415260. −0.942159 −0.471079 0.882091i \(-0.656135\pi\)
−0.471079 + 0.882091i \(0.656135\pi\)
\(182\) 14858.1 + 104480.i 0.0332495 + 0.233806i
\(183\) 0 0
\(184\) −298282. 516639.i −0.649504 1.12497i
\(185\) −189007. + 327370.i −0.406021 + 0.703249i
\(186\) 0 0
\(187\) −331777. 574654.i −0.693812 1.20172i
\(188\) 933613. 1.92651
\(189\) 0 0
\(190\) 1.35660e6 2.72626
\(191\) 285058. + 493735.i 0.565392 + 0.979287i 0.997013 + 0.0772324i \(0.0246083\pi\)
−0.431621 + 0.902055i \(0.642058\pi\)
\(192\) 0 0
\(193\) −148854. + 257823.i −0.287653 + 0.498229i −0.973249 0.229753i \(-0.926208\pi\)
0.685596 + 0.727982i \(0.259542\pi\)
\(194\) −191911. 332399.i −0.366096 0.634097i
\(195\) 0 0
\(196\) −1.30472e6 + 378747.i −2.42591 + 0.704221i
\(197\) −410678. −0.753938 −0.376969 0.926226i \(-0.623034\pi\)
−0.376969 + 0.926226i \(0.623034\pi\)
\(198\) 0 0
\(199\) 349672. 605650.i 0.625934 1.08415i −0.362425 0.932013i \(-0.618051\pi\)
0.988359 0.152137i \(-0.0486155\pi\)
\(200\) −370345. + 641457.i −0.654684 + 1.13395i
\(201\) 0 0
\(202\) 1.04816e6 1.80738
\(203\) −463086. 186218.i −0.788718 0.317162i
\(204\) 0 0
\(205\) 480177. + 831691.i 0.798025 + 1.38222i
\(206\) −38630.8 + 66910.4i −0.0634257 + 0.109857i
\(207\) 0 0
\(208\) −112016. 194018.i −0.179524 0.310945i
\(209\) 989226. 1.56650
\(210\) 0 0
\(211\) −58292.9 −0.0901384 −0.0450692 0.998984i \(-0.514351\pi\)
−0.0450692 + 0.998984i \(0.514351\pi\)
\(212\) −189059. 327460.i −0.288907 0.500402i
\(213\) 0 0
\(214\) −164399. + 284748.i −0.245395 + 0.425036i
\(215\) −500257. 866471.i −0.738069 1.27837i
\(216\) 0 0
\(217\) −1.06250e6 + 832916.i −1.53171 + 1.20075i
\(218\) 1.20915e6 1.72322
\(219\) 0 0
\(220\) −1.42533e6 + 2.46875e6i −1.98545 + 3.43890i
\(221\) 48646.7 84258.6i 0.0669997 0.116047i
\(222\) 0 0
\(223\) 25758.5 0.0346864 0.0173432 0.999850i \(-0.494479\pi\)
0.0173432 + 0.999850i \(0.494479\pi\)
\(224\) 1.47476e6 1.15610e6i 1.96382 1.53949i
\(225\) 0 0
\(226\) −4751.15 8229.23i −0.00618768 0.0107174i
\(227\) −491123. + 850649.i −0.632594 + 1.09569i 0.354425 + 0.935084i \(0.384677\pi\)
−0.987019 + 0.160601i \(0.948657\pi\)
\(228\) 0 0
\(229\) −259982. 450301.i −0.327607 0.567433i 0.654429 0.756123i \(-0.272909\pi\)
−0.982037 + 0.188691i \(0.939576\pi\)
\(230\) −824286. −1.02744
\(231\) 0 0
\(232\) 1.99713e6 2.43605
\(233\) 609703. + 1.05604e6i 0.735747 + 1.27435i 0.954395 + 0.298547i \(0.0965020\pi\)
−0.218648 + 0.975804i \(0.570165\pi\)
\(234\) 0 0
\(235\) 389660. 674912.i 0.460274 0.797218i
\(236\) 1.17621e6 + 2.03726e6i 1.37469 + 2.38104i
\(237\) 0 0
\(238\) 1.62213e6 + 652296.i 1.85628 + 0.746453i
\(239\) 909357. 1.02977 0.514884 0.857260i \(-0.327835\pi\)
0.514884 + 0.857260i \(0.327835\pi\)
\(240\) 0 0
\(241\) 320798. 555638.i 0.355786 0.616240i −0.631466 0.775404i \(-0.717546\pi\)
0.987252 + 0.159164i \(0.0508798\pi\)
\(242\) −595428. + 1.03131e6i −0.653568 + 1.13201i
\(243\) 0 0
\(244\) 957308. 1.02938
\(245\) −270749. + 1.10126e6i −0.288172 + 1.17213i
\(246\) 0 0
\(247\) 72522.6 + 125613.i 0.0756365 + 0.131006i
\(248\) 2.70096e6 4.67820e6i 2.78862 4.83003i
\(249\) 0 0
\(250\) −608196. 1.05343e6i −0.615451 1.06599i
\(251\) −1.92052e6 −1.92413 −0.962066 0.272816i \(-0.912045\pi\)
−0.962066 + 0.272816i \(0.912045\pi\)
\(252\) 0 0
\(253\) −601067. −0.590366
\(254\) −384135. 665342.i −0.373594 0.647084i
\(255\) 0 0
\(256\) 32041.3 55497.2i 0.0305570 0.0529263i
\(257\) −493184. 854221.i −0.465775 0.806747i 0.533461 0.845825i \(-0.320891\pi\)
−0.999236 + 0.0390781i \(0.987558\pi\)
\(258\) 0 0
\(259\) −102257. 719054.i −0.0947202 0.666058i
\(260\) −417978. −0.383460
\(261\) 0 0
\(262\) −372674. + 645491.i −0.335410 + 0.580948i
\(263\) 424509. 735272.i 0.378441 0.655479i −0.612395 0.790552i \(-0.709794\pi\)
0.990836 + 0.135073i \(0.0431270\pi\)
\(264\) 0 0
\(265\) −315630. −0.276098
\(266\) −2.05130e6 + 1.60806e6i −1.77756 + 1.39347i
\(267\) 0 0
\(268\) 1.46360e6 + 2.53504e6i 1.24476 + 2.15599i
\(269\) −866792. + 1.50133e6i −0.730355 + 1.26501i 0.226377 + 0.974040i \(0.427312\pi\)
−0.956732 + 0.290972i \(0.906021\pi\)
\(270\) 0 0
\(271\) 527825. + 914221.i 0.436583 + 0.756184i 0.997423 0.0717397i \(-0.0228551\pi\)
−0.560840 + 0.827924i \(0.689522\pi\)
\(272\) −3.71161e6 −3.04187
\(273\) 0 0
\(274\) −3.95160e6 −3.17978
\(275\) 373141. + 646299.i 0.297537 + 0.515349i
\(276\) 0 0
\(277\) −812463. + 1.40723e6i −0.636216 + 1.10196i 0.350041 + 0.936735i \(0.386168\pi\)
−0.986256 + 0.165223i \(0.947166\pi\)
\(278\) −29563.3 51205.2i −0.0229425 0.0397377i
\(279\) 0 0
\(280\) −638872. 4.49245e6i −0.486988 3.42443i
\(281\) 1.56484e6 1.18224 0.591118 0.806585i \(-0.298687\pi\)
0.591118 + 0.806585i \(0.298687\pi\)
\(282\) 0 0
\(283\) 347107. 601206.i 0.257630 0.446229i −0.707976 0.706236i \(-0.750392\pi\)
0.965607 + 0.260007i \(0.0837250\pi\)
\(284\) −544725. + 943491.i −0.400757 + 0.694132i
\(285\) 0 0
\(286\) −425446. −0.307560
\(287\) −1.71193e6 688406.i −1.22682 0.493333i
\(288\) 0 0
\(289\) −96015.8 166304.i −0.0676236 0.117127i
\(290\) 1.37974e6 2.38978e6i 0.963392 1.66864i
\(291\) 0 0
\(292\) −105426. 182603.i −0.0723585 0.125329i
\(293\) −999262. −0.680002 −0.340001 0.940425i \(-0.610427\pi\)
−0.340001 + 0.940425i \(0.610427\pi\)
\(294\) 0 0
\(295\) 1.96366e6 1.31374
\(296\) 1.45304e6 + 2.51673e6i 0.963934 + 1.66958i
\(297\) 0 0
\(298\) −1.77347e6 + 3.07175e6i −1.15687 + 2.00376i
\(299\) −44065.7 76324.0i −0.0285051 0.0493723i
\(300\) 0 0
\(301\) 1.78352e6 + 717195.i 1.13465 + 0.456269i
\(302\) 798346. 0.503702
\(303\) 0 0
\(304\) 2.76664e6 4.79196e6i 1.71699 2.97392i
\(305\) 399550. 692041.i 0.245936 0.425973i
\(306\) 0 0
\(307\) 800764. 0.484907 0.242453 0.970163i \(-0.422048\pi\)
0.242453 + 0.970163i \(0.422048\pi\)
\(308\) −771134. 5.42250e6i −0.463184 3.25704i
\(309\) 0 0
\(310\) −3.73198e6 6.46398e6i −2.20564 3.82029i
\(311\) −291472. + 504844.i −0.170882 + 0.295976i −0.938728 0.344658i \(-0.887995\pi\)
0.767847 + 0.640634i \(0.221328\pi\)
\(312\) 0 0
\(313\) 999546. + 1.73126e6i 0.576689 + 0.998855i 0.995856 + 0.0909459i \(0.0289890\pi\)
−0.419166 + 0.907909i \(0.637678\pi\)
\(314\) 5.05182e6 2.89150
\(315\) 0 0
\(316\) −6.33095e6 −3.56657
\(317\) 901038. + 1.56064e6i 0.503610 + 0.872279i 0.999991 + 0.00417407i \(0.00132865\pi\)
−0.496381 + 0.868105i \(0.665338\pi\)
\(318\) 0 0
\(319\) 1.00610e6 1.74262e6i 0.553561 0.958797i
\(320\) 2.02390e6 + 3.50549e6i 1.10488 + 1.91370i
\(321\) 0 0
\(322\) 1.24639e6 977079.i 0.669909 0.525158i
\(323\) 2.40301e6 1.28159
\(324\) 0 0
\(325\) −54711.8 + 94763.6i −0.0287324 + 0.0497660i
\(326\) −1.27055e6 + 2.20066e6i −0.662138 + 1.14686i
\(327\) 0 0
\(328\) 7.38295e6 3.78918
\(329\) 210815. + 1.48242e6i 0.107377 + 0.755058i
\(330\) 0 0
\(331\) −51885.5 89868.4i −0.0260301 0.0450855i 0.852717 0.522373i \(-0.174953\pi\)
−0.878747 + 0.477288i \(0.841620\pi\)
\(332\) 676824. 1.17229e6i 0.337001 0.583702i
\(333\) 0 0
\(334\) −591176. 1.02395e6i −0.289969 0.502240i
\(335\) 2.44345e6 1.18957
\(336\) 0 0
\(337\) 961978. 0.461414 0.230707 0.973023i \(-0.425896\pi\)
0.230707 + 0.973023i \(0.425896\pi\)
\(338\) 1.94081e6 + 3.36158e6i 0.924040 + 1.60048i
\(339\) 0 0
\(340\) −3.46238e6 + 5.99702e6i −1.62434 + 2.81344i
\(341\) −2.72135e6 4.71351e6i −1.26735 2.19512i
\(342\) 0 0
\(343\) −895997. 1.98614e6i −0.411217 0.911537i
\(344\) −7.69169e6 −3.50450
\(345\) 0 0
\(346\) −3.71247e6 + 6.43019e6i −1.66714 + 2.88758i
\(347\) 1.21674e6 2.10746e6i 0.542468 0.939582i −0.456294 0.889829i \(-0.650823\pi\)
0.998762 0.0497528i \(-0.0158433\pi\)
\(348\) 0 0
\(349\) −3.42269e6 −1.50419 −0.752096 0.659053i \(-0.770957\pi\)
−0.752096 + 0.659053i \(0.770957\pi\)
\(350\) −1.82437e6 733621.i −0.796053 0.320112i
\(351\) 0 0
\(352\) 3.77728e6 + 6.54244e6i 1.62488 + 2.81438i
\(353\) 1.92748e6 3.33850e6i 0.823292 1.42598i −0.0799253 0.996801i \(-0.525468\pi\)
0.903218 0.429183i \(-0.141198\pi\)
\(354\) 0 0
\(355\) 454702. + 787567.i 0.191494 + 0.331678i
\(356\) −2.97214e6 −1.24292
\(357\) 0 0
\(358\) −1.10375e6 −0.455161
\(359\) −1.24184e6 2.15094e6i −0.508547 0.880829i −0.999951 0.00989749i \(-0.996849\pi\)
0.491404 0.870932i \(-0.336484\pi\)
\(360\) 0 0
\(361\) −553154. + 958091.i −0.223397 + 0.386936i
\(362\) 2.20552e6 + 3.82007e6i 0.884584 + 1.53214i
\(363\) 0 0
\(364\) 632020. 495456.i 0.250022 0.195998i
\(365\) −176005. −0.0691503
\(366\) 0 0
\(367\) 2.03612e6 3.52666e6i 0.789111 1.36678i −0.137401 0.990516i \(-0.543875\pi\)
0.926512 0.376265i \(-0.122792\pi\)
\(368\) −1.68105e6 + 2.91166e6i −0.647083 + 1.12078i
\(369\) 0 0
\(370\) 4.01539e6 1.52484
\(371\) 477260. 374136.i 0.180020 0.141122i
\(372\) 0 0
\(373\) 2.34636e6 + 4.06402e6i 0.873218 + 1.51246i 0.858649 + 0.512565i \(0.171305\pi\)
0.0145699 + 0.999894i \(0.495362\pi\)
\(374\) −3.52424e6 + 6.10417e6i −1.30283 + 2.25656i
\(375\) 0 0
\(376\) −2.99561e6 5.18854e6i −1.09274 1.89267i
\(377\) 295040. 0.106912
\(378\) 0 0
\(379\) 5.04599e6 1.80446 0.902232 0.431251i \(-0.141928\pi\)
0.902232 + 0.431251i \(0.141928\pi\)
\(380\) −5.16173e6 8.94037e6i −1.83373 3.17612i
\(381\) 0 0
\(382\) 3.02798e6 5.24461e6i 1.06168 1.83889i
\(383\) 826418. + 1.43140e6i 0.287874 + 0.498613i 0.973302 0.229528i \(-0.0737181\pi\)
−0.685428 + 0.728141i \(0.740385\pi\)
\(384\) 0 0
\(385\) −4.24179e6 1.70572e6i −1.45847 0.586485i
\(386\) 3.16236e6 1.08030
\(387\) 0 0
\(388\) −1.46040e6 + 2.52950e6i −0.492486 + 0.853011i
\(389\) 1.45727e6 2.52407e6i 0.488278 0.845722i −0.511631 0.859205i \(-0.670959\pi\)
0.999909 + 0.0134832i \(0.00429195\pi\)
\(390\) 0 0
\(391\) −1.46010e6 −0.482992
\(392\) 6.29122e6 + 6.03569e6i 2.06785 + 1.98386i
\(393\) 0 0
\(394\) 2.18118e6 + 3.77791e6i 0.707865 + 1.22606i
\(395\) −2.64234e6 + 4.57666e6i −0.852109 + 1.47590i
\(396\) 0 0
\(397\) 237471. + 411312.i 0.0756197 + 0.130977i 0.901356 0.433080i \(-0.142573\pi\)
−0.825736 + 0.564057i \(0.809240\pi\)
\(398\) −7.42867e6 −2.35073
\(399\) 0 0
\(400\) 4.17436e6 1.30449
\(401\) 24440.9 + 42332.8i 0.00759025 + 0.0131467i 0.869796 0.493412i \(-0.164251\pi\)
−0.862205 + 0.506559i \(0.830917\pi\)
\(402\) 0 0
\(403\) 399018. 691119.i 0.122385 0.211978i
\(404\) −3.98816e6 6.90769e6i −1.21568 2.10562i
\(405\) 0 0
\(406\) 746470. + 5.24906e6i 0.224749 + 1.58040i
\(407\) 2.92801e6 0.876166
\(408\) 0 0
\(409\) −1.86947e6 + 3.23802e6i −0.552599 + 0.957130i 0.445487 + 0.895289i \(0.353031\pi\)
−0.998086 + 0.0618416i \(0.980303\pi\)
\(410\) 5.10060e6 8.83450e6i 1.49852 2.59551i
\(411\) 0 0
\(412\) 587946. 0.170645
\(413\) −2.96923e6 + 2.32765e6i −0.856581 + 0.671495i
\(414\) 0 0
\(415\) −564970. 978557.i −0.161029 0.278911i
\(416\) −553843. + 959285.i −0.156911 + 0.271778i
\(417\) 0 0
\(418\) −5.25395e6 9.10010e6i −1.47077 2.54745i
\(419\) 681425. 0.189619 0.0948097 0.995495i \(-0.469776\pi\)
0.0948097 + 0.995495i \(0.469776\pi\)
\(420\) 0 0
\(421\) 1.54803e6 0.425670 0.212835 0.977088i \(-0.431730\pi\)
0.212835 + 0.977088i \(0.431730\pi\)
\(422\) 309604. + 536249.i 0.0846301 + 0.146584i
\(423\) 0 0
\(424\) −1.21324e6 + 2.10139e6i −0.327742 + 0.567665i
\(425\) 906425. + 1.56997e6i 0.243422 + 0.421619i
\(426\) 0 0
\(427\) 216165. + 1.52004e6i 0.0573741 + 0.403446i
\(428\) 2.50210e6 0.660229
\(429\) 0 0
\(430\) −5.31390e6 + 9.20394e6i −1.38593 + 2.40051i
\(431\) −3.18855e6 + 5.52273e6i −0.826799 + 1.43206i 0.0737367 + 0.997278i \(0.476508\pi\)
−0.900536 + 0.434781i \(0.856826\pi\)
\(432\) 0 0
\(433\) 1.32669e6 0.340056 0.170028 0.985439i \(-0.445614\pi\)
0.170028 + 0.985439i \(0.445614\pi\)
\(434\) 1.33053e7 + 5.35036e6i 3.39078 + 1.36351i
\(435\) 0 0
\(436\) −4.60072e6 7.96868e6i −1.15907 2.00757i
\(437\) 1.08836e6 1.88509e6i 0.272627 0.472203i
\(438\) 0 0
\(439\) −1.92664e6 3.33704e6i −0.477133 0.826419i 0.522523 0.852625i \(-0.324991\pi\)
−0.999657 + 0.0262059i \(0.991657\pi\)
\(440\) 1.82934e7 4.50466
\(441\) 0 0
\(442\) −1.03348e6 −0.251622
\(443\) −645522. 1.11808e6i −0.156279 0.270684i 0.777245 0.629198i \(-0.216617\pi\)
−0.933524 + 0.358515i \(0.883283\pi\)
\(444\) 0 0
\(445\) −1.24048e6 + 2.14857e6i −0.296954 + 0.514339i
\(446\) −136808. 236958.i −0.0325667 0.0564072i
\(447\) 0 0
\(448\) −7.21560e6 2.90156e6i −1.69855 0.683026i
\(449\) −7.49006e6 −1.75335 −0.876677 0.481080i \(-0.840245\pi\)
−0.876677 + 0.481080i \(0.840245\pi\)
\(450\) 0 0
\(451\) 3.71934e6 6.44209e6i 0.861042 1.49137i
\(452\) −36155.4 + 62622.9i −0.00832390 + 0.0144174i
\(453\) 0 0
\(454\) 1.04337e7 2.37575
\(455\) −94381.7 663678.i −0.0213727 0.150289i
\(456\) 0 0
\(457\) −249662. 432427.i −0.0559193 0.0968550i 0.836711 0.547645i \(-0.184476\pi\)
−0.892630 + 0.450790i \(0.851142\pi\)
\(458\) −2.76161e6 + 4.78325e6i −0.615175 + 1.06551i
\(459\) 0 0
\(460\) 3.13633e6 + 5.43229e6i 0.691079 + 1.19698i
\(461\) 5.34926e6 1.17231 0.586153 0.810200i \(-0.300642\pi\)
0.586153 + 0.810200i \(0.300642\pi\)
\(462\) 0 0
\(463\) −6.52516e6 −1.41462 −0.707308 0.706906i \(-0.750091\pi\)
−0.707308 + 0.706906i \(0.750091\pi\)
\(464\) −5.62768e6 9.74743e6i −1.21348 2.10182i
\(465\) 0 0
\(466\) 6.47647e6 1.12176e7i 1.38157 2.39295i
\(467\) −1.60324e6 2.77690e6i −0.340179 0.589207i 0.644287 0.764784i \(-0.277154\pi\)
−0.984466 + 0.175577i \(0.943821\pi\)
\(468\) 0 0
\(469\) −3.69471e6 + 2.89637e6i −0.775619 + 0.608027i
\(470\) −8.27821e6 −1.72859
\(471\) 0 0
\(472\) 7.54804e6 1.30736e7i 1.55948 2.70110i
\(473\) −3.87488e6 + 6.71149e6i −0.796352 + 1.37932i
\(474\) 0 0
\(475\) −2.70260e6 −0.549602
\(476\) −1.87322e6 1.31722e7i −0.378941 2.66466i
\(477\) 0 0
\(478\) −4.82975e6 8.36536e6i −0.966840 1.67462i
\(479\) −4.43405e6 + 7.68001e6i −0.883003 + 1.52941i −0.0350175 + 0.999387i \(0.511149\pi\)
−0.847985 + 0.530019i \(0.822185\pi\)
\(480\) 0 0
\(481\) 214660. + 371801.i 0.0423046 + 0.0732737i
\(482\) −6.81525e6 −1.33618
\(483\) 0 0
\(484\) 9.06218e6 1.75841
\(485\) 1.21905e6 + 2.11146e6i 0.235325 + 0.407595i
\(486\) 0 0
\(487\) −2.92361e6 + 5.06384e6i −0.558595 + 0.967515i 0.439019 + 0.898478i \(0.355326\pi\)
−0.997614 + 0.0690371i \(0.978007\pi\)
\(488\) −3.07164e6 5.32023e6i −0.583876 1.01130i
\(489\) 0 0
\(490\) 1.15687e7 3.35829e6i 2.17668 0.631871i
\(491\) 114241. 0.0213854 0.0106927 0.999943i \(-0.496596\pi\)
0.0106927 + 0.999943i \(0.496596\pi\)
\(492\) 0 0
\(493\) 2.44400e6 4.23314e6i 0.452881 0.784414i
\(494\) 770360. 1.33430e6i 0.142029 0.246001i
\(495\) 0 0
\(496\) −3.04439e7 −5.55644
\(497\) −1.62110e6 651884.i −0.294388 0.118380i
\(498\) 0 0
\(499\) 4.67241e6 + 8.09285e6i 0.840020 + 1.45496i 0.889877 + 0.456200i \(0.150790\pi\)
−0.0498573 + 0.998756i \(0.515877\pi\)
\(500\) −4.62826e6 + 8.01638e6i −0.827928 + 1.43401i
\(501\) 0 0
\(502\) 1.02002e7 + 1.76673e7i 1.80655 + 3.12904i
\(503\) 892118. 0.157218 0.0786091 0.996906i \(-0.474952\pi\)
0.0786091 + 0.996906i \(0.474952\pi\)
\(504\) 0 0
\(505\) −6.65812e6 −1.16178
\(506\) 3.19237e6 + 5.52934e6i 0.554289 + 0.960057i
\(507\) 0 0
\(508\) −2.92320e6 + 5.06313e6i −0.502573 + 0.870481i
\(509\) 3.42011e6 + 5.92381e6i 0.585122 + 1.01346i 0.994860 + 0.101257i \(0.0322865\pi\)
−0.409739 + 0.912203i \(0.634380\pi\)
\(510\) 0 0
\(511\) 266136. 208631.i 0.0450870 0.0353448i
\(512\) −6.27068e6 −1.05716
\(513\) 0 0
\(514\) −5.23877e6 + 9.07382e6i −0.874624 + 1.51489i
\(515\) 245390. 425028.i 0.0407698 0.0706154i
\(516\) 0 0
\(517\) −6.03644e6 −0.993241
\(518\) −6.07163e6 + 4.75970e6i −0.994216 + 0.779391i
\(519\) 0 0
\(520\) 1.34113e6 + 2.32291e6i 0.217502 + 0.376725i
\(521\) 4.45943e6 7.72397e6i 0.719756 1.24665i −0.241340 0.970441i \(-0.577587\pi\)
0.961096 0.276214i \(-0.0890798\pi\)
\(522\) 0 0
\(523\) −305911. 529854.i −0.0489037 0.0847036i 0.840537 0.541754i \(-0.182239\pi\)
−0.889441 + 0.457050i \(0.848906\pi\)
\(524\) 5.67196e6 0.902413
\(525\) 0 0
\(526\) −9.01856e6 −1.42126
\(527\) −6.61064e6 1.14500e7i −1.03685 1.79588i
\(528\) 0 0
\(529\) 2.55687e6 4.42863e6i 0.397255 0.688066i
\(530\) 1.67636e6 + 2.90354e6i 0.259226 + 0.448992i
\(531\) 0 0
\(532\) 1.84026e7 + 7.40012e6i 2.81903 + 1.13360i
\(533\) 1.09070e6 0.166298
\(534\) 0 0
\(535\) 1.04430e6 1.80877e6i 0.157739 0.273212i
\(536\) 9.39229e6 1.62679e7i 1.41208 2.44580i
\(537\) 0 0
\(538\) 1.84147e7 2.74289
\(539\) 8.43587e6 2.44886e6i 1.25071 0.363071i
\(540\) 0 0
\(541\) 122172. + 211607.i 0.0179464 + 0.0310840i 0.874859 0.484377i \(-0.160954\pi\)
−0.856913 + 0.515461i \(0.827621\pi\)
\(542\) 5.60674e6 9.71116e6i 0.819808 1.41995i
\(543\) 0 0
\(544\) 9.17568e6 + 1.58927e7i 1.32936 + 2.30251i
\(545\) −7.68078e6 −1.10768
\(546\) 0 0
\(547\) −7.55551e6 −1.07968 −0.539840 0.841767i \(-0.681515\pi\)
−0.539840 + 0.841767i \(0.681515\pi\)
\(548\) 1.50355e7 + 2.60422e7i 2.13878 + 3.70447i
\(549\) 0 0
\(550\) 3.96363e6 6.86520e6i 0.558709 0.967713i
\(551\) 3.64353e6 + 6.31077e6i 0.511261 + 0.885530i
\(552\) 0 0
\(553\) −1.42956e6 1.00525e7i −0.198788 1.39785i
\(554\) 1.72605e7 2.38935
\(555\) 0 0
\(556\) −224972. + 389662.i −0.0308632 + 0.0534566i
\(557\) 1.28638e6 2.22808e6i 0.175684 0.304293i −0.764714 0.644370i \(-0.777120\pi\)
0.940398 + 0.340077i \(0.110453\pi\)
\(558\) 0 0
\(559\) −1.13631e6 −0.153804
\(560\) −2.01261e7 + 1.57773e7i −2.71200 + 2.12600i
\(561\) 0 0
\(562\) −8.31113e6 1.43953e7i −1.10999 1.92256i
\(563\) 5.53466e6 9.58632e6i 0.735903 1.27462i −0.218424 0.975854i \(-0.570091\pi\)
0.954326 0.298767i \(-0.0965752\pi\)
\(564\) 0 0
\(565\) 30180.2 + 52273.7i 0.00397742 + 0.00688909i
\(566\) −7.37416e6 −0.967546
\(567\) 0 0
\(568\) 6.99126e6 0.909253
\(569\) 1.55605e6 + 2.69515e6i 0.201485 + 0.348982i 0.949007 0.315255i \(-0.102090\pi\)
−0.747522 + 0.664237i \(0.768757\pi\)
\(570\) 0 0
\(571\) −2.86862e6 + 4.96859e6i −0.368199 + 0.637739i −0.989284 0.146004i \(-0.953359\pi\)
0.621085 + 0.783743i \(0.286692\pi\)
\(572\) 1.61878e6 + 2.80381e6i 0.206870 + 0.358310i
\(573\) 0 0
\(574\) 2.75953e6 + 1.94046e7i 0.349587 + 2.45825i
\(575\) 1.64214e6 0.207128
\(576\) 0 0
\(577\) 5.56528e6 9.63935e6i 0.695901 1.20534i −0.273975 0.961737i \(-0.588338\pi\)
0.969876 0.243599i \(-0.0783282\pi\)
\(578\) −1.01991e6 + 1.76654e6i −0.126982 + 0.219940i
\(579\) 0 0
\(580\) −2.09992e7 −2.59198
\(581\) 2.01423e6 + 809970.i 0.247554 + 0.0995472i
\(582\) 0 0
\(583\) 1.22240e6 + 2.11725e6i 0.148950 + 0.257989i
\(584\) −676542. + 1.17180e6i −0.0820848 + 0.142175i
\(585\) 0 0
\(586\) 5.30725e6 + 9.19242e6i 0.638448 + 1.10582i
\(587\) −7.71211e6 −0.923800 −0.461900 0.886932i \(-0.652832\pi\)
−0.461900 + 0.886932i \(0.652832\pi\)
\(588\) 0 0
\(589\) 1.97103e7 2.34102
\(590\) −1.04293e7 1.80641e7i −1.23346 2.13642i
\(591\) 0 0
\(592\) 8.18897e6 1.41837e7i 0.960340 1.66336i
\(593\) 4.16650e6 + 7.21660e6i 0.486558 + 0.842744i 0.999881 0.0154520i \(-0.00491872\pi\)
−0.513322 + 0.858196i \(0.671585\pi\)
\(594\) 0 0
\(595\) −1.03041e7 4.14351e6i −1.19321 0.479817i
\(596\) 2.69916e7 3.11253
\(597\) 0 0
\(598\) −468081. + 810739.i −0.0535264 + 0.0927104i
\(599\) 2.66790e6 4.62094e6i 0.303811 0.526216i −0.673185 0.739474i \(-0.735074\pi\)
0.976996 + 0.213258i \(0.0684076\pi\)
\(600\) 0 0
\(601\) −7.53972e6 −0.851470 −0.425735 0.904848i \(-0.639984\pi\)
−0.425735 + 0.904848i \(0.639984\pi\)
\(602\) −2.87493e6 2.02161e7i −0.323323 2.27356i
\(603\) 0 0
\(604\) −3.03763e6 5.26133e6i −0.338799 0.586818i
\(605\) 3.78227e6 6.55108e6i 0.420111 0.727654i
\(606\) 0 0
\(607\) 4.84283e6 + 8.38802e6i 0.533491 + 0.924034i 0.999235 + 0.0391140i \(0.0124536\pi\)
−0.465744 + 0.884920i \(0.654213\pi\)
\(608\) −2.73582e7 −3.00144
\(609\) 0 0
\(610\) −8.48831e6 −0.923627
\(611\) −442547. 766513.i −0.0479574 0.0830647i
\(612\) 0 0
\(613\) −6.83805e6 + 1.18438e7i −0.734989 + 1.27304i 0.219739 + 0.975559i \(0.429479\pi\)
−0.954728 + 0.297480i \(0.903854\pi\)
\(614\) −4.25299e6 7.36639e6i −0.455275 0.788559i
\(615\) 0 0
\(616\) −2.76612e7 + 2.16843e7i −2.93711 + 2.30247i
\(617\) −1.53796e7 −1.62642 −0.813211 0.581969i \(-0.802283\pi\)
−0.813211 + 0.581969i \(0.802283\pi\)
\(618\) 0 0
\(619\) −2.70804e6 + 4.69046e6i −0.284072 + 0.492027i −0.972384 0.233388i \(-0.925019\pi\)
0.688312 + 0.725415i \(0.258352\pi\)
\(620\) −2.83997e7 + 4.91897e7i −2.96711 + 5.13919i
\(621\) 0 0
\(622\) 6.19223e6 0.641757
\(623\) −671125. 4.71925e6i −0.0692761 0.487139i
\(624\) 0 0
\(625\) 6.09446e6 + 1.05559e7i 0.624072 + 1.08092i
\(626\) 1.06175e7 1.83901e7i 1.08290 1.87563i
\(627\) 0 0
\(628\) −1.92217e7 3.32930e7i −1.94488 3.36863i
\(629\) 7.11266e6 0.716812
\(630\) 0 0
\(631\) 1.44178e7 1.44154 0.720770 0.693174i \(-0.243788\pi\)
0.720770 + 0.693174i \(0.243788\pi\)
\(632\) 2.03136e7 + 3.51842e7i 2.02299 + 3.50392i
\(633\) 0 0
\(634\) 9.57112e6 1.65777e7i 0.945670 1.63795i
\(635\) 2.44010e6 + 4.22638e6i 0.240145 + 0.415943i
\(636\) 0 0
\(637\) 929413. + 891663.i 0.0907528 + 0.0870667i
\(638\) −2.13743e7 −2.07893
\(639\) 0 0
\(640\) 5.89350e6 1.02078e7i 0.568753 0.985109i
\(641\) 3.06909e6 5.31582e6i 0.295029 0.511005i −0.679963 0.733247i \(-0.738004\pi\)
0.974992 + 0.222242i \(0.0713375\pi\)
\(642\) 0 0
\(643\) −402177. −0.0383610 −0.0191805 0.999816i \(-0.506106\pi\)
−0.0191805 + 0.999816i \(0.506106\pi\)
\(644\) −1.11817e7 4.49641e6i −1.06241 0.427219i
\(645\) 0 0
\(646\) −1.27628e7 2.21058e7i −1.20327 2.08413i
\(647\) 6.64081e6 1.15022e7i 0.623678 1.08024i −0.365117 0.930961i \(-0.618971\pi\)
0.988795 0.149280i \(-0.0476955\pi\)
\(648\) 0 0
\(649\) −7.60502e6 1.31723e7i −0.708743 1.22758i
\(650\) 1.16233e6 0.107906
\(651\) 0 0
\(652\) 1.93373e7 1.78147
\(653\) 5.63657e6 + 9.76282e6i 0.517287 + 0.895968i 0.999798 + 0.0200780i \(0.00639144\pi\)
−0.482511 + 0.875890i \(0.660275\pi\)
\(654\) 0 0
\(655\) 2.36730e6 4.10028e6i 0.215601 0.373431i
\(656\) −2.08043e7 3.60341e7i −1.88753 3.26929i
\(657\) 0 0
\(658\) 1.25174e7 9.81269e6i 1.12707 0.883534i
\(659\) −9.29624e6 −0.833861 −0.416930 0.908938i \(-0.636894\pi\)
−0.416930 + 0.908938i \(0.636894\pi\)
\(660\) 0 0
\(661\) 314386. 544533.i 0.0279872 0.0484753i −0.851693 0.524042i \(-0.824424\pi\)
0.879680 + 0.475566i \(0.157757\pi\)
\(662\) −551146. + 954612.i −0.0488789 + 0.0846607i
\(663\) 0 0
\(664\) −8.68669e6 −0.764599
\(665\) 1.30302e7 1.02147e7i 1.14261 0.895720i
\(666\) 0 0
\(667\) −2.21385e6 3.83451e6i −0.192679 0.333730i
\(668\) −4.49874e6 + 7.79205e6i −0.390077 + 0.675633i
\(669\) 0 0
\(670\) −1.29776e7 2.24778e7i −1.11688 1.93449i
\(671\) −6.18965e6 −0.530713
\(672\) 0 0
\(673\) 5.15635e6 0.438838 0.219419 0.975631i \(-0.429584\pi\)
0.219419 + 0.975631i \(0.429584\pi\)
\(674\) −5.10923e6 8.84944e6i −0.433217 0.750354i
\(675\) 0 0
\(676\) 1.47692e7 2.55810e7i 1.24305 2.15303i
\(677\) −3.28149e6 5.68370e6i −0.275169 0.476606i 0.695009 0.719001i \(-0.255400\pi\)
−0.970178 + 0.242395i \(0.922067\pi\)
\(678\) 0 0
\(679\) −4.34617e6 1.74770e6i −0.361770 0.145476i
\(680\) 4.44379e7 3.68537
\(681\) 0 0
\(682\) −2.89071e7 + 5.00685e7i −2.37982 + 4.12196i
\(683\) −1.00766e7 + 1.74532e7i −0.826540 + 1.43161i 0.0741975 + 0.997244i \(0.476360\pi\)
−0.900737 + 0.434365i \(0.856973\pi\)
\(684\) 0 0
\(685\) 2.51013e7 2.04395
\(686\) −1.35121e7 + 1.87912e7i −1.09626 + 1.52456i
\(687\) 0 0
\(688\) 2.16743e7 + 3.75410e7i 1.74572 + 3.02367i
\(689\) −179234. + 310442.i −0.0143838 + 0.0249134i
\(690\) 0 0
\(691\) 5.05979e6 + 8.76382e6i 0.403123 + 0.698229i 0.994101 0.108458i \(-0.0345914\pi\)
−0.590978 + 0.806688i \(0.701258\pi\)
\(692\) 5.65024e7 4.48541
\(693\) 0 0
\(694\) −2.58492e7 −2.03727
\(695\) 187792. + 325265.i 0.0147474 + 0.0255432i
\(696\) 0 0
\(697\) 9.03494e6 1.56490e7i 0.704439 1.22012i
\(698\) 1.81785e7 + 3.14860e7i 1.41227 + 2.44613i
\(699\) 0 0
\(700\) 2.10677e6 + 1.48145e7i 0.162507 + 1.14272i
\(701\) 3.27446e6 0.251678 0.125839 0.992051i \(-0.459838\pi\)
0.125839 + 0.992051i \(0.459838\pi\)
\(702\) 0 0
\(703\) −5.30178e6 + 9.18295e6i −0.404607 + 0.700800i
\(704\) 1.56767e7 2.71528e7i 1.19212 2.06482i
\(705\) 0 0
\(706\) −4.09488e7 −3.09193
\(707\) 1.00677e7 7.89230e6i 0.757496 0.593820i
\(708\) 0 0
\(709\) −2.99723e6 5.19136e6i −0.223926 0.387851i 0.732071 0.681229i \(-0.238554\pi\)
−0.955997 + 0.293377i \(0.905221\pi\)
\(710\) 4.83000e6 8.36580e6i 0.359585 0.622819i
\(711\) 0 0
\(712\) 9.53647e6 + 1.65177e7i 0.704998 + 1.22109i
\(713\) −1.19762e7 −0.882260
\(714\) 0 0
\(715\) 2.70251e6 0.197698
\(716\) 4.19968e6 + 7.27406e6i 0.306150 + 0.530267i
\(717\) 0 0
\(718\) −1.31913e7 + 2.28480e7i −0.954940 + 1.65400i
\(719\) 1.23868e7 + 2.14546e7i 0.893590 + 1.54774i 0.835541 + 0.549429i \(0.185155\pi\)
0.0580490 + 0.998314i \(0.481512\pi\)
\(720\) 0 0
\(721\) 132761. + 933557.i 0.00951115 + 0.0668810i
\(722\) 1.17516e7 0.838983
\(723\) 0 0
\(724\) 1.67836e7 2.90700e7i 1.18998 2.06110i
\(725\) −2.74871e6 + 4.76091e6i −0.194215 + 0.336391i
\(726\) 0 0
\(727\) −1.16194e7 −0.815357 −0.407678 0.913126i \(-0.633662\pi\)
−0.407678 + 0.913126i \(0.633662\pi\)
\(728\) −4.78141e6 1.92272e6i −0.334370 0.134458i
\(729\) 0 0
\(730\) 934794. + 1.61911e6i 0.0649245 + 0.112453i
\(731\) −9.41277e6 + 1.63034e7i −0.651514 + 1.12846i
\(732\) 0 0
\(733\) 6.37168e6 + 1.10361e7i 0.438020 + 0.758674i 0.997537 0.0701457i \(-0.0223464\pi\)
−0.559516 + 0.828819i \(0.689013\pi\)
\(734\) −4.32567e7 −2.96356
\(735\) 0 0
\(736\) 1.66232e7 1.13115
\(737\) −9.46319e6 1.63907e7i −0.641754 1.11155i
\(738\) 0 0
\(739\) −6.04589e6 + 1.04718e7i −0.407238 + 0.705358i −0.994579 0.103982i \(-0.966842\pi\)
0.587341 + 0.809340i \(0.300175\pi\)
\(740\) −1.52782e7 2.64626e7i −1.02563 1.77645i
\(741\) 0 0
\(742\) −5.97656e6 2.40332e6i −0.398512 0.160251i
\(743\) −9.79136e6 −0.650685 −0.325343 0.945596i \(-0.605480\pi\)
−0.325343 + 0.945596i \(0.605480\pi\)
\(744\) 0 0
\(745\) 1.12654e7 1.95123e7i 0.743632 1.28801i
\(746\) 2.49238e7 4.31694e7i 1.63971 2.84007i
\(747\) 0 0
\(748\) 5.36376e7 3.50522
\(749\) 564986. + 3.97290e6i 0.0367988 + 0.258763i
\(750\) 0 0
\(751\) 8.76513e6 + 1.51816e7i 0.567098 + 0.982243i 0.996851 + 0.0792967i \(0.0252674\pi\)
−0.429753 + 0.902947i \(0.641399\pi\)
\(752\) −1.68825e7 + 2.92414e7i −1.08866 + 1.88562i
\(753\) 0 0
\(754\) −1.56701e6 2.71413e6i −0.100379 0.173861i
\(755\) −5.07125e6 −0.323778
\(756\) 0 0
\(757\) 6.01558e6 0.381538 0.190769 0.981635i \(-0.438902\pi\)
0.190769 + 0.981635i \(0.438902\pi\)
\(758\) −2.68001e7 4.64191e7i −1.69419 2.93443i
\(759\) 0 0
\(760\) −3.31240e7 + 5.73725e7i −2.08022 + 3.60305i
\(761\) 6.38402e6 + 1.10575e7i 0.399607 + 0.692139i 0.993677 0.112274i \(-0.0358133\pi\)
−0.594071 + 0.804413i \(0.702480\pi\)
\(762\) 0 0
\(763\) 1.16140e7 9.10452e6i 0.722223 0.566168i
\(764\) −4.60847e7 −2.85643
\(765\) 0 0
\(766\) 8.77849e6 1.52048e7i 0.540565 0.936286i
\(767\) 1.11509e6 1.93139e6i 0.0684416 0.118544i
\(768\) 0 0
\(769\) −6.32718e6 −0.385829 −0.192914 0.981216i \(-0.561794\pi\)
−0.192914 + 0.981216i \(0.561794\pi\)
\(770\) 6.83754e6 + 4.80805e7i 0.415597 + 2.92242i
\(771\) 0 0
\(772\) −1.20325e7 2.08409e7i −0.726628 1.25856i
\(773\) −8.10085e6 + 1.40311e7i −0.487620 + 0.844583i −0.999899 0.0142365i \(-0.995468\pi\)
0.512279 + 0.858819i \(0.328802\pi\)
\(774\) 0 0
\(775\) 7.43482e6 + 1.28