Properties

Label 63.6.e.c.37.1
Level $63$
Weight $6$
Character 63.37
Analytic conductor $10.104$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-83})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(4.19493 - 1.84460i\) of defining polynomial
Character \(\chi\) \(=\) 63.37
Dual form 63.6.e.c.46.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.69493 + 8.13186i) q^{2} +(-28.0848 - 48.6443i) q^{4} +(-35.8645 + 62.1192i) q^{5} +(-87.5000 + 95.6596i) q^{7} +226.949 q^{8} +O(q^{10})\) \(q+(-4.69493 + 8.13186i) q^{2} +(-28.0848 - 48.6443i) q^{4} +(-35.8645 + 62.1192i) q^{5} +(-87.5000 + 95.6596i) q^{7} +226.949 q^{8} +(-336.763 - 583.291i) q^{10} +(-280.305 - 485.503i) q^{11} +533.509 q^{13} +(-367.084 - 1160.65i) q^{14} +(-166.798 + 288.903i) q^{16} +(502.850 + 870.962i) q^{17} +(-684.263 + 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(1614.04 - 2795.60i) q^{23} +(-1010.03 - 1749.42i) q^{25} +(-2504.79 + 4338.42i) q^{26} +(7110.71 + 1569.80i) q^{28} +753.456 q^{29} +(-4103.21 - 7106.97i) q^{31} +(2064.97 + 3576.64i) q^{32} -9443.39 q^{34} +(-2804.15 - 8866.21i) q^{35} +(1404.33 - 2432.37i) q^{37} +(-6425.14 - 11128.7i) q^{38} +(-8139.43 + 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(-15744.6 + 27270.5i) q^{44} +(15155.6 + 26250.3i) q^{46} +(-8172.74 + 14155.6i) q^{47} +(-1494.50 - 16740.4i) q^{49} +18968.1 q^{50} +(-14983.5 - 25952.2i) q^{52} +(-14820.8 - 25670.4i) q^{53} +40212.0 q^{55} +(-19858.1 + 21709.9i) q^{56} +(-3537.43 + 6127.00i) q^{58} +(-5178.05 - 8968.65i) q^{59} +(-477.089 + 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(-19134.0 + 33141.1i) q^{65} +(9907.60 + 17160.5i) q^{67} +(28244.9 - 48921.6i) q^{68} +(85264.1 + 18823.3i) q^{70} -62125.4 q^{71} +(-13554.8 - 23477.6i) q^{73} +(13186.5 + 22839.7i) q^{74} +76869.6 q^{76} +(70969.7 + 15667.6i) q^{77} +(-22343.7 + 38700.4i) q^{79} +(-11964.3 - 20722.8i) q^{80} +(1154.14 - 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(82182.5 - 142344. i) q^{86} +(-63615.0 - 110184. i) q^{88} +(6817.66 - 11808.5i) q^{89} +(-46682.0 + 51035.2i) q^{91} -181320. q^{92} +(-76740.9 - 132919. i) q^{94} +(-49081.6 - 85011.8i) q^{95} -12919.5 q^{97} +(143147. + 66442.1i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} - 65 q^{4} - 33 q^{5} - 350 q^{7} + 750 q^{8} - 921 q^{10} - 1137 q^{11} + 1850 q^{13} - 2352 q^{14} + 895 q^{16} - 324 q^{17} - 2311 q^{19} + 7374 q^{20} + 3162 q^{22} + 1596 q^{23} - 395 q^{25} - 2508 q^{26} + 13531 q^{28} + 4434 q^{29} - 4294 q^{31} + 1017 q^{32} - 35880 q^{34} - 15414 q^{35} + 19109 q^{37} - 6828 q^{38} - 10545 q^{40} + 25716 q^{41} - 5542 q^{43} - 36579 q^{44} + 40740 q^{46} - 23160 q^{47} - 5978 q^{49} + 58704 q^{50} - 33424 q^{52} - 31653 q^{53} + 35778 q^{55} - 65625 q^{56} + 2277 q^{58} + 41097 q^{59} - 42052 q^{61} + 204114 q^{62} - 60062 q^{64} - 23106 q^{65} - 30763 q^{67} + 44748 q^{68} + 151179 q^{70} - 204192 q^{71} + 28577 q^{73} - 77784 q^{74} + 170384 q^{76} + 96873 q^{77} + 18464 q^{79} - 71511 q^{80} + 86040 q^{82} - 122358 q^{83} - 247272 q^{85} + 258510 q^{86} - 212565 q^{88} + 29322 q^{89} - 161875 q^{91} - 333816 q^{92} - 109938 q^{94} - 61662 q^{95} - 19582 q^{97} + 462021 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.69493 + 8.13186i −0.829955 + 1.43752i 0.0681181 + 0.997677i \(0.478301\pi\)
−0.898073 + 0.439847i \(0.855033\pi\)
\(3\) 0 0
\(4\) −28.0848 48.6443i −0.877650 1.52013i
\(5\) −35.8645 + 62.1192i −0.641564 + 1.11122i 0.343519 + 0.939146i \(0.388381\pi\)
−0.985084 + 0.172076i \(0.944952\pi\)
\(6\) 0 0
\(7\) −87.5000 + 95.6596i −0.674937 + 0.737876i
\(8\) 226.949 1.25373
\(9\) 0 0
\(10\) −336.763 583.291i −1.06494 1.84453i
\(11\) −280.305 485.503i −0.698472 1.20979i −0.968996 0.247076i \(-0.920530\pi\)
0.270524 0.962713i \(-0.412803\pi\)
\(12\) 0 0
\(13\) 533.509 0.875555 0.437777 0.899083i \(-0.355766\pi\)
0.437777 + 0.899083i \(0.355766\pi\)
\(14\) −367.084 1160.65i −0.500547 1.58264i
\(15\) 0 0
\(16\) −166.798 + 288.903i −0.162889 + 0.282132i
\(17\) 502.850 + 870.962i 0.422004 + 0.730932i 0.996135 0.0878311i \(-0.0279936\pi\)
−0.574132 + 0.818763i \(0.694660\pi\)
\(18\) 0 0
\(19\) −684.263 + 1185.18i −0.434850 + 0.753182i −0.997283 0.0736606i \(-0.976532\pi\)
0.562434 + 0.826842i \(0.309865\pi\)
\(20\) 4028.99 2.25228
\(21\) 0 0
\(22\) 5264.05 2.31880
\(23\) 1614.04 2795.60i 0.636201 1.10193i −0.350058 0.936728i \(-0.613838\pi\)
0.986259 0.165205i \(-0.0528286\pi\)
\(24\) 0 0
\(25\) −1010.03 1749.42i −0.323209 0.559815i
\(26\) −2504.79 + 4338.42i −0.726671 + 1.25863i
\(27\) 0 0
\(28\) 7110.71 + 1569.80i 1.71403 + 0.378398i
\(29\) 753.456 0.166365 0.0831827 0.996534i \(-0.473492\pi\)
0.0831827 + 0.996534i \(0.473492\pi\)
\(30\) 0 0
\(31\) −4103.21 7106.97i −0.766866 1.32825i −0.939254 0.343222i \(-0.888482\pi\)
0.172389 0.985029i \(-0.444852\pi\)
\(32\) 2064.97 + 3576.64i 0.356484 + 0.617448i
\(33\) 0 0
\(34\) −9443.39 −1.40098
\(35\) −2804.15 8866.21i −0.386929 1.22340i
\(36\) 0 0
\(37\) 1404.33 2432.37i 0.168642 0.292096i −0.769301 0.638887i \(-0.779395\pi\)
0.937943 + 0.346791i \(0.112729\pi\)
\(38\) −6425.14 11128.7i −0.721811 1.25021i
\(39\) 0 0
\(40\) −8139.43 + 14097.9i −0.804348 + 1.39317i
\(41\) −245.827 −0.0228387 −0.0114193 0.999935i \(-0.503635\pi\)
−0.0114193 + 0.999935i \(0.503635\pi\)
\(42\) 0 0
\(43\) −17504.5 −1.44371 −0.721853 0.692047i \(-0.756709\pi\)
−0.721853 + 0.692047i \(0.756709\pi\)
\(44\) −15744.6 + 27270.5i −1.22603 + 2.12354i
\(45\) 0 0
\(46\) 15155.6 + 26250.3i 1.05604 + 1.82911i
\(47\) −8172.74 + 14155.6i −0.539663 + 0.934725i 0.459258 + 0.888303i \(0.348115\pi\)
−0.998922 + 0.0464219i \(0.985218\pi\)
\(48\) 0 0
\(49\) −1494.50 16740.4i −0.0889213 0.996039i
\(50\) 18968.1 1.07300
\(51\) 0 0
\(52\) −14983.5 25952.2i −0.768430 1.33096i
\(53\) −14820.8 25670.4i −0.724741 1.25529i −0.959081 0.283133i \(-0.908626\pi\)
0.234340 0.972155i \(-0.424707\pi\)
\(54\) 0 0
\(55\) 40212.0 1.79246
\(56\) −19858.1 + 21709.9i −0.846188 + 0.925097i
\(57\) 0 0
\(58\) −3537.43 + 6127.00i −0.138076 + 0.239154i
\(59\) −5178.05 8968.65i −0.193659 0.335426i 0.752801 0.658248i \(-0.228702\pi\)
−0.946460 + 0.322821i \(0.895369\pi\)
\(60\) 0 0
\(61\) −477.089 + 826.343i −0.0164163 + 0.0284339i −0.874117 0.485716i \(-0.838559\pi\)
0.857701 + 0.514150i \(0.171892\pi\)
\(62\) 77057.2 2.54586
\(63\) 0 0
\(64\) −49454.8 −1.50924
\(65\) −19134.0 + 33141.1i −0.561725 + 0.972935i
\(66\) 0 0
\(67\) 9907.60 + 17160.5i 0.269638 + 0.467027i 0.968768 0.247967i \(-0.0797626\pi\)
−0.699130 + 0.714994i \(0.746429\pi\)
\(68\) 28244.9 48921.6i 0.740743 1.28300i
\(69\) 0 0
\(70\) 85264.1 + 18823.3i 2.07980 + 0.459147i
\(71\) −62125.4 −1.46259 −0.731296 0.682060i \(-0.761084\pi\)
−0.731296 + 0.682060i \(0.761084\pi\)
\(72\) 0 0
\(73\) −13554.8 23477.6i −0.297705 0.515641i 0.677905 0.735149i \(-0.262888\pi\)
−0.975611 + 0.219509i \(0.929555\pi\)
\(74\) 13186.5 + 22839.7i 0.279930 + 0.484853i
\(75\) 0 0
\(76\) 76869.6 1.52658
\(77\) 70969.7 + 15667.6i 1.36410 + 0.301145i
\(78\) 0 0
\(79\) −22343.7 + 38700.4i −0.402798 + 0.697666i −0.994062 0.108812i \(-0.965295\pi\)
0.591265 + 0.806477i \(0.298629\pi\)
\(80\) −11964.3 20722.8i −0.209008 0.362012i
\(81\) 0 0
\(82\) 1154.14 1999.03i 0.0189551 0.0328311i
\(83\) −15606.6 −0.248665 −0.124332 0.992241i \(-0.539679\pi\)
−0.124332 + 0.992241i \(0.539679\pi\)
\(84\) 0 0
\(85\) −72137.9 −1.08297
\(86\) 82182.5 142344.i 1.19821 2.07536i
\(87\) 0 0
\(88\) −63615.0 110184.i −0.875696 1.51675i
\(89\) 6817.66 11808.5i 0.0912347 0.158023i −0.816796 0.576926i \(-0.804252\pi\)
0.908031 + 0.418903i \(0.137585\pi\)
\(90\) 0 0
\(91\) −46682.0 + 51035.2i −0.590944 + 0.646050i
\(92\) −181320. −2.23345
\(93\) 0 0
\(94\) −76740.9 132919.i −0.895793 1.55156i
\(95\) −49081.6 85011.8i −0.557968 0.966429i
\(96\) 0 0
\(97\) −12919.5 −0.139417 −0.0697086 0.997567i \(-0.522207\pi\)
−0.0697086 + 0.997567i \(0.522207\pi\)
\(98\) 143147. + 66442.1i 1.50563 + 0.698841i
\(99\) 0 0
\(100\) −56733.0 + 98264.4i −0.567330 + 0.982644i
\(101\) 12571.5 + 21774.4i 0.122626 + 0.212394i 0.920802 0.390029i \(-0.127535\pi\)
−0.798177 + 0.602424i \(0.794202\pi\)
\(102\) 0 0
\(103\) 80376.6 139216.i 0.746511 1.29300i −0.202974 0.979184i \(-0.565061\pi\)
0.949485 0.313811i \(-0.101606\pi\)
\(104\) 121079. 1.09771
\(105\) 0 0
\(106\) 278331. 2.40601
\(107\) −47187.8 + 81731.6i −0.398446 + 0.690129i −0.993534 0.113531i \(-0.963784\pi\)
0.595088 + 0.803661i \(0.297117\pi\)
\(108\) 0 0
\(109\) 41696.7 + 72220.9i 0.336152 + 0.582233i 0.983705 0.179788i \(-0.0575410\pi\)
−0.647553 + 0.762020i \(0.724208\pi\)
\(110\) −188793. + 326999.i −1.48766 + 2.57670i
\(111\) 0 0
\(112\) −13041.5 41234.9i −0.0982387 0.310613i
\(113\) 179254. 1.32060 0.660301 0.751001i \(-0.270429\pi\)
0.660301 + 0.751001i \(0.270429\pi\)
\(114\) 0 0
\(115\) 115774. + 200526.i 0.816328 + 1.41392i
\(116\) −21160.7 36651.3i −0.146011 0.252898i
\(117\) 0 0
\(118\) 97242.5 0.642911
\(119\) −127315. 28106.8i −0.824163 0.181946i
\(120\) 0 0
\(121\) −76616.4 + 132703.i −0.475727 + 0.823984i
\(122\) −4479.80 7759.25i −0.0272496 0.0471976i
\(123\) 0 0
\(124\) −230476. + 399195.i −1.34608 + 2.33148i
\(125\) −79256.4 −0.453690
\(126\) 0 0
\(127\) −143674. −0.790440 −0.395220 0.918586i \(-0.629332\pi\)
−0.395220 + 0.918586i \(0.629332\pi\)
\(128\) 166108. 287707.i 0.896117 1.55212i
\(129\) 0 0
\(130\) −179666. 311191.i −0.932412 1.61498i
\(131\) 26144.9 45284.3i 0.133110 0.230553i −0.791764 0.610827i \(-0.790837\pi\)
0.924874 + 0.380274i \(0.124170\pi\)
\(132\) 0 0
\(133\) −53500.6 169159.i −0.262259 0.829215i
\(134\) −186062. −0.895150
\(135\) 0 0
\(136\) 114122. + 197664.i 0.529079 + 0.916391i
\(137\) 4705.05 + 8149.39i 0.0214172 + 0.0370957i 0.876535 0.481337i \(-0.159849\pi\)
−0.855118 + 0.518433i \(0.826516\pi\)
\(138\) 0 0
\(139\) 183094. 0.803781 0.401890 0.915688i \(-0.368353\pi\)
0.401890 + 0.915688i \(0.368353\pi\)
\(140\) −352537. + 385412.i −1.52014 + 1.66190i
\(141\) 0 0
\(142\) 291674. 505195.i 1.21389 2.10251i
\(143\) −149545. 259020.i −0.611551 1.05924i
\(144\) 0 0
\(145\) −27022.3 + 46804.1i −0.106734 + 0.184869i
\(146\) 254556. 0.988328
\(147\) 0 0
\(148\) −157762. −0.592034
\(149\) −83500.8 + 144628.i −0.308123 + 0.533685i −0.977952 0.208830i \(-0.933034\pi\)
0.669828 + 0.742516i \(0.266368\pi\)
\(150\) 0 0
\(151\) −188132. 325855.i −0.671461 1.16300i −0.977490 0.210982i \(-0.932334\pi\)
0.306029 0.952022i \(-0.401000\pi\)
\(152\) −155293. + 268976.i −0.545184 + 0.944286i
\(153\) 0 0
\(154\) −460605. + 503557.i −1.56504 + 1.71099i
\(155\) 588639. 1.96797
\(156\) 0 0
\(157\) −19537.5 33840.0i −0.0632587 0.109567i 0.832662 0.553782i \(-0.186816\pi\)
−0.895920 + 0.444215i \(0.853483\pi\)
\(158\) −209804. 363391.i −0.668608 1.15806i
\(159\) 0 0
\(160\) −296237. −0.914829
\(161\) 126197. + 399013.i 0.383694 + 1.21317i
\(162\) 0 0
\(163\) 238959. 413890.i 0.704458 1.22016i −0.262428 0.964951i \(-0.584523\pi\)
0.966887 0.255206i \(-0.0821433\pi\)
\(164\) 6904.01 + 11958.1i 0.0200444 + 0.0347178i
\(165\) 0 0
\(166\) 73272.1 126911.i 0.206381 0.357462i
\(167\) −39793.4 −0.110413 −0.0552064 0.998475i \(-0.517582\pi\)
−0.0552064 + 0.998475i \(0.517582\pi\)
\(168\) 0 0
\(169\) −86661.4 −0.233404
\(170\) 338683. 586616.i 0.898816 1.55680i
\(171\) 0 0
\(172\) 491610. + 851494.i 1.26707 + 2.19463i
\(173\) 24169.1 41862.1i 0.0613968 0.106342i −0.833693 0.552228i \(-0.813778\pi\)
0.895090 + 0.445886i \(0.147111\pi\)
\(174\) 0 0
\(175\) 255727. + 56455.5i 0.631220 + 0.139351i
\(176\) 187018. 0.455094
\(177\) 0 0
\(178\) 64016.9 + 110881.i 0.151441 + 0.262304i
\(179\) −71455.3 123764.i −0.166687 0.288711i 0.770566 0.637360i \(-0.219974\pi\)
−0.937253 + 0.348650i \(0.886640\pi\)
\(180\) 0 0
\(181\) −77245.3 −0.175257 −0.0876285 0.996153i \(-0.527929\pi\)
−0.0876285 + 0.996153i \(0.527929\pi\)
\(182\) −195842. 619219.i −0.438256 1.38569i
\(183\) 0 0
\(184\) 366305. 634459.i 0.797625 1.38153i
\(185\) 100731. + 174472.i 0.216389 + 0.374797i
\(186\) 0 0
\(187\) 281903. 488270.i 0.589516 1.02107i
\(188\) 918119. 1.89454
\(189\) 0 0
\(190\) 921739. 1.85235
\(191\) 136027. 235606.i 0.269800 0.467307i −0.699010 0.715112i \(-0.746376\pi\)
0.968810 + 0.247805i \(0.0797092\pi\)
\(192\) 0 0
\(193\) 8016.89 + 13885.7i 0.0154922 + 0.0268333i 0.873668 0.486523i \(-0.161735\pi\)
−0.858175 + 0.513357i \(0.828402\pi\)
\(194\) 60656.2 105060.i 0.115710 0.200415i
\(195\) 0 0
\(196\) −772353. + 542850.i −1.43607 + 1.00935i
\(197\) −1.03228e6 −1.89510 −0.947552 0.319603i \(-0.896451\pi\)
−0.947552 + 0.319603i \(0.896451\pi\)
\(198\) 0 0
\(199\) 440868. + 763606.i 0.789180 + 1.36690i 0.926470 + 0.376369i \(0.122827\pi\)
−0.137290 + 0.990531i \(0.543839\pi\)
\(200\) −229226. 397030.i −0.405217 0.701857i
\(201\) 0 0
\(202\) −236089. −0.407096
\(203\) −65927.4 + 72075.3i −0.112286 + 0.122757i
\(204\) 0 0
\(205\) 8816.49 15270.6i 0.0146525 0.0253788i
\(206\) 754725. + 1.30722e6i 1.23914 + 2.14626i
\(207\) 0 0
\(208\) −88988.4 + 154132.i −0.142618 + 0.247022i
\(209\) 767210. 1.21492
\(210\) 0 0
\(211\) −372813. −0.576480 −0.288240 0.957558i \(-0.593070\pi\)
−0.288240 + 0.957558i \(0.593070\pi\)
\(212\) −832480. + 1.44190e6i −1.27214 + 2.20341i
\(213\) 0 0
\(214\) −443087. 767449.i −0.661385 1.14555i
\(215\) 627791. 1.08737e6i 0.926230 1.60428i
\(216\) 0 0
\(217\) 1.03888e6 + 229348.i 1.49767 + 0.330633i
\(218\) −783054. −1.11596
\(219\) 0 0
\(220\) −1.12935e6 1.95609e6i −1.57315 2.72478i
\(221\) 268275. + 464666.i 0.369487 + 0.639971i
\(222\) 0 0
\(223\) −1.08205e6 −1.45708 −0.728541 0.685002i \(-0.759801\pi\)
−0.728541 + 0.685002i \(0.759801\pi\)
\(224\) −522825. 115422.i −0.696204 0.153697i
\(225\) 0 0
\(226\) −841584. + 1.45767e6i −1.09604 + 1.89840i
\(227\) 276524. + 478954.i 0.356179 + 0.616921i 0.987319 0.158748i \(-0.0507459\pi\)
−0.631140 + 0.775669i \(0.717413\pi\)
\(228\) 0 0
\(229\) −261512. + 452952.i −0.329536 + 0.570773i −0.982420 0.186685i \(-0.940226\pi\)
0.652884 + 0.757458i \(0.273559\pi\)
\(230\) −2.17420e6 −2.71006
\(231\) 0 0
\(232\) 170996. 0.208577
\(233\) −182090. + 315390.i −0.219734 + 0.380590i −0.954727 0.297485i \(-0.903852\pi\)
0.734993 + 0.678075i \(0.237186\pi\)
\(234\) 0 0
\(235\) −586223. 1.01537e6i −0.692458 1.19937i
\(236\) −290849. + 503766.i −0.339929 + 0.588774i
\(237\) 0 0
\(238\) 826297. 903351.i 0.945570 1.03375i
\(239\) −371841. −0.421078 −0.210539 0.977585i \(-0.567522\pi\)
−0.210539 + 0.977585i \(0.567522\pi\)
\(240\) 0 0
\(241\) 855737. + 1.48218e6i 0.949069 + 1.64384i 0.747391 + 0.664384i \(0.231306\pi\)
0.201678 + 0.979452i \(0.435360\pi\)
\(242\) −719417. 1.24607e6i −0.789664 1.36774i
\(243\) 0 0
\(244\) 53595.8 0.0576310
\(245\) 1.09350e6 + 507550.i 1.16387 + 0.540212i
\(246\) 0 0
\(247\) −365060. + 632303.i −0.380735 + 0.659452i
\(248\) −931221. 1.61292e6i −0.961443 1.66527i
\(249\) 0 0
\(250\) 372103. 644502.i 0.376542 0.652190i
\(251\) −58134.1 −0.0582434 −0.0291217 0.999576i \(-0.509271\pi\)
−0.0291217 + 0.999576i \(0.509271\pi\)
\(252\) 0 0
\(253\) −1.80969e6 −1.77748
\(254\) 674540. 1.16834e6i 0.656030 1.13628i
\(255\) 0 0
\(256\) 768453. + 1.33100e6i 0.732853 + 1.26934i
\(257\) −155920. + 270061.i −0.147254 + 0.255052i −0.930212 0.367023i \(-0.880377\pi\)
0.782957 + 0.622075i \(0.213710\pi\)
\(258\) 0 0
\(259\) 109801. + 347171.i 0.101708 + 0.321583i
\(260\) 2.14950e6 1.97199
\(261\) 0 0
\(262\) 245497. + 425214.i 0.220950 + 0.382696i
\(263\) 431983. + 748216.i 0.385103 + 0.667018i 0.991783 0.127928i \(-0.0408326\pi\)
−0.606681 + 0.794946i \(0.707499\pi\)
\(264\) 0 0
\(265\) 2.12617e6 1.85987
\(266\) 1.62676e6 + 359133.i 1.40968 + 0.311208i
\(267\) 0 0
\(268\) 556506. 963896.i 0.473296 0.819773i
\(269\) −560346. 970548.i −0.472145 0.817779i 0.527347 0.849650i \(-0.323187\pi\)
−0.999492 + 0.0318707i \(0.989854\pi\)
\(270\) 0 0
\(271\) −570058. + 987369.i −0.471515 + 0.816688i −0.999469 0.0325848i \(-0.989626\pi\)
0.527954 + 0.849273i \(0.322959\pi\)
\(272\) −335498. −0.274959
\(273\) 0 0
\(274\) −88359.6 −0.0711013
\(275\) −566233. + 980744.i −0.451506 + 0.782031i
\(276\) 0 0
\(277\) 994005. + 1.72167e6i 0.778375 + 1.34819i 0.932878 + 0.360193i \(0.117289\pi\)
−0.154502 + 0.987992i \(0.549377\pi\)
\(278\) −859615. + 1.48890e6i −0.667102 + 1.15545i
\(279\) 0 0
\(280\) −636399. 2.01218e6i −0.485104 1.53381i
\(281\) −532321. −0.402168 −0.201084 0.979574i \(-0.564446\pi\)
−0.201084 + 0.979574i \(0.564446\pi\)
\(282\) 0 0
\(283\) −1.31237e6 2.27308e6i −0.974067 1.68713i −0.682980 0.730437i \(-0.739316\pi\)
−0.291087 0.956697i \(-0.594017\pi\)
\(284\) 1.74478e6 + 3.02205e6i 1.28364 + 2.22334i
\(285\) 0 0
\(286\) 2.80842e6 2.03024
\(287\) 21509.9 23515.7i 0.0154146 0.0168521i
\(288\) 0 0
\(289\) 204212. 353705.i 0.143826 0.249113i
\(290\) −253736. 439484.i −0.177169 0.306866i
\(291\) 0 0
\(292\) −761369. + 1.31873e6i −0.522562 + 0.905104i
\(293\) −609962. −0.415082 −0.207541 0.978226i \(-0.566546\pi\)
−0.207541 + 0.978226i \(0.566546\pi\)
\(294\) 0 0
\(295\) 742834. 0.496978
\(296\) 318712. 552026.i 0.211431 0.366210i
\(297\) 0 0
\(298\) −784061. 1.35803e6i −0.511457 0.885870i
\(299\) 861104. 1.49148e6i 0.557029 0.964802i
\(300\) 0 0
\(301\) 1.53164e6 1.67447e6i 0.974409 1.06528i
\(302\) 3.53307e6 2.22913
\(303\) 0 0
\(304\) −228268. 395372.i −0.141665 0.245370i
\(305\) −34221.2 59272.8i −0.0210642 0.0364843i
\(306\) 0 0
\(307\) −1.34843e6 −0.816551 −0.408275 0.912859i \(-0.633870\pi\)
−0.408275 + 0.912859i \(0.633870\pi\)
\(308\) −1.23103e6 3.89229e6i −0.739420 2.33791i
\(309\) 0 0
\(310\) −2.76362e6 + 4.78673e6i −1.63333 + 2.82901i
\(311\) −1.66530e6 2.88439e6i −0.976320 1.69104i −0.675507 0.737353i \(-0.736075\pi\)
−0.300813 0.953683i \(-0.597258\pi\)
\(312\) 0 0
\(313\) 1.41835e6 2.45666e6i 0.818320 1.41737i −0.0885991 0.996067i \(-0.528239\pi\)
0.906919 0.421305i \(-0.138428\pi\)
\(314\) 366909. 0.210007
\(315\) 0 0
\(316\) 2.51007e6 1.41406
\(317\) −544195. + 942574.i −0.304163 + 0.526826i −0.977075 0.212897i \(-0.931710\pi\)
0.672912 + 0.739723i \(0.265043\pi\)
\(318\) 0 0
\(319\) −211198. 365805.i −0.116202 0.201267i
\(320\) 1.77367e6 3.07209e6i 0.968274 1.67710i
\(321\) 0 0
\(322\) −3.83721e6 847122.i −2.06241 0.455309i
\(323\) −1.37633e6 −0.734033
\(324\) 0 0
\(325\) −538860. 933332.i −0.282988 0.490149i
\(326\) 2.24380e6 + 3.88637e6i 1.16934 + 2.02535i
\(327\) 0 0
\(328\) −55790.4 −0.0286335
\(329\) −639004. 2.02042e6i −0.325472 1.02908i
\(330\) 0 0
\(331\) −652773. + 1.13064e6i −0.327485 + 0.567221i −0.982012 0.188817i \(-0.939535\pi\)
0.654527 + 0.756039i \(0.272868\pi\)
\(332\) 438309. + 759174.i 0.218241 + 0.378004i
\(333\) 0 0
\(334\) 186827. 323594.i 0.0916376 0.158721i
\(335\) −1.42133e6 −0.691961
\(336\) 0 0
\(337\) −3.17016e6 −1.52057 −0.760285 0.649590i \(-0.774941\pi\)
−0.760285 + 0.649590i \(0.774941\pi\)
\(338\) 406869. 704718.i 0.193715 0.335524i
\(339\) 0 0
\(340\) 2.02598e6 + 3.50910e6i 0.950469 + 1.64626i
\(341\) −2.30030e6 + 3.98424e6i −1.07127 + 1.85549i
\(342\) 0 0
\(343\) 1.73215e6 + 1.32182e6i 0.794969 + 0.606650i
\(344\) −3.97263e6 −1.81002
\(345\) 0 0
\(346\) 226945. + 393080.i 0.101913 + 0.176519i
\(347\) −857958. 1.48603e6i −0.382510 0.662526i 0.608911 0.793239i \(-0.291607\pi\)
−0.991420 + 0.130713i \(0.958273\pi\)
\(348\) 0 0
\(349\) −2.95822e6 −1.30007 −0.650034 0.759905i \(-0.725245\pi\)
−0.650034 + 0.759905i \(0.725245\pi\)
\(350\) −1.65971e6 + 1.81448e6i −0.724205 + 0.791739i
\(351\) 0 0
\(352\) 1.15765e6 2.00510e6i 0.497988 0.862541i
\(353\) 1.88490e6 + 3.26474e6i 0.805103 + 1.39448i 0.916222 + 0.400672i \(0.131223\pi\)
−0.111119 + 0.993807i \(0.535443\pi\)
\(354\) 0 0
\(355\) 2.22810e6 3.85918e6i 0.938347 1.62526i
\(356\) −765890. −0.320289
\(357\) 0 0
\(358\) 1.34191e6 0.553371
\(359\) 964935. 1.67132e6i 0.395150 0.684420i −0.597970 0.801518i \(-0.704026\pi\)
0.993120 + 0.117099i \(0.0373593\pi\)
\(360\) 0 0
\(361\) 301617. + 522416.i 0.121811 + 0.210984i
\(362\) 362662. 628148.i 0.145455 0.251936i
\(363\) 0 0
\(364\) 3.79363e6 + 837500.i 1.50073 + 0.331308i
\(365\) 1.94455e6 0.763988
\(366\) 0 0
\(367\) −1.18371e6 2.05025e6i −0.458754 0.794586i 0.540141 0.841575i \(-0.318371\pi\)
−0.998895 + 0.0469885i \(0.985038\pi\)
\(368\) 538438. + 932603.i 0.207260 + 0.358986i
\(369\) 0 0
\(370\) −1.89171e6 −0.718373
\(371\) 3.75244e6 + 828409.i 1.41540 + 0.312471i
\(372\) 0 0
\(373\) −1.76914e6 + 3.06425e6i −0.658402 + 1.14039i 0.322627 + 0.946526i \(0.395434\pi\)
−0.981029 + 0.193860i \(0.937899\pi\)
\(374\) 2.64703e6 + 4.58479e6i 0.978543 + 1.69489i
\(375\) 0 0
\(376\) −1.85480e6 + 3.21260e6i −0.676592 + 1.17189i
\(377\) 401975. 0.145662
\(378\) 0 0
\(379\) 1.79847e6 0.643139 0.321569 0.946886i \(-0.395790\pi\)
0.321569 + 0.946886i \(0.395790\pi\)
\(380\) −2.75689e6 + 4.77508e6i −0.979401 + 1.69637i
\(381\) 0 0
\(382\) 1.27728e6 + 2.21231e6i 0.447843 + 0.775687i
\(383\) 1.30407e6 2.25872e6i 0.454261 0.786802i −0.544385 0.838836i \(-0.683237\pi\)
0.998645 + 0.0520333i \(0.0165702\pi\)
\(384\) 0 0
\(385\) −3.51855e6 + 3.84667e6i −1.20980 + 1.32261i
\(386\) −150555. −0.0514313
\(387\) 0 0
\(388\) 362841. + 628460.i 0.122359 + 0.211933i
\(389\) −1.41498e6 2.45081e6i −0.474106 0.821175i 0.525455 0.850821i \(-0.323895\pi\)
−0.999560 + 0.0296466i \(0.990562\pi\)
\(390\) 0 0
\(391\) 3.24648e6 1.07392
\(392\) −339176. 3.79923e6i −0.111483 1.24876i
\(393\) 0 0
\(394\) 4.84650e6 8.39438e6i 1.57285 2.72426i
\(395\) −1.60269e6 2.77594e6i −0.516841 0.895195i
\(396\) 0 0
\(397\) 1.21531e6 2.10498e6i 0.387000 0.670303i −0.605045 0.796191i \(-0.706845\pi\)
0.992044 + 0.125888i \(0.0401781\pi\)
\(398\) −8.27939e6 −2.61993
\(399\) 0 0
\(400\) 673885. 0.210589
\(401\) −1.21592e6 + 2.10604e6i −0.377611 + 0.654041i −0.990714 0.135962i \(-0.956588\pi\)
0.613103 + 0.790003i \(0.289921\pi\)
\(402\) 0 0
\(403\) −2.18910e6 3.79163e6i −0.671433 1.16296i
\(404\) 706134. 1.22306e6i 0.215245 0.372816i
\(405\) 0 0
\(406\) −276581. 874501.i −0.0832737 0.263297i
\(407\) −1.57457e6 −0.471167
\(408\) 0 0
\(409\) 2.38733e6 + 4.13497e6i 0.705674 + 1.22226i 0.966448 + 0.256863i \(0.0826889\pi\)
−0.260774 + 0.965400i \(0.583978\pi\)
\(410\) 82785.6 + 143389.i 0.0243218 + 0.0421266i
\(411\) 0 0
\(412\) −9.02944e6 −2.62070
\(413\) 1.31102e6 + 289427.i 0.378210 + 0.0834956i
\(414\) 0 0
\(415\) 559725. 969472.i 0.159534 0.276322i
\(416\) 1.10168e6 + 1.90817e6i 0.312121 + 0.540609i
\(417\) 0 0
\(418\) −3.60200e6 + 6.23884e6i −1.00833 + 1.74648i
\(419\) 457181. 0.127219 0.0636097 0.997975i \(-0.479739\pi\)
0.0636097 + 0.997975i \(0.479739\pi\)
\(420\) 0 0
\(421\) −1.82396e6 −0.501545 −0.250773 0.968046i \(-0.580685\pi\)
−0.250773 + 0.968046i \(0.580685\pi\)
\(422\) 1.75033e6 3.03166e6i 0.478453 0.828704i
\(423\) 0 0
\(424\) −3.36358e6 5.82589e6i −0.908629 1.57379i
\(425\) 1.01579e6 1.75939e6i 0.272791 0.472488i
\(426\) 0 0
\(427\) −37302.3 117943.i −0.00990069 0.0313042i
\(428\) 5.30104e6 1.39879
\(429\) 0 0
\(430\) 5.89487e6 + 1.02102e7i 1.53746 + 2.66295i
\(431\) −1.69124e6 2.92932e6i −0.438544 0.759580i 0.559034 0.829145i \(-0.311172\pi\)
−0.997577 + 0.0695651i \(0.977839\pi\)
\(432\) 0 0
\(433\) −285266. −0.0731190 −0.0365595 0.999331i \(-0.511640\pi\)
−0.0365595 + 0.999331i \(0.511640\pi\)
\(434\) −6.74250e6 + 7.37125e6i −1.71829 + 1.87853i
\(435\) 0 0
\(436\) 2.34209e6 4.05662e6i 0.590048 1.02199i
\(437\) 2.20886e6 + 3.82585e6i 0.553304 + 0.958351i
\(438\) 0 0
\(439\) −2.17610e6 + 3.76911e6i −0.538911 + 0.933421i 0.460052 + 0.887892i \(0.347831\pi\)
−0.998963 + 0.0455294i \(0.985503\pi\)
\(440\) 9.12610e6 2.24726
\(441\) 0 0
\(442\) −5.03813e6 −1.22663
\(443\) −2.55280e6 + 4.42158e6i −0.618027 + 1.07045i 0.371819 + 0.928305i \(0.378734\pi\)
−0.989845 + 0.142148i \(0.954599\pi\)
\(444\) 0 0
\(445\) 489024. + 847015.i 0.117066 + 0.202764i
\(446\) 5.08014e6 8.79906e6i 1.20931 2.09459i
\(447\) 0 0
\(448\) 4.32729e6 4.73082e6i 1.01864 1.11363i
\(449\) −3.04163e6 −0.712016 −0.356008 0.934483i \(-0.615862\pi\)
−0.356008 + 0.934483i \(0.615862\pi\)
\(450\) 0 0
\(451\) 68906.7 + 119350.i 0.0159522 + 0.0276300i
\(452\) −5.03430e6 8.71966e6i −1.15903 2.00749i
\(453\) 0 0
\(454\) −5.19305e6 −1.18245
\(455\) −1.49604e6 4.73020e6i −0.338777 1.07115i
\(456\) 0 0
\(457\) 872162. 1.51063e6i 0.195347 0.338351i −0.751667 0.659542i \(-0.770750\pi\)
0.947014 + 0.321192i \(0.104083\pi\)
\(458\) −2.45556e6 4.25316e6i −0.547000 0.947432i
\(459\) 0 0
\(460\) 6.50295e6 1.12634e7i 1.43290 2.48186i
\(461\) 6.85701e6 1.50273 0.751367 0.659884i \(-0.229395\pi\)
0.751367 + 0.659884i \(0.229395\pi\)
\(462\) 0 0
\(463\) 5.13844e6 1.11398 0.556992 0.830518i \(-0.311955\pi\)
0.556992 + 0.830518i \(0.311955\pi\)
\(464\) −125675. + 217676.i −0.0270991 + 0.0469370i
\(465\) 0 0
\(466\) −1.70980e6 2.96147e6i −0.364738 0.631746i
\(467\) −2.29085e6 + 3.96788e6i −0.486077 + 0.841910i −0.999872 0.0160029i \(-0.994906\pi\)
0.513795 + 0.857913i \(0.328239\pi\)
\(468\) 0 0
\(469\) −2.50848e6 553784.i −0.526597 0.116254i
\(470\) 1.10091e7 2.29883
\(471\) 0 0
\(472\) −1.17516e6 2.03543e6i −0.242795 0.420534i
\(473\) 4.90660e6 + 8.49848e6i 1.00839 + 1.74658i
\(474\) 0 0
\(475\) 2.76450e6 0.562190
\(476\) 2.20839e6 + 6.98253e6i 0.446743 + 1.41252i
\(477\) 0 0
\(478\) 1.74577e6 3.02376e6i 0.349476 0.605310i
\(479\) −144261. 249868.i −0.0287284 0.0497590i 0.851304 0.524673i \(-0.175812\pi\)
−0.880032 + 0.474914i \(0.842479\pi\)
\(480\) 0 0
\(481\) 749223. 1.29769e6i 0.147655 0.255746i
\(482\) −1.60705e7 −3.15074
\(483\) 0 0
\(484\) 8.60702e6 1.67009
\(485\) 463352. 802549.i 0.0894451 0.154923i
\(486\) 0 0
\(487\) 3.90842e6 + 6.76959e6i 0.746757 + 1.29342i 0.949369 + 0.314162i \(0.101723\pi\)
−0.202613 + 0.979259i \(0.564943\pi\)
\(488\) −108275. + 187538.i −0.0205816 + 0.0356484i
\(489\) 0 0
\(490\) −9.26124e6 + 6.50929e6i −1.74253 + 1.22474i
\(491\) −3.14467e6 −0.588669 −0.294335 0.955702i \(-0.595098\pi\)
−0.294335 + 0.955702i \(0.595098\pi\)
\(492\) 0 0
\(493\) 378875. + 656232.i 0.0702068 + 0.121602i
\(494\) −3.42787e6 5.93724e6i −0.631985 1.09463i
\(495\) 0 0
\(496\) 2.73763e6 0.499656
\(497\) 5.43597e6 5.94289e6i 0.987157 1.07921i
\(498\) 0 0
\(499\) −3.36281e6 + 5.82456e6i −0.604577 + 1.04716i 0.387541 + 0.921852i \(0.373324\pi\)
−0.992118 + 0.125305i \(0.960009\pi\)
\(500\) 2.22590e6 + 3.85537e6i 0.398181 + 0.689670i
\(501\) 0 0
\(502\) 272936. 472738.i 0.0483394 0.0837262i
\(503\) 9.45056e6 1.66547 0.832737 0.553669i \(-0.186773\pi\)
0.832737 + 0.553669i \(0.186773\pi\)
\(504\) 0 0
\(505\) −1.80348e6 −0.314690
\(506\) 8.49639e6 1.47162e7i 1.47522 2.55516i
\(507\) 0 0
\(508\) 4.03506e6 + 6.98892e6i 0.693730 + 1.20158i
\(509\) −4.41851e6 + 7.65308e6i −0.755930 + 1.30931i 0.188981 + 0.981981i \(0.439481\pi\)
−0.944911 + 0.327328i \(0.893852\pi\)
\(510\) 0 0
\(511\) 3.43191e6 + 757645.i 0.581411 + 0.128355i
\(512\) −3.80044e6 −0.640707
\(513\) 0 0
\(514\) −1.46406e6 2.53583e6i −0.244429 0.423363i
\(515\) 5.76534e6 + 9.98585e6i 0.957870 + 1.65908i
\(516\) 0 0
\(517\) 9.16344e6 1.50776
\(518\) −3.33865e6 737057.i −0.546697 0.120692i
\(519\) 0 0
\(520\) −4.34246e6 + 7.52136e6i −0.704251 + 1.21980i
\(521\) 347492. + 601874.i 0.0560855 + 0.0971430i 0.892705 0.450641i \(-0.148805\pi\)
−0.836619 + 0.547784i \(0.815471\pi\)
\(522\) 0 0
\(523\) −1.79105e6 + 3.10219e6i −0.286321 + 0.495923i −0.972929 0.231105i \(-0.925766\pi\)
0.686607 + 0.727028i \(0.259099\pi\)
\(524\) −2.93710e6 −0.467294
\(525\) 0 0
\(526\) −8.11252e6 −1.27847
\(527\) 4.12660e6 7.14748e6i 0.647240 1.12105i
\(528\) 0 0
\(529\) −1.99208e6 3.45038e6i −0.309504 0.536077i
\(530\) −9.98222e6 + 1.72897e7i −1.54361 + 2.67361i
\(531\) 0 0
\(532\) −6.72609e6 + 7.35331e6i −1.03035 + 1.12643i
\(533\) −131151. −0.0199965
\(534\) 0 0
\(535\) −3.38473e6 5.86253e6i −0.511258 0.885525i
\(536\) 2.24852e6 + 3.89456e6i 0.338053 + 0.585526i
\(537\) 0 0
\(538\) 1.05231e7 1.56744
\(539\) −7.70860e6 + 5.41801e6i −1.14289 + 0.803282i
\(540\) 0 0
\(541\) 2.58423e6 4.47602e6i 0.379610 0.657504i −0.611395 0.791325i \(-0.709391\pi\)
0.991005 + 0.133821i \(0.0427248\pi\)
\(542\) −5.35277e6 9.27126e6i −0.782673 1.35563i
\(543\) 0 0
\(544\) −2.07675e6 + 3.59703e6i −0.300875 + 0.521131i
\(545\) −5.98174e6 −0.862653
\(546\) 0 0
\(547\) 8.47489e6 1.21106 0.605530 0.795822i \(-0.292961\pi\)
0.605530 + 0.795822i \(0.292961\pi\)
\(548\) 264281. 457748.i 0.0375936 0.0651141i
\(549\) 0 0
\(550\) −5.31685e6 9.20906e6i −0.749459 1.29810i
\(551\) −515562. + 892980.i −0.0723439 + 0.125303i
\(552\) 0 0
\(553\) −1.74699e6 5.52367e6i −0.242928 0.768095i
\(554\) −1.86671e7 −2.58407
\(555\) 0 0
\(556\) −5.14217e6 8.90649e6i −0.705438 1.22186i
\(557\) −5.21063e6 9.02508e6i −0.711627 1.23257i −0.964246 0.265009i \(-0.914625\pi\)
0.252619 0.967566i \(-0.418708\pi\)
\(558\) 0 0
\(559\) −9.33880e6 −1.26404
\(560\) 3.02921e6 + 668743.i 0.408187 + 0.0901134i
\(561\) 0 0
\(562\) 2.49921e6 4.32876e6i 0.333781 0.578126i
\(563\) −3.62039e6 6.27069e6i −0.481375 0.833767i 0.518396 0.855141i \(-0.326529\pi\)
−0.999772 + 0.0213739i \(0.993196\pi\)
\(564\) 0 0
\(565\) −6.42885e6 + 1.11351e7i −0.847251 + 1.46748i
\(566\) 2.46459e7 3.23373
\(567\) 0 0
\(568\) −1.40993e7 −1.83369
\(569\) 458268. 793743.i 0.0593388 0.102778i −0.834830 0.550508i \(-0.814434\pi\)
0.894169 + 0.447730i \(0.147767\pi\)
\(570\) 0 0
\(571\) −5.03538e6 8.72154e6i −0.646312 1.11944i −0.983997 0.178186i \(-0.942977\pi\)
0.337685 0.941259i \(-0.390356\pi\)
\(572\) −8.39990e6 + 1.45490e7i −1.07345 + 1.85928i
\(573\) 0 0
\(574\) 90239.2 + 285320.i 0.0114318 + 0.0361454i
\(575\) −6.52091e6 −0.822505
\(576\) 0 0
\(577\) −5.84987e6 1.01323e7i −0.731488 1.26697i −0.956247 0.292560i \(-0.905493\pi\)
0.224760 0.974414i \(-0.427840\pi\)
\(578\) 1.91752e6 + 3.32125e6i 0.238738 + 0.413506i
\(579\) 0 0
\(580\) 3.03567e6 0.374701
\(581\) 1.36558e6 1.49292e6i 0.167833 0.183484i
\(582\) 0 0
\(583\) −8.30871e6 + 1.43911e7i −1.01242 + 1.75357i
\(584\) −3.07626e6 5.32823e6i −0.373242 0.646474i
\(585\) 0 0
\(586\) 2.86373e6 4.96013e6i 0.344499 0.596690i
\(587\) 6.92367e6 0.829357 0.414678 0.909968i \(-0.363894\pi\)
0.414678 + 0.909968i \(0.363894\pi\)
\(588\) 0 0
\(589\) 1.12307e7 1.33389
\(590\) −3.48756e6 + 6.04062e6i −0.412469 + 0.714417i
\(591\) 0 0
\(592\) 468481. + 811432.i 0.0549398 + 0.0951586i
\(593\) 7.88850e6 1.36633e7i 0.921208 1.59558i 0.123660 0.992325i \(-0.460537\pi\)
0.797548 0.603255i \(-0.206130\pi\)
\(594\) 0 0
\(595\) 6.31207e6 6.90068e6i 0.730936 0.799097i
\(596\) 9.38041e6 1.08170
\(597\) 0 0
\(598\) 8.08565e6 + 1.40048e7i 0.924618 + 1.60148i
\(599\) 7.13541e6 + 1.23589e7i 0.812553 + 1.40738i 0.911072 + 0.412248i \(0.135256\pi\)
−0.0985183 + 0.995135i \(0.531410\pi\)
\(600\) 0 0
\(601\) 7.63222e6 0.861916 0.430958 0.902372i \(-0.358176\pi\)
0.430958 + 0.902372i \(0.358176\pi\)
\(602\) 6.42562e6 + 2.03167e7i 0.722643 + 2.28487i
\(603\) 0 0
\(604\) −1.05673e7 + 1.83031e7i −1.17862 + 2.04142i
\(605\) −5.49562e6 9.51869e6i −0.610419 1.05728i
\(606\) 0 0
\(607\) 1.78017e6 3.08335e6i 0.196106 0.339665i −0.751157 0.660124i \(-0.770504\pi\)
0.947262 + 0.320459i \(0.103837\pi\)
\(608\) −5.65194e6 −0.620067
\(609\) 0 0
\(610\) 642664. 0.0699294
\(611\) −4.36023e6 + 7.55214e6i −0.472505 + 0.818402i
\(612\) 0 0
\(613\) 6.86420e6 + 1.18891e7i 0.737800 + 1.27791i 0.953484 + 0.301445i \(0.0974688\pi\)
−0.215683 + 0.976463i \(0.569198\pi\)
\(614\) 6.33080e6 1.09653e7i 0.677700 1.17381i
\(615\) 0 0
\(616\) 1.61065e7 + 3.55576e6i 1.71021 + 0.377555i
\(617\) 6.51173e6 0.688626 0.344313 0.938855i \(-0.388112\pi\)
0.344313 + 0.938855i \(0.388112\pi\)
\(618\) 0 0
\(619\) −4.42555e6 7.66527e6i −0.464238 0.804083i 0.534929 0.844897i \(-0.320338\pi\)
−0.999167 + 0.0408136i \(0.987005\pi\)
\(620\) −1.65318e7 2.86339e7i −1.72719 2.99159i
\(621\) 0 0
\(622\) 3.12739e7 3.24121
\(623\) 533054. + 1.68542e6i 0.0550238 + 0.173976i
\(624\) 0 0
\(625\) 5.99884e6 1.03903e7i 0.614281 1.06397i
\(626\) 1.33181e7 + 2.30677e7i 1.35834 + 2.35271i
\(627\) 0 0
\(628\) −1.09741e6 + 1.90078e6i −0.111038 + 0.192323i
\(629\) 2.82467e6 0.284670
\(630\) 0 0
\(631\) −6.89663e6 −0.689546 −0.344773 0.938686i \(-0.612044\pi\)
−0.344773 + 0.938686i \(0.612044\pi\)
\(632\) −5.07088e6 + 8.78303e6i −0.504999 + 0.874685i
\(633\) 0 0
\(634\) −5.10992e6 8.85064e6i −0.504883 0.874483i
\(635\) 5.15280e6 8.92492e6i 0.507118 0.878355i
\(636\) 0 0
\(637\) −797329. 8.93116e6i −0.0778554 0.872086i
\(638\) 3.96623e6 0.385768
\(639\) 0 0
\(640\) 1.19147e7 + 2.06369e7i 1.14983 + 1.99157i
\(641\) −8.33473e6 1.44362e7i −0.801210 1.38774i −0.918820 0.394677i \(-0.870856\pi\)
0.117610 0.993060i \(-0.462477\pi\)
\(642\) 0 0
\(643\) −1.28697e7 −1.22756 −0.613779 0.789478i \(-0.710351\pi\)
−0.613779 + 0.789478i \(0.710351\pi\)
\(644\) 1.58655e7 1.73450e7i 1.50744 1.64801i
\(645\) 0 0
\(646\) 6.46177e6 1.11921e7i 0.609214 1.05519i
\(647\) −5.73656e6 9.93601e6i −0.538754 0.933150i −0.998971 0.0453435i \(-0.985562\pi\)
0.460217 0.887806i \(-0.347772\pi\)
\(648\) 0 0
\(649\) −2.90287e6 + 5.02792e6i −0.270530 + 0.468572i
\(650\) 1.01196e7 0.939467
\(651\) 0 0
\(652\) −2.68445e7 −2.47307
\(653\) −6.59005e6 + 1.14143e7i −0.604791 + 1.04753i 0.387293 + 0.921957i \(0.373410\pi\)
−0.992084 + 0.125573i \(0.959923\pi\)
\(654\) 0 0
\(655\) 1.87535e6 + 3.24820e6i 0.170797 + 0.295829i
\(656\) 41003.6 71020.4i 0.00372017 0.00644352i
\(657\) 0 0
\(658\) 1.94298e7 + 4.28943e6i 1.74946 + 0.386220i
\(659\) 1.13068e7 1.01421 0.507104 0.861885i \(-0.330716\pi\)
0.507104 + 0.861885i \(0.330716\pi\)
\(660\) 0 0
\(661\) −1.10160e6 1.90802e6i −0.0980661 0.169856i 0.812818 0.582518i \(-0.197932\pi\)
−0.910884 + 0.412662i \(0.864599\pi\)
\(662\) −6.12945e6 1.06165e7i −0.543596 0.941536i
\(663\) 0 0
\(664\) −3.54192e6 −0.311758
\(665\) 1.24268e7 + 2.74341e6i 1.08970 + 0.240567i
\(666\) 0 0
\(667\) 1.21611e6 2.10636e6i 0.105842 0.183323i
\(668\) 1.11759e6 + 1.93572e6i 0.0969038 + 0.167842i
\(669\) 0 0
\(670\) 6.67303e6 1.15580e7i 0.574296 0.994710i
\(671\) 534922. 0.0458653
\(672\) 0 0
\(673\) −1.89787e7 −1.61521 −0.807606 0.589723i \(-0.799237\pi\)
−0.807606 + 0.589723i \(0.799237\pi\)
\(674\) 1.48837e7 2.57793e7i 1.26200 2.18586i
\(675\) 0 0
\(676\) 2.43387e6 + 4.21558e6i 0.204847 + 0.354806i
\(677\) −9.82377e6 + 1.70153e7i −0.823771 + 1.42681i 0.0790842 + 0.996868i \(0.474800\pi\)
−0.902855 + 0.429945i \(0.858533\pi\)
\(678\) 0 0
\(679\) 1.13046e6 1.23587e6i 0.0940977 0.102873i
\(680\) −1.63717e7 −1.35775
\(681\) 0 0
\(682\) −2.15995e7 3.74115e7i −1.77821 3.07995i
\(683\) 8.13523e6 + 1.40906e7i 0.667295 + 1.15579i 0.978658 + 0.205498i \(0.0658813\pi\)
−0.311363 + 0.950291i \(0.600785\pi\)
\(684\) 0 0
\(685\) −674978. −0.0549621
\(686\) −1.88812e7 + 7.87973e6i −1.53186 + 0.639295i
\(687\) 0 0
\(688\) 2.91972e6 5.05711e6i 0.235164 0.407316i
\(689\) −7.90704e6 1.36954e7i −0.634550 1.09907i
\(690\) 0 0
\(691\) −9.72335e6 + 1.68413e7i −0.774677 + 1.34178i 0.160299 + 0.987069i \(0.448754\pi\)
−0.934976 + 0.354712i \(0.884579\pi\)
\(692\) −2.71514e6 −0.215539
\(693\) 0 0
\(694\) 1.61122e7 1.26986
\(695\) −6.56659e6 + 1.13737e7i −0.515677 + 0.893179i
\(696\) 0 0
\(697\) −123614. 214106.i −0.00963800 0.0166935i
\(698\) 1.38886e7 2.40558e7i 1.07900 1.86888i
\(699\) 0 0
\(700\) −4.43579e6 1.40252e7i −0.342157 1.08184i
\(701\) −1.49625e7 −1.15003 −0.575014 0.818144i \(-0.695003\pi\)
−0.575014 + 0.818144i \(0.695003\pi\)
\(702\) 0 0
\(703\) 1.92187e6 + 3.32877e6i 0.146668 + 0.254036i
\(704\) 1.38624e7 + 2.40104e7i 1.05416 + 1.82586i
\(705\) 0 0
\(706\) −3.53979e7 −2.67280
\(707\) −3.18293e6 702680.i −0.239485 0.0528700i
\(708\) 0 0
\(709\) −793193. + 1.37385e6i −0.0592603 + 0.102642i −0.894134 0.447800i \(-0.852208\pi\)
0.834873 + 0.550442i \(0.185541\pi\)
\(710\) 2.09215e7 + 3.62372e7i 1.55757 + 2.69779i
\(711\) 0 0
\(712\) 1.54726e6 2.67994e6i 0.114384 0.198118i
\(713\) −2.64910e7 −1.95152
\(714\) 0 0
\(715\) 2.14535e7 1.56940
\(716\) −4.01362e6 + 6.95179e6i −0.292586 + 0.506774i
\(717\) 0 0
\(718\) 9.06061e6 + 1.56934e7i 0.655913 + 1.13607i
\(719\) −9.08376e6 + 1.57335e7i −0.655305 + 1.13502i 0.326512 + 0.945193i \(0.394127\pi\)
−0.981817 + 0.189829i \(0.939207\pi\)
\(720\) 0 0
\(721\) 6.28442e6 + 1.98702e7i 0.450222 + 1.42352i
\(722\) −5.66429e6 −0.404392
\(723\) 0 0
\(724\) 2.16942e6 + 3.75754e6i 0.153814 + 0.266414i
\(725\) −761013. 1.31811e6i −0.0537709 0.0931339i
\(726\) 0 0
\(727\) 1.26903e7 0.890506 0.445253 0.895405i \(-0.353114\pi\)
0.445253 + 0.895405i \(0.353114\pi\)
\(728\) −1.05945e7 + 1.15824e7i −0.740884 + 0.809973i
\(729\) 0 0
\(730\) −9.12953e6 + 1.58128e7i −0.634076 + 1.09825i
\(731\) −8.80214e6 1.52458e7i −0.609249 1.05525i
\(732\) 0 0
\(733\) 1.55701e6 2.69681e6i 0.107036 0.185392i −0.807532 0.589824i \(-0.799197\pi\)
0.914568 + 0.404432i \(0.132531\pi\)
\(734\) 2.22298e7 1.52298
\(735\) 0 0
\(736\) 1.33318e7 0.907182
\(737\) 5.55430e6 9.62033e6i 0.376670 0.652411i
\(738\) 0 0
\(739\) −4.54950e6 7.87996e6i −0.306445 0.530778i 0.671137 0.741333i \(-0.265806\pi\)
−0.977582 + 0.210555i \(0.932473\pi\)
\(740\) 5.65804e6 9.80002e6i 0.379828 0.657881i
\(741\) 0 0
\(742\) −2.43540e7 + 2.66250e7i −1.62390 + 1.77534i
\(743\) 8.79218e6 0.584285 0.292142 0.956375i \(-0.405632\pi\)
0.292142 + 0.956375i \(0.405632\pi\)
\(744\) 0 0
\(745\) −5.98943e6 1.03740e7i −0.395362 0.684787i
\(746\) −1.66120e7 2.87729e7i −1.09289 1.89294i
\(747\) 0 0
\(748\) −3.16687e7 −2.06955
\(749\) −3.68948e6 1.16655e7i −0.240304 0.759798i
\(750\) 0 0
\(751\) 1.40459e7 2.43282e7i 0.908759 1.57402i 0.0929698 0.995669i \(-0.470364\pi\)
0.815790 0.578349i \(-0.196303\pi\)
\(752\) −2.72640e6 4.72226e6i −0.175811 0.304513i
\(753\) 0 0
\(754\) −1.88725e6 + 3.26881e6i −0.120893 + 0.209393i
\(755\) 2.69891e7 1.72314
\(756\) 0 0
\(757\) −4.18815e6 −0.265634 −0.132817 0.991141i \(-0.542402\pi\)
−0.132817 + 0.991141i \(0.542402\pi\)
\(758\) −8.44369e6 + 1.46249e7i −0.533776 + 0.924527i
\(759\) 0 0
\(760\) −1.11390e7 1.92934e7i −0.699541 1.21164i
\(761\) −196591. + 340506.i −0.0123056 + 0.0213139i −0.872113 0.489305i \(-0.837250\pi\)
0.859807 + 0.510619i \(0.170584\pi\)
\(762\) 0 0
\(763\) −1.05571e7 2.33063e6i −0.656497 0.144932i
\(764\) −1.52812e7 −0.947159
\(765\) 0 0
\(766\) 1.22451e7 + 2.12091e7i 0.754031 + 1.30602i
\(767\) −2.76254e6 4.78486e6i −0.169559 0.293684i
\(768\) 0 0
\(769\) 1.57517e7 0.960530 0.480265 0.877124i \(-0.340541\pi\)
0.480265 + 0.877124i \(0.340541\pi\)
\(770\) −1.47612e7 4.66722e7i −0.897211 2.83682i
\(771\) 0 0
\(772\) 450306. 779952.i 0.0271934 0.0471004i
\(773\) 1.44236e6 + 2.49824e6i 0.0868210 + 0.150378i 0.906166 0.422923i \(-0.138996\pi\)
−0.819345 + 0.573301i \(0.805663\pi\)
\(774\) 0