LMFDB - Embedded newform 16.6.e.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, 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:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.7
Root			$0.562915 - 3.96019i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.6.e.a.13.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.52311 - 3.39728i) q^{2} +(3.84023 - 3.84023i) q^{3} +(8.91700 - 30.7325i) q^{4} +(8.73514 + 8.73514i) q^{5} +(4.32344 - 30.4161i) q^{6} +28.0117i q^{7} +(-64.0743 - 169.300i) q^{8} +213.505i q^{9} +O(q^{10})$	\(q+(4.52311 - 3.39728i) q^{2} +(3.84023 - 3.84023i) q^{3} +(8.91700 - 30.7325i) q^{4} +(8.73514 + 8.73514i) q^{5} +(4.32344 - 30.4161i) q^{6} +28.0117i q^{7} +(-64.0743 - 169.300i) q^{8} +213.505i q^{9} +(69.1857 + 9.83427i) q^{10} +(191.858 + 191.858i) q^{11} +(-83.7765 - 152.263i) q^{12} +(-562.527 + 562.527i) q^{13} +(95.1637 + 126.700i) q^{14} +67.0898 q^{15} +(-864.974 - 548.084i) q^{16} -663.401 q^{17} +(725.337 + 965.707i) q^{18} +(1793.28 - 1793.28i) q^{19} +(346.344 - 190.561i) q^{20} +(107.571 + 107.571i) q^{21} +(1519.59 + 216.000i) q^{22} -2878.23i q^{23} +(-896.210 - 404.090i) q^{24} -2972.39i q^{25} +(-633.309 + 4455.43i) q^{26} +(1753.08 + 1753.08i) q^{27} +(860.871 + 249.781i) q^{28} +(-3909.86 + 3909.86i) q^{29} +(303.454 - 227.923i) q^{30} -4451.90 q^{31} +(-5774.36 + 459.517i) q^{32} +1473.56 q^{33} +(-3000.63 + 2253.76i) q^{34} +(-244.686 + 244.686i) q^{35} +(6561.55 + 1903.83i) q^{36} +(6043.41 + 6043.41i) q^{37} +(2018.92 - 14203.4i) q^{38} +4320.46i q^{39} +(919.161 - 2038.56i) q^{40} -12387.3i q^{41} +(852.007 + 121.107i) q^{42} +(10658.7 + 10658.7i) q^{43} +(7607.09 - 4185.48i) q^{44} +(-1865.00 + 1865.00i) q^{45} +(-9778.14 - 13018.5i) q^{46} -23383.1 q^{47} +(-5426.46 + 1216.93i) q^{48} +16022.3 q^{49} +(-10098.1 - 13444.5i) q^{50} +(-2547.61 + 2547.61i) q^{51} +(12271.8 + 22303.9i) q^{52} +(656.507 + 656.507i) q^{53} +(13885.1 + 1973.67i) q^{54} +3351.82i q^{55} +(4742.39 - 1794.83i) q^{56} -13773.2i q^{57} +(-4401.83 + 30967.6i) q^{58} +(-5988.17 - 5988.17i) q^{59} +(598.240 - 2061.84i) q^{60} +(6863.09 - 6863.09i) q^{61} +(-20136.4 + 15124.3i) q^{62} -5980.66 q^{63} +(-24557.0 + 21695.6i) q^{64} -9827.51 q^{65} +(6665.06 - 5006.09i) q^{66} +(13054.5 - 13054.5i) q^{67} +(-5915.54 + 20388.0i) q^{68} +(-11053.1 - 11053.1i) q^{69} +(-275.475 + 1938.01i) q^{70} -27879.6i q^{71} +(36146.4 - 13680.2i) q^{72} +20553.5i q^{73} +(47866.1 + 6803.84i) q^{74} +(-11414.7 - 11414.7i) q^{75} +(-39121.2 - 71102.5i) q^{76} +(-5374.28 + 5374.28i) q^{77} +(14677.8 + 19541.9i) q^{78} +103184. q^{79} +(-2768.08 - 12343.3i) q^{80} -38417.3 q^{81} +(-42083.2 - 56029.3i) q^{82} +(-8215.97 + 8215.97i) q^{83} +(4265.15 - 2346.73i) q^{84} +(-5794.90 - 5794.90i) q^{85} +(84420.9 + 11999.9i) q^{86} +30029.5i q^{87} +(20188.4 - 44774.8i) q^{88} +134430. i q^{89} +(-2099.67 + 14771.5i) q^{90} +(-15757.4 - 15757.4i) q^{91} +(-88455.2 - 25665.2i) q^{92} +(-17096.3 + 17096.3i) q^{93} +(-105764. + 79439.0i) q^{94} +31329.0 q^{95} +(-20410.2 + 23939.5i) q^{96} -53614.2 q^{97} +(72470.8 - 54432.4i) q^{98} +(-40962.8 + 40962.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.52311	−	3.39728i	0.799580	−	0.600560i
$2$	4.52311	−	3.39728i	0.799580	−	0.600560i
$3$	3.84023	−	3.84023i	0.246351	−	0.246351i	−0.573120	−	0.819471i	$-0.694267\pi$
$3$	3.84023	−	3.84023i	0.246351	−	0.246351i	0.819471	+	0.573120i	$0.194267\pi$
$4$	8.91700	−	30.7325i	0.278656	−	0.960391i
$5$	8.73514	+	8.73514i	0.156259	+	0.156259i	0.780907	−	0.624648i	$-0.214757\pi$
$5$	8.73514	+	8.73514i	0.156259	+	0.156259i	−0.624648	+	0.780907i	$0.714757\pi$
$6$	4.32344	−	30.4161i	0.0490288	−	0.344925i
$7$			28.0117i			0.216070i	0.994147	+	0.108035i	$0.0344559\pi$
$7$			28.0117i			0.216070i	−0.994147	+	0.108035i	$0.965544\pi$
$8$	−64.0743	−	169.300i	−0.353964	−	0.935259i
$9$			213.505i			0.878623i
$10$	69.1857	+	9.83427i	0.218784	+	0.0310987i
$11$	191.858	+	191.858i	0.478078	+	0.478078i	0.904517	−	0.426439i	$-0.140232\pi$
$11$	191.858	+	191.858i	0.478078	+	0.478078i	−0.426439	+	0.904517i	$0.640232\pi$
$12$	−83.7765	−	152.263i	−0.167946	−	0.305240i
$13$	−562.527	+	562.527i	−0.923177	+	0.923177i	−0.997253	−	0.0740753i	$-0.976399\pi$
$13$	−562.527	+	562.527i	−0.923177	+	0.923177i	0.0740753	+	0.997253i	$0.476399\pi$
$14$	95.1637	+	126.700i	0.129763	+	0.172765i
$15$	67.0898			0.0769890
$16$	−864.974	−	548.084i	−0.844701	−	0.535238i
$17$	−663.401			−0.556741			−0.278371	−	0.960474i	$-0.589794\pi$
$17$	−663.401			−0.556741			−0.278371	+	0.960474i	$0.589794\pi$
$18$	725.337	+	965.707i	0.527665	+	0.702529i
$19$	1793.28	−	1793.28i	1.13963	−	1.13963i	0.151111	−	0.988517i	$-0.451715\pi$
$19$	1793.28	−	1793.28i	1.13963	−	1.13963i	0.988517	−	0.151111i	$-0.0482851\pi$
$20$	346.344	−	190.561i	0.193612	−	0.106527i
$21$	107.571	+	107.571i	0.0532291	+	0.0532291i
$22$	1519.59	+	216.000i	0.669376	+	0.0951472i
$23$		−	2878.23i		−	1.13450i	−0.823545	−	0.567252i	$-0.808007\pi$
$23$		−	2878.23i		−	1.13450i	0.823545	−	0.567252i	$-0.191993\pi$
$24$	−896.210	−	404.090i	−0.317601	−	0.143202i
$25$		−	2972.39i		−	0.951166i
$26$	−633.309	+	4455.43i	−0.183731	+	1.29258i
$27$	1753.08	+	1753.08i	0.462800	+	0.462800i
$28$	860.871	+	249.781i	0.207512	+	0.0602093i
$29$	−3909.86	+	3909.86i	−0.863309	+	0.863309i	−0.991721	−	0.128412i	$-0.959012\pi$
$29$	−3909.86	+	3909.86i	−0.863309	+	0.863309i	0.128412	+	0.991721i	$0.459012\pi$
$30$	303.454	−	227.923i	0.0615588	−	0.0462365i
$31$	−4451.90			−0.832034			−0.416017	−	0.909357i	$-0.636574\pi$
$31$	−4451.90			−0.832034			−0.416017	+	0.909357i	$0.636574\pi$
$32$	−5774.36	+	459.517i	−0.996849	+	0.0793280i
$33$	1473.56			0.235550
$34$	−3000.63	+	2253.76i	−0.445159	+	0.334356i
$35$	−244.686	+	244.686i	−0.0337629	+	0.0337629i
$36$	6561.55	+	1903.83i	0.843821	+	0.244834i
$37$	6043.41	+	6043.41i	0.725734	+	0.725734i	0.969767	−	0.244033i	$-0.0784705\pi$
$37$	6043.41	+	6043.41i	0.725734	+	0.725734i	−0.244033	+	0.969767i	$0.578471\pi$
$38$	2018.92	−	14203.4i	0.226809	−	1.59564i
$39$			4320.46i			0.454851i
$40$	919.161	−	2038.56i	0.0908325	−	0.201453i
$41$		−	12387.3i		−	1.15085i	−0.817855	−	0.575425i	$-0.804837\pi$
$41$		−	12387.3i		−	1.15085i	0.817855	−	0.575425i	$-0.195163\pi$
$42$	852.007	+	121.107i	0.0745281	+	0.0105937i
$43$	10658.7	+	10658.7i	0.879088	+	0.879088i	0.993440	−	0.114352i	$-0.0364792\pi$
$43$	10658.7	+	10658.7i	0.879088	+	0.879088i	−0.114352	+	0.993440i	$0.536479\pi$
$44$	7607.09	−	4185.48i	0.592361	−	0.325922i
$45$	−1865.00	+	1865.00i	−0.137293	+	0.137293i
$46$	−9778.14	−	13018.5i	−0.681337	−	0.907126i
$47$	−23383.1			−1.54404			−0.772019	−	0.635599i	$-0.780753\pi$
$47$	−23383.1			−1.54404			−0.772019	+	0.635599i	$0.780753\pi$
$48$	−5426.46	+	1216.93i	−0.339949	+	0.0762365i
$49$	16022.3			0.953314
$50$	−10098.1	−	13444.5i	−0.571232	−	0.760534i
$51$	−2547.61	+	2547.61i	−0.137154	+	0.137154i
$52$	12271.8	+	22303.9i	0.629362	+	1.14386i
$53$	656.507	+	656.507i	0.0321033	+	0.0321033i	0.722976	−	0.690873i	$-0.242774\pi$
$53$	656.507	+	656.507i	0.0321033	+	0.0321033i	−0.690873	+	0.722976i	$0.742774\pi$
$54$	13885.1	+	1973.67i	0.647985	+	0.0921066i
$55$			3351.82i			0.149408i
$56$	4742.39	−	1794.83i	0.202082	−	0.0764811i
$57$		−	13773.2i		−	0.561496i
$58$	−4401.83	+	30967.6i	−0.171816	+	1.20875i
$59$	−5988.17	−	5988.17i	−0.223957	−	0.223957i	0.586206	−	0.810162i	$-0.300621\pi$
$59$	−5988.17	−	5988.17i	−0.223957	−	0.223957i	−0.810162	+	0.586206i	$0.800621\pi$
$60$	598.240	−	2061.84i	0.0214535	−	0.0739395i
$61$	6863.09	−	6863.09i	0.236154	−	0.236154i	−0.579101	−	0.815255i	$-0.696596\pi$
$61$	6863.09	−	6863.09i	0.236154	−	0.236154i	0.815255	+	0.579101i	$0.196596\pi$
$62$	−20136.4	+	15124.3i	−0.665278	+	0.499686i
$63$	−5980.66			−0.189844
$64$	−24557.0	+	21695.6i	−0.749419	+	0.662096i
$65$	−9827.51			−0.288509
$66$	6665.06	−	5006.09i	0.188341	−	0.141462i
$67$	13054.5	−	13054.5i	0.355281	−	0.355281i	−0.506789	−	0.862070i	$-0.669168\pi$
$67$	13054.5	−	13054.5i	0.355281	−	0.355281i	0.862070	+	0.506789i	$0.169168\pi$
$68$	−5915.54	+	20388.0i	−0.155139	+	0.534689i
$69$	−11053.1	−	11053.1i	−0.279486	−	0.279486i
$70$	−275.475	+	1938.01i	−0.00671950	+	0.0472728i
$71$		−	27879.6i		−	0.656357i	−0.944616	−	0.328179i	$-0.893565\pi$
$71$		−	27879.6i		−	0.656357i	0.944616	−	0.328179i	$-0.106435\pi$
$72$	36146.4	−	13680.2i	0.821740	−	0.311001i
$73$			20553.5i			0.451419i	0.974195	+	0.225709i	$0.0724700\pi$
$73$			20553.5i			0.451419i	−0.974195	+	0.225709i	$0.927530\pi$
$74$	47866.1	+	6803.84i	1.01613	+	0.144436i
$75$	−11414.7	−	11414.7i	−0.234320	−	0.234320i
$76$	−39121.2	−	71102.5i	−0.776924	−	1.41205i
$77$	−5374.28	+	5374.28i	−0.103298	+	0.103298i
$78$	14677.8	+	19541.9i	0.273165	+	0.363690i
$79$	103184.			1.86014			0.930071	−	0.367380i	$-0.119745\pi$
$79$	103184.			1.86014			0.930071	+	0.367380i	$0.119745\pi$
$80$	−2768.08	−	12343.3i	−0.0483564	−	0.215628i
$81$	−38417.3			−0.650601
$82$	−42083.2	−	56029.3i	−0.691154	−	0.920196i
$83$	−8215.97	+	8215.97i	−0.130907	+	0.130907i	−0.769524	−	0.638617i	$-0.779507\pi$
$83$	−8215.97	+	8215.97i	−0.130907	+	0.130907i	0.638617	+	0.769524i	$0.279507\pi$
$84$	4265.15	−	2346.73i	0.0659533	−	0.0362881i
$85$	−5794.90	−	5794.90i	−0.0869958	−	0.0869958i
$86$	84420.9	+	11999.9i	1.23085	+	0.174956i
$87$			30029.5i			0.425353i
$88$	20188.4	−	44774.8i	0.277904	−	0.616349i
$89$			134430.i			1.79896i	0.436961	+	0.899480i	$0.356055\pi$
$89$			134430.i			1.79896i	−0.436961	+	0.899480i	$0.643945\pi$
$90$	−2099.67	+	14771.5i	−0.0273240	+	0.192229i
$91$	−15757.4	−	15757.4i	−0.199471	−	0.199471i
$92$	−88455.2	−	25665.2i	−1.08957	−	0.316136i
$93$	−17096.3	+	17096.3i	−0.204972	+	0.204972i
$94$	−105764.	+	79439.0i	−1.23458	+	0.927287i
$95$	31329.0			0.356154
$96$	−20410.2	+	23939.5i	−0.226032	+	0.265117i
$97$	−53614.2			−0.578563			−0.289282	−	0.957244i	$-0.593416\pi$
$97$	−53614.2			−0.578563			−0.289282	+	0.957244i	$0.593416\pi$
$98$	72470.8	−	54432.4i	0.762250	−	0.572522i
$99$	−40962.8	+	40962.8i	−0.420050	+	0.420050i
$100$	−91349.1	−	26504.8i	−0.913491	−	0.265048i
$101$	6782.61	+	6782.61i	0.0661596	+	0.0661596i	0.739412	−	0.673253i	$-0.235103\pi$
$101$	6782.61	+	6782.61i	0.0661596	+	0.0661596i	−0.673253	+	0.739412i	$0.735103\pi$
$102$	−2868.17	+	20178.0i	−0.0272964	+	0.192034i
$103$			23843.1i			0.221447i	0.993851	+	0.110724i	$0.0353169\pi$
$103$			23843.1i			0.221447i	−0.993851	+	0.110724i	$0.964683\pi$
$104$	131279.	+	59192.3i	1.19018	+	0.536638i
$105$			1879.30i			0.0166350i
$106$	5199.79	+	739.115i	0.0449491	+	0.00638921i
$107$	−69846.1	−	69846.1i	−0.589770	−	0.589770i	0.347799	−	0.937569i	$-0.386929\pi$
$107$	−69846.1	−	69846.1i	−0.589770	−	0.589770i	−0.937569	+	0.347799i	$0.886929\pi$
$108$	69508.9	−	38244.4i	0.573431	−	0.315507i
$109$	140543.	−	140543.i	1.13304	−	1.13304i	0.143365	−	0.989670i	$-0.454208\pi$
$109$	140543.	−	140543.i	1.13304	−	1.13304i	0.989670	−	0.143365i	$-0.0457924\pi$
$110$	11387.1	+	15160.6i	0.0897283	+	0.119464i
$111$	46416.1			0.357570
$112$	15352.8	−	24229.4i	0.115649	−	0.182515i
$113$	95402.3			0.702850			0.351425	−	0.936216i	$-0.385697\pi$
$113$	95402.3			0.702850			0.351425	+	0.936216i	$0.385697\pi$
$114$	−46791.3	−	62297.5i	−0.337212	−	0.448961i
$115$	25141.7	−	25141.7i	0.177276	−	0.177276i
$116$	85295.6	+	155024.i	0.588547	+	1.06968i
$117$	−120103.	−	120103.i	−0.811125	−	0.811125i
$118$	−47428.6	−	6741.65i	−0.313571	−	0.0445719i
$119$		−	18583.0i		−	0.120295i
$120$	−4298.74	−	11358.3i	−0.0272513	−	0.0720046i
$121$		−	87431.8i		−	0.542883i
$122$	7726.67	−	54358.3i	0.0469995	−	0.330649i
$123$	−47570.2	−	47570.2i	−0.283513	−	0.283513i
$124$	−39697.6	+	136818.i	−0.231851	+	0.799078i
$125$	53261.6	−	53261.6i	0.304887	−	0.304887i
$126$	−27051.1	+	20318.0i	−0.151796	+	0.114013i
$127$	−115026.			−0.632829			−0.316415	−	0.948621i	$-0.602479\pi$
$127$	−115026.			−0.632829			−0.316415	+	0.948621i	$0.602479\pi$
$128$	−37367.9	+	181558.i	−0.201592	+	0.979470i
$129$	81863.5			0.433128
$130$	−44450.9	+	33386.8i	−0.230686	+	0.173267i
$131$	−117580.	+	117580.i	−0.598625	+	0.598625i	−0.939946	−	0.341322i	$-0.889125\pi$
$131$	−117580.	+	117580.i	−0.598625	+	0.598625i	0.341322	+	0.939946i	$0.389125\pi$
$132$	13139.7	−	45286.1i	0.0656374	−	0.226220i
$133$	50232.8	+	50232.8i	0.246240	+	0.246240i
$134$	14697.1	−	103396.i	0.0707082	−	0.497443i
$135$			30626.9i			0.144633i
$136$	42507.0	+	112314.i	0.197066	+	0.520697i
$137$		−	25473.5i		−	0.115954i	−0.998318	−	0.0579772i	$-0.981535\pi$
$137$		−	25473.5i		−	0.115954i	0.998318	−	0.0579772i	$-0.0184651\pi$
$138$	−87544.4	−	12443.8i	−0.391319	−	0.0556233i
$139$	191375.	+	191375.i	0.840132	+	0.840132i	0.988876	−	0.148744i	$-0.0475229\pi$
$139$	191375.	+	191375.i	0.840132	+	0.840132i	−0.148744	+	0.988876i	$0.547523\pi$
$140$	5337.96	+	9701.70i	0.0230173	+	0.0418338i
$141$	−89796.5	+	89796.5i	−0.380375	+	0.380375i
$142$	−94714.7	−	126102.i	−0.394182	−	0.524810i
$143$	−215851.			−0.882702
$144$	117019.	−	184677.i	0.470272	−	0.742174i
$145$	−68306.3			−0.269799
$146$	69826.1	+	92965.9i	0.271104	+	0.360945i
$147$	61529.4	−	61529.4i	0.234849	−	0.234849i
$148$	239618.	−	131840.i	0.899219	−	0.494758i
$149$	238914.	+	238914.i	0.881610	+	0.881610i	0.993698	−	0.112088i	$-0.0357540\pi$
$149$	238914.	+	238914.i	0.881610	+	0.881610i	−0.112088	+	0.993698i	$0.535754\pi$
$150$	−90408.6	−	12851.0i	−0.328081	−	0.0466345i
$151$			259983.i			0.927902i	0.885861	+	0.463951i	$0.153569\pi$
$151$			259983.i			0.927902i	−0.885861	+	0.463951i	$0.846431\pi$
$152$	−418504.	−	188699.i	−1.46923	−	0.662460i
$153$		−	141640.i		−	0.489166i
$154$	−6050.52	+	42566.4i	−0.0205585	+	0.144632i
$155$	−38887.9	−	38887.9i	−0.130013	−	0.130013i
$156$	132779.	+	38525.6i	0.436834	+	0.126747i
$157$	−208630.	+	208630.i	−0.675505	+	0.675505i	−0.958980	−	0.283475i	$-0.908513\pi$
$157$	−208630.	+	208630.i	−0.675505	+	0.675505i	0.283475	+	0.958980i	$0.408513\pi$
$158$	466714.	−	350546.i	1.48733	−	1.11713i
$159$	5042.27			0.0158173
$160$	−54453.8	−	46425.9i	−0.168162	−	0.143371i
$161$	80624.2			0.245132
$162$	−173766.	+	130514.i	−0.520207	+	0.390724i
$163$	72021.3	−	72021.3i	0.212320	−	0.212320i	−0.592932	−	0.805253i	$-0.702030\pi$
$163$	72021.3	−	72021.3i	0.212320	−	0.212320i	0.805253	+	0.592932i	$0.202030\pi$
$164$	−380694.	−	110458.i	−1.10527	−	0.320691i
$165$	12871.7	+	12871.7i	0.0368067	+	0.0368067i
$166$	−9249.78	+	65073.6i	−0.0260532	+	0.183288i
$167$		−	633922.i		−	1.75891i	−0.475979	−	0.879457i	$-0.657906\pi$
$167$		−	633922.i		−	1.75891i	0.475979	−	0.879457i	$-0.342094\pi$
$168$	11319.3	−	25104.4i	0.0309418	−	0.0686241i
$169$		−	261581.i		−	0.704513i
$170$	−45897.8	−	6524.06i	−0.121806	−	0.0173139i
$171$	382874.	+	382874.i	1.00130	+	1.00130i
$172$	422612.	−	232525.i	1.08923	−	0.599305i
$173$	−317844.	+	317844.i	−0.807418	+	0.807418i	−0.984242	−	0.176824i	$-0.943418\pi$
$173$	−317844.	+	317844.i	−0.807418	+	0.807418i	0.176824	+	0.984242i	$0.443418\pi$
$174$	102019.	+	135827.i	0.255450	+	0.340104i
$175$	83262.0			0.205519
$176$	−60798.1	−	271107.i	−0.147948	−	0.659719i
$177$	−45991.8			−0.110344
$178$	456697.	+	608042.i	1.08038	+	1.43841i
$179$	437684.	−	437684.i	1.02100	−	1.02100i	0.0212302	−	0.999775i	$-0.493242\pi$
$179$	437684.	−	437684.i	1.02100	−	1.02100i	0.999775	−	0.0212302i	$-0.00675830\pi$
$180$	40685.9	+	73946.3i	0.0935971	+	0.170112i
$181$	−83922.0	−	83922.0i	−0.190405	−	0.190405i	0.605466	−	0.795871i	$-0.292987\pi$
$181$	−83922.0	−	83922.0i	−0.190405	−	0.190405i	−0.795871	+	0.605466i	$0.792987\pi$
$182$	−124804.	−	17740.1i	−0.279287	−	0.0396988i
$183$		−	52711.7i		−	0.116353i
$184$	−487284.	+	184421.i	−1.06105	+	0.401573i
$185$			105580.i			0.226805i
$186$	−19247.5	+	135409.i	−0.0407936	+	0.286990i
$187$	−127279.	−	127279.i	−0.266166	−	0.266166i
$188$	−208507.	+	718622.i	−0.430256	+	1.48288i
$189$	−49106.9	+	49106.9i	−0.0999973	+	0.0999973i
$190$	141705.	−	106433.i	0.284774	−	0.213892i
$191$	−477461.			−0.947010			−0.473505	−	0.880791i	$-0.657011\pi$
$191$	−477461.			−0.947010			−0.473505	+	0.880791i	$0.657011\pi$
$192$	−10988.4	+	177620.i	−0.0215120	+	0.347728i
$193$	−581329.			−1.12338			−0.561692	−	0.827346i	$-0.689849\pi$
$193$	−581329.			−1.12338			−0.561692	+	0.827346i	$0.689849\pi$
$194$	−242503.	+	182142.i	−0.462607	+	0.347462i
$195$	−37739.9	+	37739.9i	−0.0710745	+	0.0710745i
$196$	142871.	−	492407.i	0.265647	−	0.915554i
$197$	−29515.9	−	29515.9i	−0.0541864	−	0.0541864i	0.679494	−	0.733681i	$-0.262199\pi$
$197$	−29515.9	−	29515.9i	−0.0541864	−	0.0541864i	−0.733681	+	0.679494i	$0.762199\pi$
$198$	−46117.1	+	324441.i	−0.0835985	+	0.588129i
$199$			68026.0i			0.121771i	0.998145	+	0.0608853i	$0.0193924\pi$
$199$			68026.0i			0.121771i	−0.998145	+	0.0608853i	$0.980608\pi$
$200$	−503226.	+	190454.i	−0.889587	+	0.336679i
$201$		−	100264.i		−	0.175048i
$202$	53720.9	+	7636.06i	0.0926327	+	0.0131671i
$203$	−109522.	−	109522.i	−0.186535	−	0.186535i
$204$	55577.4	+	101011.i	0.0935024	+	0.169940i
$205$	108205.	−	108205.i	0.179830	−	0.179830i
$206$	81001.8	+	107845.i	0.132992	+	0.177065i
$207$	614517.			0.996800
$208$	794883.	−	178260.i	1.27393	−	0.285690i
$209$	688109.			1.08966
$210$	6384.51	+	8500.29i	0.00999033	+	0.0133010i
$211$	176742.	−	176742.i	0.273296	−	0.273296i	−0.557129	−	0.830426i	$-0.688097\pi$
$211$	176742.	−	176742.i	0.273296	−	0.273296i	0.830426	+	0.557129i	$0.188097\pi$
$212$	26030.2	−	14322.0i	0.0397775	−	0.0218859i
$213$	−107064.	−	107064.i	−0.161694	−	0.161694i
$214$	−553208.	−	78634.8i	−0.825760	−	0.117376i
$215$			186210.i			0.274731i
$216$	184469.	−	409125.i	0.269023	−	0.596652i
$217$		−	124705.i		−	0.179778i
$218$	158228.	−	1.11316e6i	0.225497	−	1.58641i
$219$	78930.3	+	78930.3i	0.111207	+	0.111207i
$220$	103010.	+	29888.2i	0.143490	+	0.0416334i
$221$	373181.	−	373181.i	0.513971	−	0.513971i
$222$	209945.	−	157688.i	0.285906	−	0.214742i
$223$	−777882.			−1.04749			−0.523747	−	0.851874i	$-0.675466\pi$
$223$	−777882.			−1.04749			−0.523747	+	0.851874i	$0.675466\pi$
$224$	−12871.9	−	161750.i	−0.0171404	−	0.215389i
$225$	634622.			0.835716
$226$	431515.	−	324108.i	0.561985	−	0.422104i
$227$	−906710.	+	906710.i	−1.16789	+	1.16789i	−0.185192	+	0.982702i	$0.559291\pi$
$227$	−906710.	+	906710.i	−1.16789	+	1.16789i	−0.982702	+	0.185192i	$0.940709\pi$
$228$	−423284.	−	122815.i	−0.539256	−	0.156464i
$229$	156955.	+	156955.i	0.197782	+	0.197782i	0.799048	−	0.601267i	$-0.205337\pi$
$229$	156955.	+	156955.i	0.197782	+	0.197782i	−0.601267	+	0.799048i	$0.705337\pi$
$230$	28305.3	−	199132.i	0.0352816	−	0.248211i
$231$			41276.9i			0.0508953i
$232$	912461.	+	411417.i	1.11300	+	0.501837i
$233$			1.03950e6i			1.25440i	0.778859	+	0.627199i	$0.215799\pi$
$233$			1.03950e6i			1.25440i	−0.778859	+	0.627199i	$0.784201\pi$
$234$	−951258.	−	135215.i	−1.13569	−	0.161430i
$235$	−204255.	−	204255.i	−0.241270	−	0.241270i
$236$	−237428.	+	130635.i	−0.277493	+	0.152679i
$237$	396251.	−	396251.i	0.458247	−	0.458247i
$238$	−63131.6	−	84052.9i	−0.0722445	−	0.0961857i
$239$	1.07523e6			1.21760			0.608802	−	0.793322i	$-0.291650\pi$
$239$	1.07523e6			1.21760			0.608802	+	0.793322i	$0.291650\pi$
$240$	−58031.0	−	36770.8i	−0.0650327	−	0.0412074i
$241$	−1.29926e6			−1.44096			−0.720482	−	0.693474i	$-0.756079\pi$
$241$	−1.29926e6			−1.44096			−0.720482	+	0.693474i	$0.756079\pi$
$242$	−297030.	−	395464.i	−0.326034	−	0.434078i
$243$	−573531.	+	573531.i	−0.623076	+	0.623076i
$244$	−149722.	−	272118.i	−0.160994	−	0.292606i
$245$	139957.	+	139957.i	0.148964	+	0.148964i
$246$	−376774.	−	53555.9i	−0.396957	−	0.0564248i
$247$			2.01753e6i			2.10416i
$248$	285252.	+	753706.i	0.294510	+	0.778167i
$249$			63102.4i			0.0644982i
$250$	59963.4	−	421852.i	0.0606787	−	0.426885i
$251$	−843150.	−	843150.i	−0.844735	−	0.844735i	0.144735	−	0.989470i	$-0.453767\pi$
$251$	−843150.	−	843150.i	−0.844735	−	0.844735i	−0.989470	+	0.144735i	$0.953767\pi$
$252$	−53329.5	+	183801.i	−0.0529013	+	0.182325i
$253$	552212.	−	552212.i	0.542381	−	0.542381i
$254$	−520275.	+	390775.i	−0.505997	+	0.380052i
$255$	−44507.4			−0.0428630
$256$	447785.	+	948156.i	0.427041	+	0.904232i
$257$	819237.			0.773707			0.386854	−	0.922141i	$-0.373562\pi$
$257$	819237.			0.773707			0.386854	+	0.922141i	$0.373562\pi$
$258$	370278.	−	278113.i	0.346320	−	0.260119i
$259$	−169286.	+	169286.i	−0.156810	+	0.156810i
$260$	−87631.9	+	302024.i	−0.0803949	+	0.277082i
$261$	−834776.	−	834776.i	−0.758523	−	0.758523i
$262$	−132375.	+	931277.i	−0.119138	+	0.838158i
$263$		−	1.59886e6i		−	1.42535i	−0.701496	−	0.712673i	$-0.747484\pi$
$263$		−	1.59886e6i		−	1.42535i	0.701496	−	0.712673i	$-0.252516\pi$
$264$	−94417.3	−	249473.i	−0.0833761	−	0.220300i
$265$			11469.4i			0.0100329i
$266$	397863.	+	56553.5i	0.344770	+	0.0490067i
$267$	516242.	+	516242.i	0.443175	+	0.443175i
$268$	−284790.	−	517603.i	−0.242207	−	0.440210i
$269$	224438.	−	224438.i	0.189110	−	0.189110i	−0.606201	−	0.795311i	$-0.707307\pi$
$269$	224438.	−	224438.i	0.189110	−	0.189110i	0.795311	+	0.606201i	$0.207307\pi$
$270$	104048.	+	138529.i	0.0868609	+	0.115646i
$271$	1.16216e6			0.961266			0.480633	−	0.876922i	$-0.340407\pi$
$271$	1.16216e6			0.961266			0.480633	+	0.876922i	$0.340407\pi$
$272$	573824.	+	363599.i	0.470280	+	0.297989i
$273$	−121024.			−0.0982797
$274$	−86540.5	−	115219.i	−0.0696375	−	0.0927148i
$275$	570278.	−	570278.i	0.454732	−	0.454732i
$276$	−438248.	+	241128.i	−0.346296	+	0.190535i
$277$	25062.3	+	25062.3i	0.0196256	+	0.0196256i	0.716851	−	0.697226i	$-0.245583\pi$
$277$	25062.3	+	25062.3i	0.0196256	+	0.0196256i	−0.697226	+	0.716851i	$0.745583\pi$
$278$	1.51576e6	+	215455.i	1.17630	+	0.167203i
$279$		−	950504.i		−	0.731044i
$280$	57103.5	+	25747.3i	0.0435279	+	0.0196262i
$281$			107864.i			0.0814910i	0.999170	+	0.0407455i	$0.0129733\pi$
$281$			107864.i			0.0814910i	−0.999170	+	0.0407455i	$0.987027\pi$
$282$	−101096.	+	711223.i	−0.0757023	+	0.532578i
$283$	−1.82013e6	−	1.82013e6i	−1.35094	−	1.35094i	−0.884609	−	0.466334i	$-0.845575\pi$
$283$	−1.82013e6	−	1.82013e6i	−1.35094	−	1.35094i	−0.466334	−	0.884609i	$-0.654425\pi$
$284$	−856809.	−	248602.i	−0.630360	−	0.182898i
$285$	120311.	−	120311.i	0.0877388	−	0.0877388i
$286$	−976317.	+	733306.i	−0.705790	+	0.530115i
$287$	346991.			0.248664
$288$	−98109.3	−	1.23286e6i	−0.0696994	−	0.875854i
$289$	−979757.			−0.690039
$290$	−308957.	+	232056.i	−0.215726	+	0.162031i
$291$	−205891.	+	205891.i	−0.142529	+	0.142529i
$292$	631662.	+	183276.i	0.433539	+	0.125791i
$293$	−357804.	−	357804.i	−0.243487	−	0.243487i	0.574804	−	0.818291i	$-0.305078\pi$
$293$	−357804.	−	357804.i	−0.243487	−	0.243487i	−0.818291	+	0.574804i	$0.805078\pi$
$294$	69271.6	−	487337.i	0.0467398	−	0.328822i
$295$		−	104615.i		−	0.0699904i
$296$	635921.	−	1.41038e6i	0.421866	−	0.935633i
$297$			672687.i			0.442509i
$298$	1.89229e6	+	268977.i	1.23438	+	0.175458i
$299$	1.61908e6	+	1.61908e6i	1.04735	+	1.04735i
$300$	−452586.	+	249017.i	−0.290334	+	0.159744i
$301$	−298568.	+	298568.i	−0.189945	+	0.189945i
$302$	883233.	+	1.17593e6i	0.557260	+	0.741932i
$303$	52093.5			0.0325969
$304$	−2.53400e6	+	568272.i	−1.57262	+	0.352673i
$305$	119900.			0.0738023
$306$	−481189.	−	640651.i	−0.293773	−	0.391127i
$307$	2.19534e6	−	2.19534e6i	1.32940	−	1.32940i	0.423512	−	0.905890i	$-0.360797\pi$
$307$	2.19534e6	−	2.19534e6i	1.32940	−	1.32940i	0.905890	−	0.423512i	$-0.139203\pi$
$308$	117243.	+	213088.i	0.0704221	+	0.127992i
$309$	91563.1	+	91563.1i	0.0545537	+	0.0545537i
$310$	−308008.	−	43781.2i	−0.182036	−	0.0258752i
$311$			1.47806e6i			0.866547i	0.901263	+	0.433273i	$0.142642\pi$
$311$			1.47806e6i			0.866547i	−0.901263	+	0.433273i	$0.857358\pi$
$312$	731454.	−	276831.i	0.425403	−	0.161001i
$313$			617807.i			0.356445i	0.983990	+	0.178222i	$0.0570346\pi$
$313$			617807.i			0.356445i	−0.983990	+	0.178222i	$0.942965\pi$
$314$	−234882.	+	1.65243e6i	−0.134439	+	0.945801i
$315$	−52241.9	−	52241.9i	−0.0296649	−	0.0296649i
$316$	920095.	−	3.17111e6i	0.518340	−	1.78646i
$317$	−2.02184e6	+	2.02184e6i	−1.13005	+	1.13005i	−0.139882	+	0.990168i	$0.544672\pi$
$317$	−2.02184e6	+	2.02184e6i	−1.13005	+	1.13005i	−0.990168	+	0.139882i	$0.955328\pi$
$318$	22806.8	−	17130.0i	0.0126472	−	0.00949926i
$319$	−1.50028e6			−0.825458
$320$	−404022.	−	24994.7i	−0.220562	−	0.0136450i
$321$	−536450.			−0.290580
$322$	364672.	−	273903.i	0.196003	−	0.147217i
$323$	−1.18966e6	+	1.18966e6i	−0.634478	+	0.634478i
$324$	−342567.	+	1.18066e6i	−0.181294	+	0.624831i
$325$	1.67205e6	+	1.67205e6i	0.878095	+	0.878095i
$326$	81083.7	−	570436.i	0.0422561	−	0.297278i
$327$		−	1.07944e6i		−	0.558248i
$328$	−2.09718e6	+	793711.i	−1.07634	+	0.407359i
$329$		−	655002.i		−	0.333621i
$330$	101949.	+	14491.4i	0.0515346	+	0.00732529i
$331$	1.50720e6	+	1.50720e6i	0.756136	+	0.756136i	0.975617	−	0.219481i	$-0.0704364\pi$
$331$	1.50720e6	+	1.50720e6i	0.756136	+	0.756136i	−0.219481	+	0.975617i	$0.570436\pi$
$332$	179236.	+	325759.i	0.0892440	+	0.162200i
$333$	−1.29030e6	+	1.29030e6i	−0.637646	+	0.637646i
$334$	−2.15361e6	−	2.86730e6i	−1.05633	−	1.40639i
$335$	228065.			0.111032
$336$	−34088.4	−	152005.i	−0.0164724	−	0.0734529i
$337$	96831.6			0.0464454			0.0232227	−	0.999730i	$-0.492607\pi$
$337$	96831.6			0.0464454			0.0232227	+	0.999730i	$0.492607\pi$
$338$	−888662.	−	1.18316e6i	−0.423102	−	0.563314i
$339$	366367.	−	366367.i	0.173148	−	0.173148i
$340$	−229765.	+	126419.i	−0.107792	+	0.0593081i
$341$	−854133.	−	854133.i	−0.397777	−	0.397777i
$342$	3.03251e6	+	431051.i	1.40196	+	0.199280i
$343$			919607.i			0.422053i
$344$	1.12157e6	−	2.48746e6i	0.511010	−	1.13334i
$345$		−	193100.i		−	0.0873442i
$346$	−357838.	+	2.51745e6i	−0.160693	+	1.13050i
$347$	838484.	+	838484.i	0.373827	+	0.373827i	0.868869	−	0.495042i	$-0.164847\pi$
$347$	838484.	+	838484.i	0.373827	+	0.373827i	−0.495042	+	0.868869i	$0.664847\pi$
$348$	922882.	+	267773.i	0.408506	+	0.118527i
$349$	1.50056e6	−	1.50056e6i	0.659463	−	0.659463i	−0.295790	−	0.955253i	$-0.595583\pi$
$349$	1.50056e6	−	1.50056e6i	0.659463	−	0.659463i	0.955253	+	0.295790i	$0.0955830\pi$
$350$	376603.	−	282864.i	0.164329	−	0.123426i
$351$	−1.97231e6			−0.854493
$352$	−1.19602e6	−	1.01970e6i	−0.514496	−	0.438646i
$353$	1.14207e6			0.487817			0.243908	−	0.969798i	$-0.421570\pi$
$353$	1.14207e6			0.487817			0.243908	+	0.969798i	$0.421570\pi$
$354$	−208026.	+	156247.i	−0.0882286	+	0.0662680i
$355$	243532.	−	243532.i	0.102562	−	0.102562i
$356$	4.13138e6	+	1.19871e6i	1.72771	+	0.501292i
$357$	−71363.0	−	71363.0i	−0.0296348	−	0.0296348i
$358$	492757.	−	3.46662e6i	0.203201	−	1.42955i
$359$		−	2.07162e6i		−	0.848349i	−0.905580	−	0.424174i	$-0.860564\pi$
$359$		−	2.07162e6i		−	0.848349i	0.905580	−	0.424174i	$-0.139436\pi$
$360$	435243.	+	196246.i	0.177001	+	0.0798075i
$361$		−	3.95557e6i		−	1.59750i
$362$	−664694.	−	94481.8i	−0.266594	−	0.0378945i
$363$	−335758.	−	335758.i	−0.133740	−	0.133740i
$364$	−624772.	+	343755.i	−0.247154	+	0.135986i
$365$	−179538.	+	179538.i	−0.0705382	+	0.0705382i
$366$	−179076.	−	238421.i	−0.0698772	−	0.0930338i
$367$	−119073.			−0.0461473			−0.0230737	−	0.999734i	$-0.507345\pi$
$367$	−119073.			−0.0461473			−0.0230737	+	0.999734i	$0.507345\pi$
$368$	−1.57751e6	+	2.48959e6i	−0.607229	+	0.958316i
$369$	2.64476e6			1.01116
$370$	358685.	+	477550.i	0.136210	+	0.181349i
$371$	−18389.9	+	18389.9i	−0.00693657	+	0.00693657i
$372$	372964.	+	677860.i	0.139737	+	0.253970i
$373$	3.03626e6	+	3.03626e6i	1.12997	+	1.12997i	0.990181	+	0.139789i	$0.0446423\pi$
$373$	3.03626e6	+	3.03626e6i	1.12997	+	1.12997i	0.139789	+	0.990181i	$0.455358\pi$
$374$	−1.00810e6	−	143294.i	−0.372669	−	0.0529724i
$375$		−	409073.i		−	0.150218i
$376$	1.49826e6	+	3.95876e6i	0.546534	+	1.44408i
$377$		−	4.39880e6i		−	1.59397i
$378$	−55286.0	+	388946.i	−0.0199015	+	0.140010i
$379$	−738378.	−	738378.i	−0.264047	−	0.264047i	0.562649	−	0.826696i	$-0.309782\pi$
$379$	−738378.	−	738378.i	−0.264047	−	0.264047i	−0.826696	+	0.562649i	$0.809782\pi$
$380$	279361.	−	962819.i	0.0992445	−	0.342047i
$381$	−441726.	+	441726.i	−0.155898	+	0.155898i
$382$	−2.15961e6	+	1.62207e6i	−0.757210	+	0.568736i
$383$	−4.53961e6			−1.58133			−0.790664	−	0.612251i	$-0.790264\pi$
$383$	−4.53961e6			−1.58133			−0.790664	+	0.612251i	$0.790264\pi$
$384$	553723.	+	840726.i	0.191631	+	0.290955i
$385$	−93890.2			−0.0322826
$386$	−2.62941e6	+	1.97493e6i	−0.898236	+	0.674659i
$387$	−2.27569e6	+	2.27569e6i	−0.772387	+	0.772387i
$388$	−478078.	+	1.64770e6i	−0.161220	+	0.555647i
$389$	−2.17974e6	−	2.17974e6i	−0.730349	−	0.730349i	0.240340	−	0.970689i	$-0.422741\pi$
$389$	−2.17974e6	−	2.17974e6i	−0.730349	−	0.730349i	−0.970689	+	0.240340i	$0.922741\pi$
$390$	−42488.6	+	298914.i	−0.0141453	+	0.0995142i
$391$			1.90942e6i			0.631625i
$392$	−1.02662e6	−	2.71258e6i	−0.337439	−	0.891595i
$393$			903066.i			0.294943i
$394$	−233777.	−	33229.9i	−0.0758686	−	0.0107842i
$395$	901329.	+	901329.i	0.290664	+	0.290664i
$396$	893623.	+	1.62415e6i	0.286363	+	0.520462i
$397$	1.54162e6	−	1.54162e6i	0.490908	−	0.490908i	−0.417684	−	0.908592i	$-0.637158\pi$
$397$	1.54162e6	−	1.54162e6i	0.490908	−	0.490908i	0.908592	+	0.417684i	$0.137158\pi$
$398$	231103.	+	307689.i	0.0731305	+	0.0973654i
$399$	385810.			0.121323
$400$	−1.62912e6	+	2.57104e6i	−0.509100	+	0.803451i
$401$	−2.06724e6			−0.641992			−0.320996	−	0.947081i	$-0.604018\pi$
$401$	−2.06724e6			−0.641992			−0.320996	+	0.947081i	$0.604018\pi$
$402$	−340626.	−	453506.i	−0.105126	−	0.139964i
$403$	2.50431e6	−	2.50431e6i	0.768115	−	0.768115i
$404$	268927.	−	147966.i	0.0819749	−	0.0451033i
$405$	−335581.	−	335581.i	−0.101662	−	0.101662i
$406$	−867456.	−	123303.i	−0.261176	−	0.0371243i
$407$			2.31895e6i			0.693915i
$408$	594546.	+	268074.i	0.176822	+	0.0797267i
$409$			1.75464e6i			0.518657i	0.965789	+	0.259329i	$0.0835012\pi$
$409$			1.75464e6i			0.518657i	−0.965789	+	0.259329i	$0.916499\pi$
$410$	121821.	−	857027.i	0.0357899	−	0.251788i
$411$	−97824.0	−	97824.0i	−0.0285654	−	0.0285654i
$412$	732760.	+	212609.i	0.212676	+	0.0617077i
$413$	167739.	−	167739.i	0.0483904	−	0.0483904i
$414$	2.77953e6	−	2.08769e6i	0.797022	−	0.598638i
$415$	−143535.			−0.0409108
$416$	2.98975e6	−	3.50673e6i	0.847034	−	0.993502i
$417$	1.46984e6			0.413934
$418$	3.11239e6	−	2.33770e6i	0.871272	−	0.654407i
$419$	−1.56587e6	+	1.56587e6i	−0.435734	+	0.435734i	−0.890573	−	0.454840i	$-0.849697\pi$
$419$	−1.56587e6	+	1.56587e6i	−0.435734	+	0.435734i	0.454840	+	0.890573i	$0.349697\pi$
$420$	57755.7	+	16757.7i	0.0159761	+	0.00463545i
$421$	2.86763e6	+	2.86763e6i	0.788529	+	0.788529i	0.981253	−	0.192724i	$-0.0617323\pi$
$421$	2.86763e6	+	2.86763e6i	0.788529	+	0.788529i	−0.192724	+	0.981253i	$0.561732\pi$
$422$	198981.	−	1.39987e6i	0.0543915	−	0.382653i
$423$		−	4.99242e6i		−	1.35663i
$424$	69081.4	−	153212.i	0.0186615	−	0.0413883i
$425$			1.97189e6i			0.529554i
$426$	−847987.	−	120536.i	−0.226394	−	0.0321804i
$427$	192247.	+	192247.i	0.0510259	+	0.0510259i
$428$	−2.76936e6	+	1.52373e6i	−0.730753	+	0.402067i
$429$	−828917.	+	828917.i	−0.217454	+	0.217454i
$430$	632608.	+	842249.i	0.164992	+	0.219669i
$431$	5.39462e6			1.39884			0.699419	−	0.714712i	$-0.253442\pi$
$431$	5.39462e6			1.39884			0.699419	+	0.714712i	$0.253442\pi$
$432$	−555536.	−	2.47721e6i	−0.143220	−	0.638636i
$433$	477220.			0.122320			0.0611602	−	0.998128i	$-0.480520\pi$
$433$	477220.			0.122320			0.0611602	+	0.998128i	$0.480520\pi$
$434$	−423659.	−	564056.i	−0.107967	−	0.143747i
$435$	−262312.	+	262312.i	−0.0664653	+	0.0664653i
$436$	−3.06602e6	−	5.57247e6i	−0.772429	−	1.40388i
$437$	−5.16146e6	−	5.16146e6i	−1.29291	−	1.29291i
$438$	625158.	+	88862.0i	0.155706	+	0.0221325i
$439$			4.17692e6i			1.03442i	0.855860	+	0.517208i	$0.173029\pi$
$439$			4.17692e6i			1.03442i	−0.855860	+	0.517208i	$0.826971\pi$
$440$	567462.	−	214765.i	0.139735	−	0.0528850i
$441$			3.42086e6i			0.837603i
$442$	420138.	−	2.95574e6i	0.102291	−	0.719631i
$443$	−244827.	−	244827.i	−0.0592720	−	0.0592720i	0.676849	−	0.736121i	$-0.263345\pi$
$443$	−244827.	−	244827.i	−0.0592720	−	0.0592720i	−0.736121	+	0.676849i	$0.763345\pi$
$444$	413892.	−	1.42648e6i	0.0996392	−	0.343407i
$445$	−1.17427e6	+	1.17427e6i	−0.281104	+	0.281104i
$446$	−3.51845e6	+	2.64268e6i	−0.837556	+	0.629083i
$447$	1.83497e6			0.434370
$448$	−607731.	−	687883.i	−0.143059	−	0.161927i
$449$	−2.93133e6			−0.686198			−0.343099	−	0.939299i	$-0.611477\pi$
$449$	−2.93133e6			−0.686198			−0.343099	+	0.939299i	$0.611477\pi$
$450$	2.87046e6	−	2.15599e6i	0.668222	−	0.501897i
$451$	2.37661e6	−	2.37661e6i	0.550196	−	0.550196i
$452$	850703.	−	2.93195e6i	0.195854	−	0.675011i
$453$	998392.	+	998392.i	0.228589	+	0.228589i
$454$	−1.02080e6	+	7.18149e6i	−0.232435	+	1.63522i
$455$		−	275286.i		−	0.0623383i
$456$	−2.33180e6	+	882507.i	−0.525144	+	0.198749i
$457$			4.24533e6i			0.950869i	0.879751	+	0.475434i	$0.157709\pi$
$457$			4.24533e6i			0.950869i	−0.879751	+	0.475434i	$0.842291\pi$
$458$	1.24314e6	+	176704.i	0.276922	+	0.0393626i
$459$	−1.16300e6	−	1.16300e6i	−0.257660	−	0.257660i
$460$	−548480.	−	996857.i	−0.120855	−	0.219654i
$461$	1.71290e6	−	1.71290e6i	0.375388	−	0.375388i	−0.494047	−	0.869435i	$-0.664483\pi$
$461$	1.71290e6	−	1.71290e6i	0.375388	−	0.375388i	0.869435	+	0.494047i	$0.164483\pi$
$462$	140229.	+	186700.i	0.0305656	+	0.0406948i
$463$	1.39183e6			0.301741			0.150871	−	0.988553i	$-0.451792\pi$
$463$	1.39183e6			0.301741			0.150871	+	0.988553i	$0.451792\pi$
$464$	5.52486e6	−	1.23900e6i	1.19131	−	0.267163i
$465$	−298677.			−0.0640574
$466$	3.53148e6	+	4.70178e6i	0.753341	+	1.00299i
$467$	−1.72514e6	+	1.72514e6i	−0.366043	+	0.366043i	−0.866032	−	0.499989i	$-0.833338\pi$
$467$	−1.72514e6	+	1.72514e6i	−0.366043	+	0.366043i	0.499989	+	0.866032i	$0.333338\pi$
$468$	−4.76201e6	+	2.62010e6i	−1.00502	+	0.552972i
$469$	365678.	+	365678.i	0.0767657	+	0.0767657i
$470$	−1.61778e6	−	229956.i	−0.337811	−	0.0480176i
$471$			1.60238e6i			0.332822i
$472$	−630109.	+	1.39748e6i	−0.130185	+	0.288730i
$473$			4.08991e6i			0.840545i
$474$	446111.	−	3.13846e6i	0.0912005	−	0.641610i
$475$	−5.33032e6	−	5.33032e6i	−1.08398	−	1.08398i
$476$	−571102.	−	165705.i	−0.115530	−	0.0335210i
$477$	−140168.	+	140168.i	−0.0282067	+	0.0282067i
$478$	4.86338e6	−	3.65285e6i	0.973572	−	0.731244i
$479$	6.45862e6			1.28618			0.643089	−	0.765792i	$-0.277653\pi$
$479$	6.45862e6			1.28618			0.643089	+	0.765792i	$0.277653\pi$
$480$	−387401.	+	30828.9i	−0.0767463	+	0.00610738i
$481$	−6.79916e6			−1.33996
$482$	−5.87668e6	+	4.41394e6i	−1.15217	+	0.865384i
$483$	309615.	−	309615.i	0.0603885	−	0.0603885i
$484$	−2.68700e6	−	779630.i	−0.521380	−	0.151278i
$485$	−468328.	−	468328.i	−0.0904056	−	0.0904056i
$486$	−645697.	+	4.54258e6i	−0.124005	+	0.872393i
$487$		−	3.55379e6i		−	0.679000i	−0.940606	−	0.339500i	$-0.889742\pi$
$487$		−	3.55379e6i		−	0.679000i	0.940606	−	0.339500i	$-0.110258\pi$
$488$	−1.60167e6	−	722173.i	−0.304455	−	0.137275i
$489$		−	553156.i		−	0.104611i
$490$	1.10852e6	+	157568.i	0.208570	+	0.0296468i
$491$	1.82904e6	+	1.82904e6i	0.342388	+	0.342388i	0.857264	−	0.514876i	$-0.172162\pi$
$491$	1.82904e6	+	1.82904e6i	0.342388	+	0.342388i	−0.514876	+	0.857264i	$0.672162\pi$
$492$	−1.88614e6	+	1.03777e6i	−0.351285	+	0.193280i
$493$	2.59380e6	−	2.59380e6i	0.480640	−	0.480640i
$494$	6.85412e6	+	9.12552e6i	1.26367	+	1.68244i
$495$	−715631.			−0.131273
$496$	3.85078e6	+	2.44001e6i	0.702820	+	0.445336i
$497$	780955.			0.141819
$498$	214376.	+	285419.i	0.0387350	+	0.0515714i
$499$	−692847.	+	692847.i	−0.124562	+	0.124562i	−0.766640	−	0.642078i	$-0.778073\pi$
$499$	−692847.	+	692847.i	−0.124562	+	0.124562i	0.642078	+	0.766640i	$0.278073\pi$
$500$	−1.16193e6	−	2.11180e6i	−0.207852	−	0.377770i
$501$	−2.43440e6	−	2.43440e6i	−0.433310	−	0.433310i
$502$	−6.67807e6	−	949243.i	−1.18275	−	0.168119i
$503$		−	4.55001e6i		−	0.801849i	−0.916111	−	0.400924i	$-0.868689\pi$
$503$		−	4.55001e6i		−	0.801849i	0.916111	−	0.400924i	$-0.131311\pi$
$504$	383207.	+	1.01252e6i	0.0671980	+	0.177554i
$505$			118494.i			0.0206761i
$506$	621696.	−	4.37373e6i	0.107945	−	0.759409i
$507$	−1.00453e6	−	1.00453e6i	−0.173557	−	0.173557i
$508$	−1.02569e6	+	3.53503e6i	−0.176342	+	0.607763i
$509$	1.05841e6	−	1.05841e6i	0.181075	−	0.181075i	−0.610749	−	0.791824i	$-0.709132\pi$
$509$	1.05841e6	−	1.05841e6i	0.181075	−	0.181075i	0.791824	+	0.610749i	$0.209132\pi$
$510$	−201312.	+	151204.i	−0.0342724	+	0.0257418i
$511$	−575741.			−0.0975382
$512$	5.24653e6	+	2.76736e6i	0.884499	+	0.466543i
$513$	6.28752e6			1.05484
$514$	3.70550e6	−	2.78318e6i	0.618641	−	0.464657i
$515$	−208273.	+	208273.i	−0.0346031	+	0.0346031i
$516$	729977.	−	2.51587e6i	0.120694	−	0.415972i
$517$	−4.48625e6	−	4.48625e6i	−0.738171	−	0.738171i
$518$	−190587.	+	1.34081e6i	−0.0312083	+	0.219555i
$519$			2.44119e6i			0.397816i
$520$	629691.	+	1.66380e6i	0.102122	+	0.269831i
$521$		−	6.15364e6i		−	0.993202i	−0.867979	−	0.496601i	$-0.834581\pi$
$521$		−	6.15364e6i		−	0.993202i	0.867979	−	0.496601i	$-0.165419\pi$
$522$	−6.61175e6	−	939815.i	−1.06204	−	0.150961i
$523$	−3.11937e6	−	3.11937e6i	−0.498669	−	0.498669i	0.412354	−	0.911024i	$-0.364707\pi$
$523$	−3.11937e6	−	3.11937e6i	−0.498669	−	0.498669i	−0.911024	+	0.412354i	$0.864707\pi$
$524$	2.56506e6	+	4.66198e6i	0.408103	+	0.741724i
$525$	319745.	−	319745.i	0.0506297	−	0.0506297i
$526$	−5.43176e6	−	7.23180e6i	−0.856005	−	1.13968i
$527$	2.95339e6			0.463228
$528$	−1.27459e6	−	807633.i	−0.198969	−	0.126075i
$529$	−1.84786e6			−0.287098
$530$	38964.6	+	51877.2i	0.00602533	+	0.00802207i
$531$	1.27851e6	−	1.27851e6i	0.196773	−	0.196773i
$532$	1.99170e6	−	1.09585e6i	0.305103	−	0.167870i
$533$	6.96822e6	+	6.96822e6i	1.06244	+	1.06244i
$534$	4.08884e6	+	581201.i	0.620507	+	0.0882009i
$535$		−	1.22023e6i		−	0.184314i
$536$	−3.04658e6	−	1.37366e6i	−0.458037	−	0.206523i
$537$		−	3.36161e6i		−	0.503050i
$538$	252678.	−	1.77763e6i	0.0376368	−	0.264781i
$539$	3.07402e6	+	3.07402e6i	0.455758	+	0.455758i
$540$	941240.	+	273100.i	0.138904	+	0.0403030i
$541$	3.23194e6	−	3.23194e6i	0.474756	−	0.474756i	−0.428694	−	0.903450i	$-0.641026\pi$
$541$	3.23194e6	−	3.23194e6i	0.474756	−	0.474756i	0.903450	+	0.428694i	$0.141026\pi$
$542$	5.25658e6	−	3.94819e6i	0.768609	−	0.577297i
$543$	−644559.			−0.0938130
$544$	3.83072e6	−	304844.i	0.554987	−	0.0441652i
$545$	2.45533e6			0.354094
$546$	−547403.	+	411151.i	−0.0785825	+	0.0590228i
$547$	−5.66538e6	+	5.66538e6i	−0.809582	+	0.809582i	−0.984571	−	0.174988i	$-0.944011\pi$
$547$	−5.66538e6	+	5.66538e6i	−0.809582	+	0.809582i	0.174988	+	0.984571i	$0.444011\pi$
$548$	−782864.	−	227147.i	−0.111361	−	0.0323114i
$549$	1.46531e6	+	1.46531e6i	0.207490	+	0.207490i
$550$	642036.	−	4.51682e6i	0.0905009	−	0.636688i
$551$			1.40229e7i			1.96770i
$552$	−1.16306e6	+	2.57950e6i	−0.162464	+	0.360319i
$553$			2.89037e6i			0.401921i
$554$	198503.	+	28215.9i	0.0274785	+	0.00390588i
$555$	405451.	+	405451.i	0.0558735	+	0.0558735i
$556$	7.58792e6	−	4.17494e6i	1.04096	−	0.572747i
$557$	−1.14924e6	+	1.14924e6i	−0.156955	+	0.156955i	−0.781216	−	0.624261i	$-0.785400\pi$
$557$	−1.14924e6	+	1.14924e6i	−0.156955	+	0.156955i	0.624261	+	0.781216i	$0.285400\pi$
$558$	−3.22913e6	−	4.29923e6i	−0.439035	−	0.584528i
$559$	−1.19916e7			−1.62311
$560$	345756.	−	77538.8i	0.0465908	−	0.0104484i
$561$	−977559.			−0.131140
$562$	366443.	+	487879.i	0.0489402	+	0.0651586i
$563$	−716166.	+	716166.i	−0.0952232	+	0.0952232i	−0.753114	−	0.657890i	$-0.771449\pi$
$563$	−716166.	+	716166.i	−0.0952232	+	0.0952232i	0.657890	+	0.753114i	$0.271449\pi$
$564$	1.95896e6	+	3.56039e6i	0.259315	+	0.471302i
$565$	833353.	+	833353.i	0.109827	+	0.109827i
$566$	−1.44162e7	−	2.04916e6i	−1.89151	−	0.268865i
$567$		−	1.07614e6i		−	0.140575i
$568$	−4.72001e6	+	1.78637e6i	−0.613864	+	0.232327i
$569$			3.49909e6i			0.453079i	0.974002	+	0.226540i	$0.0727413\pi$
$569$			3.49909e6i			0.453079i	−0.974002	+	0.226540i	$0.927259\pi$
$570$	135449.	−	952906.i	0.0174618	−	0.122847i
$571$	4.24730e6	+	4.24730e6i	0.545159	+	0.545159i	0.925037	−	0.379878i	$-0.124034\pi$
$571$	4.24730e6	+	4.24730e6i	0.545159	+	0.545159i	−0.379878	+	0.925037i	$0.624034\pi$
$572$	−1.92474e6	+	6.63364e6i	−0.245970	+	0.847738i
$573$	−1.83356e6	+	1.83356e6i	−0.233297	+	0.233297i
$574$	1.56948e6	−	1.17883e6i	0.198827	−	0.149338i
$575$	−8.55523e6			−1.07910
$576$	−4.63212e6	−	5.24304e6i	−0.581733	−	0.658456i
$577$	2.94459e6			0.368201			0.184101	−	0.982907i	$-0.441063\pi$
$577$	2.94459e6			0.368201			0.184101	+	0.982907i	$0.441063\pi$
$578$	−4.43154e6	+	3.32851e6i	−0.551741	+	0.414410i
$579$	−2.23243e6	+	2.23243e6i	−0.276746	+	0.276746i
$580$	−609088.	+	2.09922e6i	−0.0751813	+	0.259113i
$581$	−230144.	−	230144.i	−0.0282852	−	0.0282852i
$582$	−231798.	+	1.63073e6i	−0.0283663	+	0.199561i
$583$			251913.i			0.0306958i
$584$	3.47972e6	−	1.31695e6i	0.422194	−	0.159786i
$585$		−	2.09822e6i		−	0.253491i
$586$	−2.83395e6	−	402826.i	−0.340916	−	0.0484589i
$587$	3.78400e6	+	3.78400e6i	0.453269	+	0.453269i	0.896438	−	0.443169i	$-0.146146\pi$
$587$	3.78400e6	+	3.78400e6i	0.453269	+	0.453269i	−0.443169	+	0.896438i	$0.646146\pi$
$588$	−1.34230e6	−	2.43961e6i	−0.160105	−	0.290990i
$589$	−7.98348e6	+	7.98348e6i	−0.948209	+	0.948209i
$590$	−355406.	−	473185.i	−0.0420334	−	0.0559629i
$591$	−226696.			−0.0266977
$592$	−1.91510e6	−	8.53968e6i	−0.224588	−	1.00147i
$593$	1.12147e7			1.30964			0.654821	−	0.755784i	$-0.272744\pi$
$593$	1.12147e7			1.30964			0.654821	+	0.755784i	$0.272744\pi$
$594$	2.28531e6	+	3.04264e6i	0.265753	+	0.353821i
$595$	162325.	−	162325.i	0.0187972	−	0.0187972i
$596$	9.47283e6	−	5.21204e6i	1.09236	−	0.601024i
$597$	261235.	+	261235.i	0.0299983	+	0.0299983i
$598$	1.28238e7	+	1.82281e6i	1.46643	+	0.208444i
$599$		−	1.03597e7i		−	1.17972i	−0.807506	−	0.589860i	$-0.799183\pi$
$599$		−	1.03597e7i		−	1.17972i	0.807506	−	0.589860i	$-0.200817\pi$
$600$	−1.20112e6	+	2.66389e6i	−0.136209	+	0.302091i
$601$		−	1.26288e7i		−	1.42618i	−0.701073	−	0.713090i	$-0.747295\pi$
$601$		−	1.26288e7i		−	1.42618i	0.701073	−	0.713090i	$-0.252705\pi$
$602$	−336137.	+	2.36478e6i	−0.0378029	+	0.265949i
$603$	2.78720e6	+	2.78720e6i	0.312158	+	0.312158i
$604$	7.98992e6	+	2.31827e6i	0.891148	+	0.258566i
$605$	763729.	−	763729.i	0.0848303	−	0.0848303i
$606$	235624.	−	176976.i	0.0260639	−	0.0195764i
$607$	−137659.			−0.0151647			−0.00758235	−	0.999971i	$-0.502414\pi$
$607$	−137659.			−0.0151647			−0.00758235	+	0.999971i	$0.502414\pi$
$608$	−9.53098e6	+	1.11791e7i	−1.04563	+	1.22644i
$609$	−841178.			−0.0919062
$610$	542321.	−	407334.i	0.0590109	−	0.0443227i
$611$	1.31536e7	−	1.31536e7i	1.42542	−	1.42542i
$612$	−4.35294e6	−	1.26300e6i	−0.469790	−	0.136309i
$613$	3.46214e6	+	3.46214e6i	0.372129	+	0.372129i	0.868252	−	0.496123i	$-0.165244\pi$
$613$	3.46214e6	+	3.46214e6i	0.372129	+	0.372129i	−0.496123	+	0.868252i	$0.665244\pi$
$614$	2.47158e6	−	1.73880e7i	0.264578	−	1.86135i
$615$		−	831065.i		−	0.0886027i
$616$	1.25422e6	+	565512.i	0.133175	+	0.0600469i
$617$		−	4.66033e6i		−	0.492838i	−0.969163	−	0.246419i	$-0.920746\pi$
$617$		−	4.66033e6i		−	0.492838i	0.969163	−	0.246419i	$-0.0792539\pi$
$618$	725215.	+	103084.i	0.0763828	+	0.0108573i
$619$	−1.08290e6	−	1.08290e6i	−0.113595	−	0.113595i	0.648024	−	0.761620i	$-0.275596\pi$
$619$	−1.08290e6	−	1.08290e6i	−0.113595	−	0.113595i	−0.761620	+	0.648024i	$0.775596\pi$
$620$	−1.54189e6	+	848360.i	−0.161092	+	0.0886342i
$621$	5.04578e6	−	5.04578e6i	0.525048	−	0.525048i
$622$	5.02139e6	+	6.68544e6i	0.520413	+	0.692873i
$623$	−3.76562e6			−0.388702
$624$	2.36798e6	−	3.73709e6i	0.243453	−	0.384213i
$625$	−8.35824e6			−0.855884
$626$	2.09886e6	+	2.79441e6i	0.214066	+	0.285006i
$627$	2.64250e6	−	2.64250e6i	0.268439	−	0.268439i
$628$	4.55138e6	+	8.27209e6i	0.460515	+	0.836982i
$629$	−4.00920e6	−	4.00920e6i	−0.404046	−	0.404046i
$630$	−413776.	−	58815.4i	−0.0415349	−	0.00590391i
$631$			2.10213e6i			0.210177i	0.994463	+	0.105089i	$0.0335126\pi$
$631$			2.10213e6i			0.210177i	−0.994463	+	0.105089i	$0.966487\pi$
$632$	−6.61147e6	−	1.74691e7i	−0.658423	−	1.73971i
$633$		−	1.35746e6i		−	0.134653i
$634$	−2.27624e6	+	1.60137e7i	−0.224903	+	1.58223i
$635$	−1.00477e6	−	1.00477e6i	−0.0988852	−	0.0988852i
$636$	44962.0	−	154962.i	0.00440760	−	0.0151908i
$637$	−9.01300e6	+	9.01300e6i	−0.880078	+	0.880078i
$638$	−6.78592e6	+	5.09686e6i	−0.660020	+	0.495737i
$639$	5.95244e6			0.576690
$640$	−1.91235e6	+	1.25952e6i	−0.184551	+	0.121550i
$641$	−1.01356e7			−0.974322			−0.487161	−	0.873312i	$-0.661968\pi$
$641$	−1.01356e7			−0.974322			−0.487161	+	0.873312i	$0.661968\pi$
$642$	−2.42642e6	+	1.82247e6i	−0.232342	+	0.174511i
$643$	7.82677e6	−	7.82677e6i	0.746543	−	0.746543i	−0.227285	−	0.973828i	$-0.572985\pi$
$643$	7.82677e6	−	7.82677e6i	0.746543	−	0.746543i	0.973828	+	0.227285i	$0.0729849\pi$
$644$	718926.	−	2.47778e6i	0.0683077	−	0.235423i
$645$	715089.	+	715089.i	0.0676801	+	0.0676801i
$646$	−1.33935e6	+	9.42257e6i	−0.126274	+	0.888358i
$647$		−	1.14962e7i		−	1.07967i	−0.841770	−	0.539837i	$-0.818486\pi$
$647$		−	1.14962e7i		−	1.07967i	0.841770	−	0.539837i	$-0.181514\pi$
$648$	2.46156e6	+	6.50405e6i	0.230289	+	0.608480i
$649$		−	2.29776e6i		−	0.214137i
$650$	1.32433e7	+	1.88245e6i	1.22946	+	0.174759i
$651$	−478897.	−	478897.i	−0.0442884	−	0.0442884i
$652$	−1.57118e6	−	2.85561e6i	−0.144746	−	0.263075i
$653$	−6.64617e6	+	6.64617e6i	−0.609942	+	0.609942i	−0.942931	−	0.332989i	$-0.891943\pi$
$653$	−6.64617e6	+	6.64617e6i	−0.609942	+	0.609942i	0.332989	+	0.942931i	$0.391943\pi$
$654$	−3.66714e6	−	4.88240e6i	−0.335261	−	0.446364i
$655$	−2.05415e6			−0.187081
$656$	−6.78930e6	+	1.07147e7i	−0.615978	+	0.972124i
$657$	−4.38829e6			−0.396627
$658$	−2.22523e6	−	2.96265e6i	−0.200359	−	0.266756i
$659$	−7.49421e6	+	7.49421e6i	−0.672221	+	0.672221i	−0.958228	−	0.286006i	$-0.907672\pi$
$659$	−7.49421e6	+	7.49421e6i	−0.672221	+	0.672221i	0.286006	+	0.958228i	$0.407672\pi$
$660$	510358.	−	280803.i	0.0456053	−	0.0250924i
$661$	2.34156e6	+	2.34156e6i	0.208450	+	0.208450i	0.803609	−	0.595158i	$-0.202911\pi$
$661$	2.34156e6	+	2.34156e6i	0.208450	+	0.208450i	−0.595158	+	0.803609i	$0.702911\pi$
$662$	1.19376e7	+	1.69684e6i	1.05870	+	0.150486i
$663$		−	2.86620e6i		−	0.253234i
$664$	1.91740e6	+	864531.i	0.168769	+	0.0760957i
$665$			877580.i			0.0769543i
$666$	−1.45266e6	+	1.02197e7i	−0.126905	+	0.892794i
$667$	1.12535e7	+	1.12535e7i	0.979427	+	0.979427i
$668$	−1.94820e7	−	5.65268e6i	−1.68924	−	0.490132i
$669$	−2.98724e6	+	2.98724e6i	−0.258051	+	0.258051i
$670$	1.03156e6	−	774801.i	0.0887787	−	0.0666812i
$671$	2.63348e6			0.225800
$672$	−670588.	−	571726.i	−0.0572839	−	0.0488387i
$673$	9.65048e6			0.821318			0.410659	−	0.911789i	$-0.365299\pi$
$673$	9.65048e6			0.821318			0.410659	+	0.911789i	$0.365299\pi$
$674$	437980.	−	328964.i	0.0371368	−	0.0278932i
$675$	5.21086e6	−	5.21086e6i	0.440200	−	0.440200i
$676$	−8.03903e6	−	2.33251e6i	−0.676608	−	0.196317i
$677$	5.31841e6	+	5.31841e6i	0.445974	+	0.445974i	0.894014	−	0.448039i	$-0.147878\pi$
$677$	5.31841e6	+	5.31841e6i	0.445974	+	0.445974i	−0.448039	+	0.894014i	$0.647878\pi$
$678$	412466.	−	2.90176e6i	0.0344599	−	0.242431i
$679$		−	1.50183e6i		−	0.125010i
$680$	−609772.	+	1.35238e6i	−0.0505702	+	0.112157i
$681$			6.96394e6i			0.575423i
$682$	−6.76507e6	−	961608.i	−0.556943	−	0.0791657i
$683$	−1.26533e7	−	1.26533e7i	−1.03790	−	1.03790i	−0.999253	−	0.0386419i	$-0.987697\pi$
$683$	−1.26533e7	−	1.26533e7i	−1.03790	−	1.03790i	−0.0386419	−	0.999253i	$-0.512303\pi$
$684$	1.51808e7	−	8.35259e6i	1.24066	−	0.682623i
$685$	222514.	−	222514.i	0.0181189	−	0.0181189i
$686$	3.12416e6	+	4.15948e6i	0.253468	+	0.337465i
$687$	1.20549e6			0.0974474
$688$	−3.37764e6	−	1.50613e7i	−0.272046	−	1.21309i
$689$	−738607.			−0.0592741
$690$	−656014.	−	873412.i	−0.0524554	−	0.0698387i
$691$	−9.67217e6	+	9.67217e6i	−0.770600	+	0.770600i	−0.978211	−	0.207611i	$-0.933431\pi$
$691$	−9.67217e6	+	9.67217e6i	−0.770600	+	0.770600i	0.207611	+	0.978211i	$0.433431\pi$
$692$	6.93393e6	+	1.26024e7i	0.550445	+	1.00043i
$693$	−1.14744e6	−	1.14744e6i	−0.0907603	−	0.0907603i
$694$	6.64112e6	+	943989.i	0.523410	+	0.0743992i
$695$			3.34337e6i			0.262556i
$696$	5.08399e6	−	1.92412e6i	0.397816	−	0.150560i
$697$			8.21777e6i			0.640726i
$698$	1.68938e6	−	1.18850e7i	0.131246	−	0.923340i
$699$	3.99192e6	+	3.99192e6i	0.309022	+	0.309022i
$700$	742447.	−	2.55885e6i	0.0572691	−	0.197378i
$701$	2.90818e6	−	2.90818e6i	0.223525	−	0.223525i	−0.586456	−	0.809981i	$-0.699477\pi$
$701$	2.90818e6	−	2.90818e6i	0.223525	−	0.223525i	0.809981	+	0.586456i	$0.199477\pi$
$702$	−8.92099e6	+	6.70050e6i	−0.683235	+	0.513174i
$703$	2.16750e7			1.65413
$704$	−8.87393e6	−	548982.i	−0.674814	−	0.0417471i
$705$	−1.56877e6			−0.118874
$706$	5.16572e6	−	3.87994e6i	0.390049	−	0.292963i
$707$	−189993.	+	189993.i	−0.0142951	+	0.0142951i
$708$	−410109.	+	1.41344e6i	−0.0307480	+	0.105973i
$709$	−1.62802e7	−	1.62802e7i	−1.21631	−	1.21631i	−0.968914	−	0.247396i	$-0.920425\pi$
$709$	−1.62802e7	−	1.62802e7i	−1.21631	−	1.21631i	−0.247396	−	0.968914i	$-0.579575\pi$
$710$	274175.	−	1.92887e6i	0.0204119	−	0.143601i
$711$			2.20304e7i			1.63436i
$712$	2.27590e7	−	8.61352e6i	1.68249	−	0.636767i
$713$			1.28136e7i			0.943945i
$714$	−565222.	−	80342.5i	−0.0414929	−	0.00589793i
$715$	−1.88549e6	−	1.88549e6i	−0.137930	−	0.137930i
$716$	−9.54829e6	−	1.73539e7i	−0.696054	−	1.26507i
$717$	4.12912e6	−	4.12912e6i	0.299958	−	0.299958i
$718$	−7.03788e6	−	9.37017e6i	−0.509484	−	0.678323i
$719$	−1.68399e7			−1.21484			−0.607419	−	0.794381i	$-0.707795\pi$
$719$	−1.68399e7			−1.21484			−0.607419	+	0.794381i	$0.707795\pi$
$720$	2.63535e6	−	591000.i	0.189455	−	0.0424871i
$721$	−667888.			−0.0478482
$722$	−1.34382e7	−	1.78915e7i	−0.959396	−	1.27733i
$723$	−4.98945e6	+	4.98945e6i	−0.354982	+	0.354982i
$724$	−3.32746e6	+	1.83080e6i	−0.235921	+	0.129806i
$725$	1.16216e7	+	1.16216e7i	0.821150	+	0.821150i
$726$	−2.65933e6	−	378006.i	−0.187254	−	0.0266169i
$727$		−	9.93566e6i		−	0.697205i	−0.937271	−	0.348603i	$-0.886656\pi$
$727$		−	9.93566e6i		−	0.697205i	0.937271	−	0.348603i	$-0.113344\pi$
$728$	−1.65808e6	+	3.67736e6i	−0.115952	+	0.257163i
$729$		−	4.93043e6i		−	0.343610i
$730$	−202129.	+	1.42201e6i	−0.0140385	+	0.0987633i
$731$	−7.07098e6	−	7.07098e6i	−0.489425	−	0.489425i
$732$	−1.61996e6	−	470030.i	−0.111745	−	0.0324226i
$733$	1.88711e7	−	1.88711e7i	1.29729	−	1.29729i	0.367113	−	0.930176i	$-0.380346\pi$
$733$	1.88711e7	−	1.88711e7i	1.29729	−	1.29729i	0.930176	−	0.367113i	$-0.119654\pi$
$734$	−538578.	+	404523.i	−0.0368985	+	0.0277142i
$735$	1.07494e6			0.0733946
$736$	1.32260e6	+	1.66199e7i	0.0899979	+	1.13093i
$737$	5.00922e6			0.339704
$738$	1.19625e7	−	8.98500e6i	0.808505	−	0.607263i
$739$	−4.06846e6	+	4.06846e6i	−0.274043	+	0.274043i	−0.830725	−	0.556682i	$-0.812074\pi$
$739$	−4.06846e6	+	4.06846e6i	−0.274043	+	0.274043i	0.556682	+	0.830725i	$0.312074\pi$
$740$	3.24474e6	+	941457.i	0.217821	+	0.0632006i
$741$	7.74778e6	+	7.74778e6i	0.518360	+	0.518360i
$742$	−20703.9	+	145655.i	−0.00138052	+	0.00971217i
$743$			9.53269e6i			0.633495i	0.948510	+	0.316748i	$0.102591\pi$
$743$			9.53269e6i			0.633495i	−0.948510	+	0.316748i	$0.897409\pi$
$744$	3.98984e6	+	1.79897e6i	0.264255	+	0.119149i
$745$			4.17390e6i			0.275519i
$746$	2.40484e7	+	3.41831e6i	1.58212	+	0.224887i
$747$	−1.75415e6	−	1.75415e6i	−0.115018	−	0.115018i
$748$	−5.04654e6	+	2.77665e6i	−0.329792	+	0.181454i
$749$	1.95651e6	−	1.95651e6i	0.127432	−	0.127432i
$750$	−1.38974e6	−	1.85028e6i	−0.0902150	−	0.120112i
$751$	7.24411e6			0.468689			0.234345	−	0.972154i	$-0.424706\pi$
$751$	7.24411e6			0.468689			0.234345	+	0.972154i	$0.424706\pi$
$752$	2.02258e7	+	1.28159e7i	1.30425	+	0.826428i
$753$	−6.47577e6			−0.416202
$754$	−1.49440e7	−	1.98963e7i	−0.957277	−	1.27451i
$755$	−2.27098e6	+	2.27098e6i	−0.144993	+	0.144993i
$756$	1.07129e6	+	1.94707e6i	0.0681716	+	0.123901i
$757$	−1.61055e7	−	1.61055e7i	−1.02149	−	1.02149i	−0.999764	−	0.0217275i	$-0.993083\pi$
$757$	−1.61055e7	−	1.61055e7i	−1.02149	−	1.02149i	−0.0217275	−	0.999764i	$-0.506917\pi$
$758$	−5.84824e6	−	831288.i	−0.369702	−	0.0525507i
$759$		−	4.24124e6i		−	0.267232i
$760$	−2.00739e6	−	5.30400e6i	−0.126066	−	0.333096i
$761$		−	2.02681e6i		−	0.126868i	−0.997986	−	0.0634340i	$-0.979795\pi$
$761$		−	2.02681e6i		−	0.126868i	0.997986	−	0.0634340i	$-0.0202052\pi$
$762$	−497308.	+	3.49864e6i	−0.0310268	+	0.218279i
$763$	3.93686e6	+	3.93686e6i	0.244815	+	0.244815i
$764$	−4.25752e6	+	1.46736e7i	−0.263890	+	0.909500i
$765$	1.23724e6	−	1.23724e6i	0.0764365	−	0.0764365i
$766$	−2.05332e7	+	1.54223e7i	−1.26440	+	0.949682i
$767$	6.73701e6			0.413503
$768$	5.36073e6	+	1.92154e6i	0.327960	+	0.117556i
$769$	1.87247e7			1.14182			0.570910	−	0.821012i	$-0.306590\pi$
$769$	1.87247e7			1.14182			0.570910	+	0.821012i	$0.306590\pi$
$770$	−424676.	+	318971.i	−0.0258125	+	0.0193876i
$771$	3.14606e6	−	3.14606e6i	0.190603	−	0.190603i
$772$	−5.18371e6	+	1.78657e7i	−0.313038	+	1.07889i
$773$	−7.39341e6	−	7.39341e6i	−0.445037	−	0.445037i	0.448664	−	0.893701i	$-0.351900\pi$
$773$	−7.39341e6	−	7.39341e6i	−0.445037	−	0.445037i	−0.893701	+	0.448664i	$0.851900\pi$
$774$	−2.56203e6	+	1.80243e7i	−0.153721	+	1.08145i
$775$			1.32328e7i			0.791403i
$776$	3.43530e6	+	9.07689e6i	0.204791	+	0.541106i
$777$			1.30020e6i			0.0772603i
$778$	−1.72644e7	−	2.45401e6i	−1.02259	−	0.145354i
$779$	−2.22139e7	−	2.22139e7i	−1.31154	−	1.31154i
$780$	823314.	+	1.49637e6i	0.0484539	+	0.0880646i
$781$	5.34893e6	−	5.34893e6i	0.313790	−	0.313790i
$782$	6.48683e6	+	8.63651e6i	0.379328	+	0.505035i
$783$	−1.37086e7			−0.799079
$784$	−1.38589e7	−	8.78158e6i	−0.805265	−	0.510250i
$785$	−3.64483e6			−0.211107
$786$	3.06797e6	+	4.08467e6i	0.177131	+	0.235831i
$787$	−1.30646e7	+	1.30646e7i	−0.751896	+	0.751896i	−0.974833	−	0.222937i	$-0.928436\pi$
$787$	−1.30646e7	+	1.30646e7i	−0.751896	+	0.751896i	0.222937	+	0.974833i	$0.428436\pi$
$788$	−1.17029e6	+	643904.i	−0.0671395	+	0.0369408i
$789$	−6.13998e6	−	6.13998e6i	−0.351135	−	0.351135i
$790$	7.13888e6	+	1.01474e6i	0.406970	+	0.0578480i
$791$			2.67239e6i			0.151865i
$792$	9.55965e6	+	4.31033e6i	0.541538	+	0.244173i
$793$			7.72135e6i			0.436024i
$794$	1.73560e6	−	1.22102e7i	0.0977006	−	0.687339i
$795$	44045.0	+	44045.0i	0.00247160	+	0.00247160i
$796$	2.09061e6	+	606588.i	0.116947	+	0.0339321i
$797$	1.46175e7	−	1.46175e7i	0.815131	−	0.815131i	−0.170267	−	0.985398i	$-0.554463\pi$
$797$	1.46175e7	−	1.46175e7i	0.815131	−	0.815131i	0.985398	+	0.170267i	$0.0544631\pi$
$798$	1.74506e6	−	1.31071e6i	0.0970071	−	0.0728615i
$799$	1.55124e7			0.859630
$800$	1.36587e6	+	1.71637e7i	0.0754542	+	0.948169i
$801$	−2.87016e7			−1.58061
$802$	−9.35034e6	+	7.02298e6i	−0.513324	+	0.385554i
$803$	−3.94337e6	+	3.94337e6i	−0.215813	+	0.215813i
$804$	−3.08137e6	−	894056.i	−0.168114	−	0.0487781i
$805$	704264.	+	704264.i	0.0383041	+	0.0383041i
$806$	2.81943e6	−	1.98351e7i	0.152870	−	1.07547i
$807$		−	1.72378e6i		−	0.0931748i
$808$	713704.	−	1.58289e6i	0.0384583	−	0.0852945i
$809$		−	2.86509e6i		−	0.153910i	−0.997035	−	0.0769551i	$-0.975480\pi$
$809$		−	2.86509e6i		−	0.153910i	0.997035	−	0.0769551i	$-0.0245198\pi$
$810$	−2.65793e6	−	377806.i	−0.142341	−	0.0202328i
$811$	−2.82668e6	−	2.82668e6i	−0.150912	−	0.150912i	0.627613	−	0.778525i	$-0.284032\pi$
$811$	−2.82668e6	−	2.82668e6i	−0.150912	−	0.150912i	−0.778525	+	0.627613i	$0.784032\pi$
$812$	−4.34249e6	+	2.38928e6i	−0.231126	+	0.127168i
$813$	4.46297e6	−	4.46297e6i	0.236808	−	0.236808i
$814$	7.87813e6	+	1.04889e7i	0.416737	+	0.554840i
$815$	1.25823e6			0.0663539
$816$	3.59992e6	−	807313.i	0.189264	−	0.0424440i
$817$	3.82279e7			2.00367
$818$	5.96101e6	+	7.93644e6i	0.311484	+	0.414708i
$819$	3.36428e6	−	3.36428e6i	0.175260	−	0.175260i
$820$	−2.36055e6	−	4.29028e6i	−0.122597	−	0.222818i
$821$	1.42183e7	+	1.42183e7i	0.736191	+	0.736191i	0.971839	−	0.235647i	$-0.0757210\pi$
$821$	1.42183e7	+	1.42183e7i	0.736191	+	0.736191i	−0.235647	+	0.971839i	$0.575721\pi$
$822$	−774803.	−	110133.i	−0.0399956	−	0.00568510i
$823$		−	3.16278e7i		−	1.62768i	−0.581088	−	0.813841i	$-0.697373\pi$
$823$		−	3.16278e7i		−	1.62768i	0.581088	−	0.813841i	$-0.302627\pi$
$824$	4.03664e6	−	1.52773e6i	0.207111	−	0.0783844i
$825$		−	4.38000e6i		−	0.224047i
$826$	188845.	−	1.32856e6i	0.00963067	−	0.0677533i
$827$	7.48208e6	+	7.48208e6i	0.380416	+	0.380416i	0.871252	−	0.490836i	$-0.163309\pi$
$827$	7.48208e6	+	7.48208e6i	0.380416	+	0.380416i	−0.490836	+	0.871252i	$0.663309\pi$
$828$	5.47965e6	−	1.88857e7i	0.277765	−	0.957318i
$829$	−2.07352e7	+	2.07352e7i	−1.04790	+	1.04790i	−0.0491107	+	0.998793i	$0.515639\pi$
$829$	−2.07352e7	+	2.07352e7i	−1.04790	+	1.04790i	−0.998793	+	0.0491107i	$0.984361\pi$
$830$	−649225.	+	487629.i	−0.0327115	+	0.0245694i
$831$	192490.			0.00966954
$832$	1.60961e6	−	2.60183e7i	0.0806144	−	1.30308i
$833$	−1.06292e7			−0.530749
$834$	6.64827e6	−	4.99347e6i	0.330974	−	0.248592i
$835$	5.53739e6	−	5.53739e6i	0.274846	−	0.274846i
$836$	6.13587e6	−	2.11473e7i	0.303641	−	1.04650i
$837$	−7.80455e6	−	7.80455e6i	−0.385065	−	0.385065i
$838$	−1.76290e6	+	1.24023e7i	−0.0867198	+	0.610088i
$839$			5.53194e6i			0.271314i	0.990756	+	0.135657i	$0.0433145\pi$
$839$			5.53194e6i			0.271314i	−0.990756	+	0.135657i	$0.956685\pi$
$840$	318166.	−	120415.i	0.0155581	−	0.00588820i
$841$		−	1.00629e7i		−	0.490604i
$842$	2.27127e7	+	3.22846e6i	1.10405	+	0.156933i
$843$	414221.	+	414221.i	0.0200754	+	0.0200754i
$844$	−3.85572e6	−	7.00774e6i	−0.186316	−	0.338627i
$845$	2.28494e6	−	2.28494e6i	0.110086	−	0.110086i
$846$	−1.69607e7	−	2.25813e7i	−0.814735	−	1.08473i
$847$	2.44912e6			0.117301
$848$	−208041.	−	927683.i	−0.00993481	−	0.0443006i
$849$	−1.39794e7			−0.665611
$850$	6.69905e6	+	8.91906e6i	0.318029	+	0.423421i
$851$	1.73943e7	−	1.73943e7i	0.823348	−	0.823348i
$852$	−4.24503e6	+	2.33565e6i	−0.200347	+	0.110232i
$853$	1.05005e6	+	1.05005e6i	0.0494125	+	0.0494125i	0.731381	−	0.681969i	$-0.238876\pi$
$853$	1.05005e6	+	1.05005e6i	0.0494125	+	0.0494125i	−0.681969	+	0.731381i	$0.738876\pi$
$854$	1.52267e6	+	216437.i	0.0714433	+	0.0101552i
$855$			6.68891e6i			0.312925i
$856$	−7.34960e6	+	1.63003e7i	−0.342830	+	0.760345i
$857$			3.18114e7i			1.47955i	0.672852	+	0.739777i	$0.265069\pi$
$857$			3.18114e7i			1.47955i	−0.672852	+	0.739777i	$0.734931\pi$
$858$	−933218.	+	6.56534e6i	−0.0432778	+	0.304466i
$859$	1.56482e7	+	1.56482e7i	0.723572	+	0.723572i	0.969331	−	0.245759i	$-0.0790372\pi$
$859$	1.56482e7	+	1.56482e7i	0.723572	+	0.723572i	−0.245759	+	0.969331i	$0.579037\pi$
$860$	5.72271e6	+	1.66044e6i	0.263849	+	0.0765554i
$861$	1.33252e6	−	1.33252e6i	0.0612586	−	0.0612586i
$862$	2.44004e7	−	1.83270e7i	1.11848	−	0.840086i
$863$	6.33821e6			0.289694			0.144847	−	0.989454i	$-0.453731\pi$
$863$	6.33821e6			0.289694			0.144847	+	0.989454i	$0.453731\pi$
$864$	−1.09285e7	−	9.31737e6i	−0.498054	−	0.424628i
$865$	−5.55282e6			−0.252333
$866$	2.15852e6	−	1.62125e6i	0.0978049	−	0.0734607i
$867$	−3.76249e6	+	3.76249e6i	−0.169992	+	0.169992i
$868$	−3.83251e6	−	1.11200e6i	−0.172657	−	0.0500962i
$869$	1.97968e7	+	1.97968e7i	0.889293	+	0.889293i
$870$	−295318.	+	2.07761e6i	−0.0132279	+	0.0930606i
$871$			1.46870e7i			0.655975i
$872$	−3.27992e7	−	1.47887e7i	−1.46074	−	0.658628i
$873$		−	1.14469e7i		−	0.508339i
$874$	−4.08807e7	−	5.81092e6i	−1.81026	−	0.257316i
$875$	1.49195e6	+	1.49195e6i	0.0658770	+	0.0658770i
$876$	3.12955e6	−	1.72190e6i	0.137791	−	0.0758139i
$877$	−2.46152e7	+	2.46152e7i	−1.08070	+	1.08070i	−0.0842560	+	0.996444i	$0.526851\pi$
$877$	−2.46152e7	+	2.46152e7i	−1.08070	+	1.08070i	−0.996444	+	0.0842560i	$0.973149\pi$
$878$	1.41902e7	+	1.88927e7i	0.621228	+	0.827098i
$879$	−2.74810e6			−0.119966
$880$	1.83708e6	−	2.89923e6i	0.0799688	−	0.126205i
$881$	−1.93261e7			−0.838891			−0.419445	−	0.907781i	$-0.637775\pi$
$881$	−1.93261e7			−0.838891			−0.419445	+	0.907781i	$0.637775\pi$
$882$	1.16216e7	+	1.54729e7i	0.503031	+	0.669731i
$883$	−1.14580e7	+	1.14580e7i	−0.494546	+	0.494546i	−0.909735	−	0.415189i	$-0.863715\pi$
$883$	−1.14580e7	+	1.14580e7i	−0.494546	+	0.494546i	0.415189	+	0.909735i	$0.363715\pi$
$884$	−8.14113e6	−	1.47964e7i	−0.350392	−	0.636834i
$885$	−401745.	−	401745.i	−0.0172422	−	0.0172422i
$886$	−1.93912e6	−	275633.i	−0.0829890	−	0.0117963i
$887$		−	1.19088e7i		−	0.508228i	−0.967174	−	0.254114i	$-0.918216\pi$
$887$		−	1.19088e7i		−	0.508228i	0.967174	−	0.254114i	$-0.0817839\pi$
$888$	−2.97408e6	−	7.85824e6i	−0.126567	−	0.334421i
$889$		−	3.22208e6i		−	0.136736i
$890$	−1.32202e6	+	9.30064e6i	−0.0559453	+	0.393584i
$891$	−7.37068e6	−	7.37068e6i	−0.311038	−	0.311038i
$892$	−6.93638e6	+	2.39063e7i	−0.291891	+	1.00600i
$893$	−4.19324e7	+	4.19324e7i	−1.75963	+	1.75963i
$894$	8.29977e6	−	6.23390e6i	0.347314	−	0.260865i
$895$	7.64646e6			0.319082
$896$	−5.08576e6	−	1.04674e6i	−0.211634	−	0.0435581i
$897$	1.24353e7			0.516030
$898$	−1.32587e7	+	9.95855e6i	−0.548670	+	0.412103i
$899$	1.74063e7	−	1.74063e7i	0.718302	−	0.718302i
$900$	5.65893e6	−	1.95035e7i	0.232878	−	0.802614i
$901$	−435527.	−	435527.i	−0.0178732	−	0.0178732i
$902$	2.67566e6	−	1.88237e7i	0.109500	−	0.770351i
$903$			2.29314e6i			0.0935861i
$904$	−6.11284e6	−	1.61516e7i	−0.248784	−	0.657347i
$905$		−	1.46614e6i		−	0.0595051i
$906$	7.90765e6	+	1.12402e6i	0.320057	+	0.0454939i
$907$	2.14692e7	+	2.14692e7i	0.866558	+	0.866558i	0.992090	−	0.125532i	$-0.0400637\pi$
$907$	2.14692e7	+	2.14692e7i	0.866558	+	0.866558i	−0.125532	+	0.992090i	$0.540064\pi$
$908$	1.97803e7	+	3.59506e7i	0.796194	+	1.44708i
$909$	−1.44812e6	+	1.44812e6i	−0.0581294	+	0.0581294i
$910$	−935222.	−	1.24515e6i	−0.0374379	−	0.0498445i
$911$	−3.33971e7			−1.33325			−0.666627	−	0.745391i	$-0.732263\pi$
$911$	−3.33971e7			−1.33325			−0.666627	+	0.745391i	$0.732263\pi$
$912$	−7.54885e6	+	1.19134e7i	−0.300534	+	0.474297i
$913$	−3.15260e6			−0.125168
$914$	1.44226e7	+	1.92021e7i	0.571053	+	0.760296i
$915$	460444.	−	460444.i	0.0181813	−	0.0181813i
$916$	6.22319e6	−	3.42405e6i	0.245061	−	0.134835i
$917$	−3.29362e6	−	3.29362e6i	−0.129345	−	0.129345i
$918$	−9.21138e6	−	1.30934e6i	−0.360760	−	0.0512796i
$919$		−	2.78332e7i		−	1.08711i	−0.839373	−	0.543556i	$-0.817077\pi$
$919$		−	2.78332e7i		−	1.08711i	0.839373	−	0.543556i	$-0.182923\pi$
$920$	−5.86743e6	−	2.64555e6i	−0.228549	−	0.103050i
$921$		−	1.68612e7i		−	0.654998i
$922$	1.92844e6	−	1.35668e7i	0.0747098	−	0.525595i
$923$	1.56830e7	+	1.56830e7i	0.605934	+	0.605934i
$924$	1.26854e6	+	368066.i	0.0488794	+	0.0141823i
$925$	1.79634e7	−	1.79634e7i	0.690294	−	0.690294i
$926$	6.29542e6	−	4.72845e6i	0.241266	−	0.181214i
$927$	−5.09064e6			−0.194569
$928$	2.07803e7	−	2.43736e7i	0.792104	−	0.929073i
$929$	2.77050e7			1.05322			0.526609	−	0.850108i	$-0.323463\pi$
$929$	2.77050e7			1.05322			0.526609	+	0.850108i	$0.323463\pi$
$930$	−1.35095e6	+	1.01469e6i	−0.0512190	+	0.0384703i
$931$	2.87325e7	−	2.87325e7i	1.08642	−	1.08642i
$932$	3.19465e7	+	9.26924e6i	1.20471	+	0.349546i
$933$	5.67610e6	+	5.67610e6i	0.213474	+	0.213474i
$934$	−1.94222e6	+	1.36638e7i	−0.0728501	+	0.512512i
$935$		−	2.22360e6i		−	0.0831816i
$936$	−1.26379e7	+	2.80288e7i	−0.471503	+	1.04572i
$937$		−	1.14126e7i		−	0.424653i	−0.977199	−	0.212327i	$-0.931896\pi$
$937$		−	1.14126e7i		−	0.424653i	0.977199	−	0.212327i	$-0.0681041\pi$
$938$	2.89631e6	+	411691.i	0.107483	+	0.0152779i
$939$	2.37252e6	+	2.37252e6i	0.0878104	+	0.0878104i
$940$	−8.09861e6	+	4.45592e6i	−0.298945	+	0.164482i
$941$	1.72720e7	−	1.72720e7i	0.635869	−	0.635869i	−0.313665	−	0.949534i	$-0.601557\pi$
$941$	1.72720e7	−	1.72720e7i	0.635869	−	0.635869i	0.949534	+	0.313665i	$0.101557\pi$
$942$	5.44372e6	+	7.24772e6i	0.199879	+	0.266118i
$943$	−3.56536e7			−1.30564
$944$	1.89759e6	+	8.46163e6i	0.0693064	+	0.309047i
$945$	−857912.			−0.0312509
$946$	1.38946e7	+	1.84991e7i	0.504798	+	0.672083i
$947$	−6.99199e6	+	6.99199e6i	−0.253353	+	0.253353i	−0.822344	−	0.568991i	$-0.807334\pi$
$947$	−6.99199e6	+	6.99199e6i	−0.253353	+	0.253353i	0.568991	+	0.822344i	$0.307334\pi$
$948$	−8.64442e6	−	1.57112e7i	−0.312403	−	0.567790i
$949$	−1.15619e7	−	1.15619e7i	−0.416740	−	0.416740i
$950$	−4.22182e7	−	6.00103e6i	−1.51772	−	0.215733i
$951$			1.55286e7i			0.556777i
$952$	−3.14610e6	+	1.19069e6i	−0.112507	+	0.0425802i
$953$		−	5.13807e7i		−	1.83260i	−0.400494	−	0.916299i	$-0.631161\pi$
$953$		−	5.13807e7i		−	1.83260i	0.400494	−	0.916299i	$-0.368839\pi$
$954$	−157805.	+	1.11018e6i	−0.00561371	+	0.0394933i
$955$	−4.17069e6	−	4.17069e6i	−0.147979	−	0.147979i
$956$	9.58782e6	−	3.30445e7i	0.339293	−	1.16938i
$957$	−5.76141e6	+	5.76141e6i	−0.203352	+	0.203352i
$958$	2.92130e7	−	2.19417e7i	1.02840	−	0.772426i
$959$	713557.			0.0250543
$960$	−1.64752e6	+	1.45555e6i	−0.0576970	+	0.0509741i
$961$	−8.80975e6			−0.307720
$962$	−3.07533e7	+	2.30986e7i	−1.07141	+	0.804727i
$963$	1.49125e7	−	1.49125e7i	0.518185	−	0.518185i
$964$	−1.15855e7	+	3.99295e7i	−0.401533	+	1.38389i
$965$	−5.07799e6	−	5.07799e6i	−0.175539	−	0.175539i
$966$	348574.	−	2.45227e6i	0.0120185	−	0.0845524i
$967$		−	4.37686e7i		−	1.50521i	−0.658474	−	0.752603i	$-0.728798\pi$
$967$		−	4.37686e7i		−	1.50521i	0.658474	−	0.752603i	$-0.271202\pi$
$968$	−1.48022e7	+	5.60214e6i	−0.507736	+	0.192161i
$969$			9.13713e6i			0.312608i
$970$	−3.70934e6	−	527257.i	−0.126581	−	0.0179926i
$971$	−2.31145e7	−	2.31145e7i	−0.786749	−	0.786749i	0.194211	−	0.980960i	$-0.437785\pi$
$971$	−2.31145e7	−	2.31145e7i	−0.786749	−	0.786749i	−0.980960	+	0.194211i	$0.937785\pi$
$972$	1.25119e7	+	2.27402e7i	0.424772	+	0.772020i
$973$	−5.36074e6	+	5.36074e6i	−0.181528	+	0.181528i
$974$	−1.20732e7	−	1.60742e7i	−0.407780	−	0.542915i
$975$	1.28421e7			0.432639
$976$	−9.69795e6	+	2.17485e6i	−0.325878	+	0.0730810i
$977$	1.42151e7			0.476445			0.238223	−	0.971211i	$-0.423435\pi$
$977$	1.42151e7			0.476445			0.238223	+	0.971211i	$0.423435\pi$
$978$	−1.87923e6	−	2.50198e6i	−0.0628249	−	0.0836445i
$979$	−2.57915e7	+	2.57915e7i	−0.860044	+	0.860044i
$980$	5.54924e6	−	3.05324e6i	0.184573	−	0.101554i
$981$	3.00067e7	+	3.00067e7i	0.995510	+	0.995510i
$982$	1.44867e7	+	2.05918e6i	0.479391	+	0.0681422i
$983$			4.12375e7i			1.36116i	0.732675	+	0.680579i	$0.238272\pi$
$983$			4.12375e7i			1.36116i	−0.732675	+	0.680579i	$0.761728\pi$
$984$	−5.00560e6	+	1.11017e7i	−0.164804	+	0.365511i
$985$		−	515651.i		−	0.0169342i
$986$	2.92018e6	−	2.05439e7i	0.0956571	−	0.672963i
$987$	−2.51536e6	−	2.51536e6i	−0.0821877	−	0.0821877i
$988$	6.20038e7	+	1.79903e7i	2.02081	+	0.586337i
$989$	3.06781e7	−	3.06781e7i	0.997329	−	0.997329i
$990$	−3.23687e6	+	2.43120e6i	−0.104963	+	0.0788374i
$991$	−3.91749e7			−1.26714			−0.633568	−	0.773687i	$-0.718410\pi$
$991$	−3.91749e7			−1.26714			−0.633568	+	0.773687i	$0.718410\pi$
$992$	2.57069e7	−	2.04572e6i	0.829412	−	0.0660036i
$993$	1.15759e7			0.372549
$994$	3.53235e6	−	2.65312e6i	0.113396	−	0.0851709i
$995$	−594217.	+	594217.i	−0.0190277	+	0.0190277i
$996$	1.93929e6	+	562684.i	0.0619434	+	0.0179728i
$997$	683406.	+	683406.i	0.0217741	+	0.0217741i	0.717910	−	0.696136i	$-0.245099\pi$
$997$	683406.	+	683406.i	0.0217741	+	0.0217741i	−0.696136	+	0.717910i	$0.745099\pi$
$998$	−780028.	+	5.48762e6i	−0.0247904	+	0.174404i
$999$			2.11892e7i			0.671739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.5.7	✓	18
3.2	odd	2		144.6.k.a.37.3		18
4.3	odd	2		64.6.e.a.49.4		18
8.3	odd	2		128.6.e.a.97.6		18
8.5	even	2		128.6.e.b.97.4		18
12.11	even	2		576.6.k.a.433.4		18
16.3	odd	4		64.6.e.a.17.4		18
16.5	even	4		128.6.e.b.33.4		18
16.11	odd	4		128.6.e.a.33.6		18
16.13	even	4	inner	16.6.e.a.13.7	yes	18
32.3	odd	8		1024.6.a.l.1.8		18
32.13	even	8		1024.6.a.k.1.8		18
32.19	odd	8		1024.6.a.l.1.11		18
32.29	even	8		1024.6.a.k.1.11		18
48.29	odd	4		144.6.k.a.109.3		18
48.35	even	4		576.6.k.a.145.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.7	✓	18	1.1	even	1	trivial
16.6.e.a.13.7	yes	18	16.13	even	4	inner
64.6.e.a.17.4		18	16.3	odd	4
64.6.e.a.49.4		18	4.3	odd	2
128.6.e.a.33.6		18	16.11	odd	4
128.6.e.a.97.6		18	8.3	odd	2
128.6.e.b.33.4		18	16.5	even	4
128.6.e.b.97.4		18	8.5	even	2
144.6.k.a.37.3		18	3.2	odd	2
144.6.k.a.109.3		18	48.29	odd	4
576.6.k.a.145.4		18	48.35	even	4
576.6.k.a.433.4		18	12.11	even	2
1024.6.a.k.1.8		18	32.13	even	8
1024.6.a.k.1.11		18	32.29	even	8
1024.6.a.l.1.8		18	32.3	odd	8
1024.6.a.l.1.11		18	32.19	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.52311 - 3.39728i) q^{2} +(3.84023 - 3.84023i) q^{3} +(8.91700 - 30.7325i) q^{4} +(8.73514 + 8.73514i) q^{5} +(4.32344 - 30.4161i) q^{6} +28.0117i q^{7} +(-64.0743 - 169.300i) q^{8} +213.505i q^{9} +O(q^{10})\)	\(q+(4.52311 - 3.39728i) q^{2} +(3.84023 - 3.84023i) q^{3} +(8.91700 - 30.7325i) q^{4} +(8.73514 + 8.73514i) q^{5} +(4.32344 - 30.4161i) q^{6} +28.0117i q^{7} +(-64.0743 - 169.300i) q^{8} +213.505i q^{9} +(69.1857 + 9.83427i) q^{10} +(191.858 + 191.858i) q^{11} +(-83.7765 - 152.263i) q^{12} +(-562.527 + 562.527i) q^{13} +(95.1637 + 126.700i) q^{14} +67.0898 q^{15} +(-864.974 - 548.084i) q^{16} -663.401 q^{17} +(725.337 + 965.707i) q^{18} +(1793.28 - 1793.28i) q^{19} +(346.344 - 190.561i) q^{20} +(107.571 + 107.571i) q^{21} +(1519.59 + 216.000i) q^{22} -2878.23i q^{23} +(-896.210 - 404.090i) q^{24} -2972.39i q^{25} +(-633.309 + 4455.43i) q^{26} +(1753.08 + 1753.08i) q^{27} +(860.871 + 249.781i) q^{28} +(-3909.86 + 3909.86i) q^{29} +(303.454 - 227.923i) q^{30} -4451.90 q^{31} +(-5774.36 + 459.517i) q^{32} +1473.56 q^{33} +(-3000.63 + 2253.76i) q^{34} +(-244.686 + 244.686i) q^{35} +(6561.55 + 1903.83i) q^{36} +(6043.41 + 6043.41i) q^{37} +(2018.92 - 14203.4i) q^{38} +4320.46i q^{39} +(919.161 - 2038.56i) q^{40} -12387.3i q^{41} +(852.007 + 121.107i) q^{42} +(10658.7 + 10658.7i) q^{43} +(7607.09 - 4185.48i) q^{44} +(-1865.00 + 1865.00i) q^{45} +(-9778.14 - 13018.5i) q^{46} -23383.1 q^{47} +(-5426.46 + 1216.93i) q^{48} +16022.3 q^{49} +(-10098.1 - 13444.5i) q^{50} +(-2547.61 + 2547.61i) q^{51} +(12271.8 + 22303.9i) q^{52} +(656.507 + 656.507i) q^{53} +(13885.1 + 1973.67i) q^{54} +3351.82i q^{55} +(4742.39 - 1794.83i) q^{56} -13773.2i q^{57} +(-4401.83 + 30967.6i) q^{58} +(-5988.17 - 5988.17i) q^{59} +(598.240 - 2061.84i) q^{60} +(6863.09 - 6863.09i) q^{61} +(-20136.4 + 15124.3i) q^{62} -5980.66 q^{63} +(-24557.0 + 21695.6i) q^{64} -9827.51 q^{65} +(6665.06 - 5006.09i) q^{66} +(13054.5 - 13054.5i) q^{67} +(-5915.54 + 20388.0i) q^{68} +(-11053.1 - 11053.1i) q^{69} +(-275.475 + 1938.01i) q^{70} -27879.6i q^{71} +(36146.4 - 13680.2i) q^{72} +20553.5i q^{73} +(47866.1 + 6803.84i) q^{74} +(-11414.7 - 11414.7i) q^{75} +(-39121.2 - 71102.5i) q^{76} +(-5374.28 + 5374.28i) q^{77} +(14677.8 + 19541.9i) q^{78} +103184. q^{79} +(-2768.08 - 12343.3i) q^{80} -38417.3 q^{81} +(-42083.2 - 56029.3i) q^{82} +(-8215.97 + 8215.97i) q^{83} +(4265.15 - 2346.73i) q^{84} +(-5794.90 - 5794.90i) q^{85} +(84420.9 + 11999.9i) q^{86} +30029.5i q^{87} +(20188.4 - 44774.8i) q^{88} +134430. i q^{89} +(-2099.67 + 14771.5i) q^{90} +(-15757.4 - 15757.4i) q^{91} +(-88455.2 - 25665.2i) q^{92} +(-17096.3 + 17096.3i) q^{93} +(-105764. + 79439.0i) q^{94} +31329.0 q^{95} +(-20410.2 + 23939.5i) q^{96} -53614.2 q^{97} +(72470.8 - 54432.4i) q^{98} +(-40962.8 + 40962.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

Modular forms

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