LMFDB - Embedded newform 66.6.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,6,Mod(25,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("66.25");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	66.e (of order $5$, degree $4$, 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:	$10.5853321077$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 89x^{6} + 22551x^{4} + 4006069x^{2} + 405257161 $ x^8 + 89x^6 + 22551x^4 + 4006069*x^2 + 405257161
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-10.5047 + 7.63209i$ of defining polynomial
Character	$\chi$	$=$	66.31
Dual form			66.6.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-9.47098 - 29.1487i) q^{5} +(11.1246 + 34.2380i) q^{6} +(1.28786 + 0.935685i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-9.47098 - 29.1487i) q^{5} +(11.1246 + 34.2380i) q^{6} +(1.28786 + 0.935685i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} -122.595 q^{10} +(-119.850 + 382.997i) q^{11} +144.000 q^{12} +(-289.220 + 890.129i) q^{13} +(5.15144 - 3.74274i) q^{14} +(223.158 + 162.134i) q^{15} +(79.1084 + 243.470i) q^{16} +(121.877 + 375.100i) q^{17} +(-262.122 - 190.442i) q^{18} +(-1730.20 + 1257.07i) q^{19} +(-151.536 + 466.379i) q^{20} -14.3269 q^{21} +(1308.87 + 929.347i) q^{22} -90.5594 q^{23} +(177.994 - 547.809i) q^{24} +(1768.23 - 1284.70i) q^{25} +(3028.76 + 2200.52i) q^{26} +(225.273 + 693.320i) q^{27} +(-7.87070 - 24.2235i) q^{28} +(854.075 + 620.522i) q^{29} +(892.633 - 648.536i) q^{30} +(-1290.47 + 3971.67i) q^{31} +1024.00 q^{32} +(-1153.44 - 3422.68i) q^{33} +1577.61 q^{34} +(15.0767 - 46.4013i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-9318.86 - 6770.54i) q^{37} +(2643.52 + 8135.91i) q^{38} +(-2602.98 - 8011.16i) q^{39} +(1586.90 + 1152.95i) q^{40} +(1075.99 - 781.752i) q^{41} +(-17.7091 + 54.5029i) q^{42} -17727.1 q^{43} +(5153.29 - 3830.49i) q^{44} -2482.55 q^{45} +(-111.938 + 344.508i) q^{46} +(8078.28 - 5869.21i) q^{47} +(-1863.98 - 1354.26i) q^{48} +(-5192.87 - 15982.0i) q^{49} +(-2701.62 - 8314.72i) q^{50} +(-2871.71 - 2086.42i) q^{51} +(12115.0 - 8802.08i) q^{52} +(-7853.15 + 24169.5i) q^{53} +2916.00 q^{54} +(12299.0 - 133.898i) q^{55} -101.880 q^{56} +(5947.91 - 18305.8i) q^{57} +(3416.30 - 2482.09i) q^{58} +(6942.17 + 5043.78i) q^{59} +(-1363.82 - 4197.41i) q^{60} +(-12159.0 - 37421.5i) q^{61} +(13514.0 + 9818.51i) q^{62} +(104.317 - 75.7905i) q^{63} +(1265.73 - 3895.53i) q^{64} +28685.3 q^{65} +(-14446.4 + 157.276i) q^{66} +6661.08 q^{67} +(1950.04 - 6001.60i) q^{68} +(659.377 - 479.065i) q^{69} +(-157.885 - 114.710i) q^{70} +(9026.52 + 27780.8i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-311.338 - 226.200i) q^{73} +(-37275.4 + 27082.2i) q^{74} +(-6078.64 + 18708.1i) q^{75} +34218.4 q^{76} +(-512.715 + 381.105i) q^{77} -33693.7 q^{78} +(-7944.07 + 24449.3i) q^{79} +(6347.61 - 4611.81i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(-1643.97 - 5059.60i) q^{82} +(31405.1 + 96655.1i) q^{83} +(185.452 + 134.739i) q^{84} +(9779.38 - 7105.14i) q^{85} +(-21911.9 + 67437.9i) q^{86} -9501.25 q^{87} +(-8202.22 - 24339.0i) q^{88} -55800.4 q^{89} +(-3068.60 + 9444.18i) q^{90} +(-1205.36 + 875.742i) q^{91} +(1172.22 + 851.671i) q^{92} +(-11614.3 - 35745.1i) q^{93} +(-12342.5 - 37986.3i) q^{94} +(53028.6 + 38527.5i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(-51711.3 + 159151. i) q^{97} -67217.9 q^{98} +(26504.5 + 18819.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 150 q^{5} - 72 q^{6} + 474 q^{7} - 128 q^{8} - 162 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 150 * q^5 - 72 * q^6 + 474 * q^7 - 128 * q^8 - 162 * q^9	\( 8 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 150 q^{5} - 72 q^{6} + 474 q^{7} - 128 q^{8} - 162 q^{9} - 1200 q^{10} - 582 q^{11} + 1152 q^{12} + 510 q^{13} + 1896 q^{14} - 512 q^{16} + 2004 q^{17} - 648 q^{18} - 540 q^{19} + 2400 q^{20} - 1224 q^{21} + 672 q^{22} - 9944 q^{23} - 1152 q^{24} + 12228 q^{25} - 600 q^{26} - 1458 q^{27} - 6496 q^{28} - 11964 q^{29} - 9160 q^{31} + 8192 q^{32} + 4302 q^{33} + 2896 q^{34} + 42634 q^{35} - 2592 q^{36} - 718 q^{37} + 7560 q^{38} + 4590 q^{39} - 1666 q^{41} - 14616 q^{42} - 70528 q^{43} - 32 q^{44} - 24300 q^{45} + 56664 q^{46} + 51914 q^{47} - 4608 q^{48} - 23052 q^{49} - 52888 q^{50} - 21294 q^{51} - 2400 q^{52} - 53636 q^{53} + 23328 q^{54} + 104980 q^{55} - 8704 q^{56} + 17010 q^{57} - 47856 q^{58} - 17600 q^{59} + 21600 q^{60} - 10618 q^{61} + 77640 q^{62} + 38394 q^{63} - 8192 q^{64} + 116324 q^{65} - 2232 q^{66} - 182364 q^{67} + 32064 q^{68} - 82746 q^{69} - 79104 q^{70} + 29954 q^{71} - 10368 q^{72} + 127228 q^{73} - 2872 q^{74} - 118998 q^{75} - 43200 q^{76} - 33046 q^{77} - 25920 q^{78} + 39938 q^{79} - 13122 q^{81} - 51624 q^{82} + 208842 q^{83} + 68256 q^{84} + 125910 q^{85} + 51528 q^{86} + 36864 q^{87} + 30592 q^{88} - 344008 q^{89} + 48600 q^{90} + 282622 q^{91} - 147104 q^{92} - 82440 q^{93} - 106544 q^{94} + 31306 q^{95} - 18432 q^{96} - 26202 q^{97} + 323072 q^{98} + 13608 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 150 * q^5 - 72 * q^6 + 474 * q^7 - 128 * q^8 - 162 * q^9 - 1200 * q^10 - 582 * q^11 + 1152 * q^12 + 510 * q^13 + 1896 * q^14 - 512 * q^16 + 2004 * q^17 - 648 * q^18 - 540 * q^19 + 2400 * q^20 - 1224 * q^21 + 672 * q^22 - 9944 * q^23 - 1152 * q^24 + 12228 * q^25 - 600 * q^26 - 1458 * q^27 - 6496 * q^28 - 11964 * q^29 - 9160 * q^31 + 8192 * q^32 + 4302 * q^33 + 2896 * q^34 + 42634 * q^35 - 2592 * q^36 - 718 * q^37 + 7560 * q^38 + 4590 * q^39 - 1666 * q^41 - 14616 * q^42 - 70528 * q^43 - 32 * q^44 - 24300 * q^45 + 56664 * q^46 + 51914 * q^47 - 4608 * q^48 - 23052 * q^49 - 52888 * q^50 - 21294 * q^51 - 2400 * q^52 - 53636 * q^53 + 23328 * q^54 + 104980 * q^55 - 8704 * q^56 + 17010 * q^57 - 47856 * q^58 - 17600 * q^59 + 21600 * q^60 - 10618 * q^61 + 77640 * q^62 + 38394 * q^63 - 8192 * q^64 + 116324 * q^65 - 2232 * q^66 - 182364 * q^67 + 32064 * q^68 - 82746 * q^69 - 79104 * q^70 + 29954 * q^71 - 10368 * q^72 + 127228 * q^73 - 2872 * q^74 - 118998 * q^75 - 43200 * q^76 - 33046 * q^77 - 25920 * q^78 + 39938 * q^79 - 13122 * q^81 - 51624 * q^82 + 208842 * q^83 + 68256 * q^84 + 125910 * q^85 + 51528 * q^86 + 36864 * q^87 + 30592 * q^88 - 344008 * q^89 + 48600 * q^90 + 282622 * q^91 - 147104 * q^92 - 82440 * q^93 - 106544 * q^94 + 31306 * q^95 - 18432 * q^96 - 26202 * q^97 + 323072 * q^98 + 13608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$2$	1.23607	−	3.80423i	0.218508	−	0.672499i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$3$	−7.28115	+	5.29007i	−0.467086	+	0.339358i
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	−9.47098	−	29.1487i	−0.169422	−	0.521428i	0.829913	−	0.557893i	$-0.188390\pi$
$5$	−9.47098	−	29.1487i	−0.169422	−	0.521428i	−0.999335	+	0.0364655i	$0.988390\pi$
$6$	11.1246	+	34.2380i	0.126156	+	0.388267i
$7$	1.28786	+	0.935685i	0.00993398	+	0.00721746i	0.592741	−	0.805393i	$-0.298046\pi$
$7$	1.28786	+	0.935685i	0.00993398	+	0.00721746i	−0.582807	+	0.812610i	$0.698046\pi$
$8$	−51.7771	+	37.6183i	−0.286031	+	0.207813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	−122.595			−0.387679
$11$	−119.850	+	382.997i	−0.298645	+	0.954364i
$11$	−119.850	+	382.997i	−0.298645	+	0.954364i
$12$	144.000			0.288675
$13$	−289.220	+	890.129i	−0.474647	+	1.46081i	0.371786	+	0.928318i	$0.378745\pi$
$13$	−289.220	+	890.129i	−0.474647	+	1.46081i	−0.846433	+	0.532495i	$0.821255\pi$
$14$	5.15144	−	3.74274i	0.00702439	−	0.00510352i
$15$	223.158	+	162.134i	0.256085	+	0.186057i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	121.877	+	375.100i	0.102282	+	0.314793i	0.989083	−	0.147359i	$-0.0470774\pi$
$17$	121.877	+	375.100i	0.102282	+	0.314793i	−0.886801	+	0.462152i	$0.847077\pi$
$18$	−262.122	−	190.442i	−0.190687	−	0.138542i
$19$	−1730.20	+	1257.07i	−1.09955	+	0.798867i	−0.980986	−	0.194080i	$-0.937828\pi$
$19$	−1730.20	+	1257.07i	−1.09955	+	0.798867i	−0.118560	+	0.992947i	$0.537828\pi$
$20$	−151.536	+	466.379i	−0.0847111	+	0.260714i
$21$	−14.3269			−0.00708933
$22$	1308.87	+	929.347i	0.576552	+	0.409375i
$23$	−90.5594			−0.0356955			−0.0178478	−	0.999841i	$-0.505681\pi$
$23$	−90.5594			−0.0356955			−0.0178478	+	0.999841i	$0.505681\pi$
$24$	177.994	−	547.809i	0.0630778	−	0.194134i
$25$	1768.23	−	1284.70i	0.565834	−	0.411102i
$26$	3028.76	+	2200.52i	0.878680	+	0.638399i
$27$	225.273	+	693.320i	0.0594703	+	0.183031i
$28$	−7.87070	−	24.2235i	−0.00189722	−	0.00583905i
$29$	854.075	+	620.522i	0.188582	+	0.137013i	0.678071	−	0.734997i	$-0.262816\pi$
$29$	854.075	+	620.522i	0.188582	+	0.137013i	−0.489488	+	0.872010i	$0.662816\pi$
$30$	892.633	−	648.536i	0.181080	−	0.131562i
$31$	−1290.47	+	3971.67i	−0.241182	+	0.742282i	0.755059	+	0.655657i	$0.227608\pi$
$31$	−1290.47	+	3971.67i	−0.241182	+	0.742282i	−0.996241	+	0.0866253i	$0.972392\pi$
$32$	1024.00			0.176777
$33$	−1153.44	−	3422.68i	−0.184378	−	0.547118i
$34$	1577.61			0.234047
$35$	15.0767	−	46.4013i	0.00208035	−	0.00640265i
$36$	−1048.49	+	761.770i	−0.134836	+	0.0979642i
$37$	−9318.86	−	6770.54i	−1.11907	−	0.813054i	−0.135004	−	0.990845i	$-0.543105\pi$
$37$	−9318.86	−	6770.54i	−1.11907	−	0.813054i	−0.984068	+	0.177791i	$0.943105\pi$
$38$	2643.52	+	8135.91i	0.296977	+	0.914002i
$39$	−2602.98	−	8011.16i	−0.274038	−	0.843401i
$40$	1586.90	+	1152.95i	0.156820	+	0.113936i
$41$	1075.99	−	781.752i	0.0999651	−	0.0726289i	−0.536680	−	0.843786i	$-0.680322\pi$
$41$	1075.99	−	781.752i	0.0999651	−	0.0726289i	0.636645	+	0.771157i	$0.280322\pi$
$42$	−17.7091	+	54.5029i	−0.00154908	+	0.00476756i
$43$	−17727.1			−1.46206			−0.731032	−	0.682343i	$-0.760961\pi$
$43$	−17727.1			−1.46206			−0.731032	+	0.682343i	$0.760961\pi$
$44$	5153.29	−	3830.49i	0.401285	−	0.298279i
$45$	−2482.55			−0.182754
$46$	−111.938	+	344.508i	−0.00779976	+	0.0240052i
$47$	8078.28	−	5869.21i	0.533426	−	0.387557i	−0.288212	−	0.957567i	$-0.593061\pi$
$47$	8078.28	−	5869.21i	0.533426	−	0.387557i	0.821638	+	0.570010i	$0.193061\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	−5192.87	−	15982.0i	−0.308970	−	0.950913i
$50$	−2701.62	−	8314.72i	−0.152827	−	0.470352i
$51$	−2871.71	−	2086.42i	−0.154602	−	0.112325i
$52$	12115.0	−	8802.08i	0.621321	−	0.451416i
$53$	−7853.15	+	24169.5i	−0.384020	+	1.18189i	0.553168	+	0.833070i	$0.313419\pi$
$53$	−7853.15	+	24169.5i	−0.384020	+	1.18189i	−0.937189	+	0.348823i	$0.886581\pi$
$54$	2916.00			0.136083
$55$	12299.0	−	133.898i	0.548229	−	0.00596851i
$56$	−101.880			−0.00434131
$57$	5947.91	−	18305.8i	0.242481	−	0.746279i
$58$	3416.30	−	2482.09i	0.133348	−	0.0968829i
$59$	6942.17	+	5043.78i	0.259636	+	0.188637i	0.709987	−	0.704215i	$-0.248701\pi$
$59$	6942.17	+	5043.78i	0.259636	+	0.188637i	−0.450350	+	0.892852i	$0.648701\pi$
$60$	−1363.82	−	4197.41i	−0.0489080	−	0.150523i
$61$	−12159.0	−	37421.5i	−0.418382	−	1.28765i	−0.909191	−	0.416380i	$-0.863299\pi$
$61$	−12159.0	−	37421.5i	−0.418382	−	1.28765i	0.490809	−	0.871267i	$-0.336701\pi$
$62$	13514.0	+	9818.51i	0.446484	+	0.324389i
$63$	104.317	−	75.7905i	0.00331133	−	0.00240582i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	28685.3			0.842124
$66$	−14446.4	+	157.276i	−0.408224	+	0.00444429i
$67$	6661.08			0.181283			0.0906417	−	0.995884i	$-0.471108\pi$
$67$	6661.08			0.181283			0.0906417	+	0.995884i	$0.471108\pi$
$68$	1950.04	−	6001.60i	0.0511412	−	0.157396i
$69$	659.377	−	479.065i	0.0166729	−	0.0121136i
$70$	−157.885	−	114.710i	−0.00385120	−	0.00279806i
$71$	9026.52	+	27780.8i	0.212508	+	0.654031i	0.999321	+	0.0368403i	$0.0117293\pi$
$71$	9026.52	+	27780.8i	0.212508	+	0.654031i	−0.786814	+	0.617191i	$0.788271\pi$
$72$	1601.94	+	4930.28i	0.0364180	+	0.112083i
$73$	−311.338	−	226.200i	−0.00683793	−	0.00496804i	0.584361	−	0.811494i	$-0.301345\pi$
$73$	−311.338	−	226.200i	−0.00683793	−	0.00496804i	−0.591199	+	0.806526i	$0.701345\pi$
$74$	−37275.4	+	27082.2i	−0.791304	+	0.574916i
$75$	−6078.64	+	18708.1i	−0.124782	+	0.384041i
$76$	34218.4			0.679557
$77$	−512.715	+	381.105i	−0.00985482	+	0.00732518i
$78$	−33693.7			−0.627065
$79$	−7944.07	+	24449.3i	−0.143211	+	0.440757i	−0.996777	−	0.0802278i	$-0.974435\pi$
$79$	−7944.07	+	24449.3i	−0.143211	+	0.440757i	0.853566	+	0.520985i	$0.174435\pi$
$80$	6347.61	−	4611.81i	0.110888	−	0.0805650i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	−1643.97	−	5059.60i	−0.0269996	−	0.0830963i
$83$	31405.1	+	96655.1i	0.500386	+	1.54003i	0.808391	+	0.588646i	$0.200339\pi$
$83$	31405.1	+	96655.1i	0.500386	+	1.54003i	−0.308004	+	0.951385i	$0.599661\pi$
$84$	185.452	+	134.739i	0.00286769	+	0.00208350i
$85$	9779.38	−	7105.14i	0.146813	−	0.106666i
$86$	−21911.9	+	67437.9i	−0.319473	+	0.983236i
$87$	−9501.25			−0.134581
$88$	−8202.22	−	24339.0i	−0.112908	−	0.335040i
$89$	−55800.4			−0.746728			−0.373364	−	0.927685i	$-0.621796\pi$
$89$	−55800.4			−0.746728			−0.373364	+	0.927685i	$0.621796\pi$
$90$	−3068.60	+	9444.18i	−0.0399332	+	0.122902i
$91$	−1205.36	+	875.742i	−0.0152585	+	0.0110859i
$92$	1172.22	+	851.671i	0.0144391	+	0.0104907i
$93$	−11614.3	−	35745.1i	−0.139247	−	0.428557i
$94$	−12342.5	−	37986.3i	−0.144073	−	0.443412i
$95$	53028.6	+	38527.5i	0.602839	+	0.437988i
$96$	−7455.90	+	5417.03i	−0.0825700	+	0.0599906i
$97$	−51711.3	+	159151.i	−0.558028	+	1.71743i	0.129780	+	0.991543i	$0.458573\pi$
$97$	−51711.3	+	159151.i	−0.558028	+	1.71743i	−0.687809	+	0.725892i	$0.741427\pi$
$98$	−67217.9			−0.707000
$99$	26504.5	+	18819.3i	0.271789	+	0.192981i
$100$	−34970.5			−0.349705
$101$	−11435.6	+	35195.1i	−0.111546	+	0.343304i	−0.991211	−	0.132290i	$-0.957767\pi$
$101$	−11435.6	+	35195.1i	−0.111546	+	0.343304i	0.879665	+	0.475594i	$0.157767\pi$
$102$	−11486.9	+	8345.69i	−0.109320	+	0.0794258i
$103$	−63969.1	−	46476.3i	−0.594124	−	0.431657i	0.249664	−	0.968333i	$-0.419680\pi$
$103$	−63969.1	−	46476.3i	−0.594124	−	0.431657i	−0.843789	+	0.536676i	$0.819680\pi$
$104$	−18510.1	−	56968.3i	−0.167813	−	0.516475i
$105$	135.690	+	417.612i	0.00120109	+	0.00369657i
$106$	82239.2	+	59750.3i	0.710910	+	0.516506i
$107$	143789.	−	104469.i	1.21413	−	0.882120i	0.218534	−	0.975829i	$-0.429872\pi$
$107$	143789.	−	104469.i	1.21413	−	0.882120i	0.995600	+	0.0937094i	$0.0298725\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	19984.5			0.161112			0.0805560	−	0.996750i	$-0.474330\pi$
$109$	19984.5			0.161112			0.0805560	+	0.996750i	$0.474330\pi$
$110$	14693.0	−	46953.6i	0.115779	−	0.369987i
$111$	103669.			0.798620
$112$	−125.931	+	387.576i	−0.000948611	+	0.00291952i
$113$	169582.	−	123208.i	1.24935	−	0.907703i	0.251163	−	0.967945i	$-0.419187\pi$
$113$	169582.	−	123208.i	1.24935	−	0.907703i	0.998184	+	0.0602416i	$0.0191871\pi$
$114$	−62287.3	−	45254.4i	−0.448888	−	0.326136i
$115$	857.686	+	2639.69i	0.00604761	+	0.0186126i
$116$	−5219.64	−	16064.4i	−0.0360160	−	0.110846i
$117$	61332.3	+	44560.5i	0.414214	+	0.300944i
$118$	27768.7	−	20175.1i	0.183591	−	0.133386i
$119$	−194.015	+	597.115i	−0.00125593	+	0.00386537i
$120$	−17653.7			−0.111913
$121$	−132323.	−	91804.3i	−0.821622	−	0.570033i
$122$	−157389.			−0.957361
$123$	−3698.92	+	11384.1i	−0.0220451	+	0.0678479i
$124$	54056.1	−	39274.1i	0.315712	−	0.229378i
$125$	−131680.	−	95670.8i	−0.753778	−	0.547652i
$126$	−159.382	−	490.526i	−0.000894359	−	0.00275255i
$127$	35056.5	+	107893.i	0.192868	+	0.593585i	0.999995	+	0.00320783i	$0.00102109\pi$
$127$	35056.5	+	107893.i	0.192868	+	0.593585i	−0.807127	+	0.590377i	$0.798979\pi$
$128$	−13254.9	−	9630.27i	−0.0715077	−	0.0519534i
$129$	129074.	−	93777.6i	0.682910	−	0.496163i
$130$	35457.0	−	109125.i	0.184011	−	0.566327i
$131$	30840.5			0.157015			0.0785077	−	0.996914i	$-0.474984\pi$
$131$	30840.5			0.157015			0.0785077	+	0.996914i	$0.474984\pi$
$132$	−17258.4	+	55151.6i	−0.0862115	+	0.275501i
$133$	−3404.48			−0.0166887
$134$	8233.55	−	25340.3i	0.0396119	−	0.121913i
$135$	18075.8	−	13132.9i	0.0853618	−	0.0620190i
$136$	−20421.1	−	14836.8i	−0.0946741	−	0.0687848i
$137$	−86723.1	−	266906.i	−0.394760	−	1.21495i	−0.929148	−	0.369708i	$-0.879458\pi$
$137$	−86723.1	−	266906.i	−0.394760	−	1.21495i	0.534388	−	0.845239i	$-0.320542\pi$
$138$	−1007.44	−	3100.57i	−0.00450319	−	0.0138594i
$139$	165065.	+	119927.i	0.724633	+	0.526477i	0.887861	−	0.460111i	$-0.152191\pi$
$139$	165065.	+	119927.i	0.724633	+	0.526477i	−0.163228	+	0.986588i	$0.552191\pi$
$140$	−631.541	+	458.841i	−0.00272321	+	0.00197853i
$141$	−27770.6	+	85469.3i	−0.117635	+	0.362045i
$142$	116842.			0.486269
$143$	−306254.	−	217452.i	−1.25240	−	0.889251i
$144$	20736.0			0.0833333
$145$	9998.47	−	30772.1i	0.0394924	−	0.121545i
$146$	−1245.35	+	904.800i	−0.00483514	+	0.00351294i
$147$	122356.	+	88896.8i	0.467016	+	0.339307i
$148$	56951.8	+	175280.i	0.213724	+	0.657774i
$149$	−74110.4	−	228088.i	−0.273472	−	0.841661i	−0.989620	−	0.143712i	$-0.954096\pi$
$149$	−74110.4	−	228088.i	−0.273472	−	0.841661i	0.716147	−	0.697949i	$-0.245904\pi$
$150$	63656.3	+	46249.0i	0.231001	+	0.167832i
$151$	−387792.	+	281748.i	−1.38407	+	1.00558i	−0.387579	+	0.921836i	$0.626689\pi$
$151$	−387792.	+	281748.i	−1.38407	+	1.00558i	−0.996487	+	0.0837468i	$0.973311\pi$
$152$	42296.3	−	130175.i	0.148489	−	0.457001i
$153$	31946.7			0.110331
$154$	816.060	+	2421.55i	0.00277281	+	0.00822796i
$155$	127991.			0.427908
$156$	−41647.7	+	128179.i	−0.137019	+	0.421700i
$157$	111107.	−	80724.3i	0.359744	−	0.261370i	−0.393201	−	0.919453i	$-0.628632\pi$
$157$	111107.	−	80724.3i	0.359744	−	0.261370i	0.752945	+	0.658083i	$0.228632\pi$
$158$	83191.4	+	60442.1i	0.265116	+	0.192618i
$159$	−70678.3	−	217526.i	−0.221714	−	0.682366i
$160$	−9698.29	−	29848.3i	−0.0299499	−	0.0921763i
$161$	−116.628	−	84.7350i	−0.000354599	−	0.000257631i
$162$	−21231.8	+	15425.8i	−0.0635624	+	0.0461808i
$163$	−61790.6	+	190172.i	−0.182160	+	0.560631i	−0.999888	−	0.0149741i	$-0.995233\pi$
$163$	−61790.6	+	190172.i	−0.182160	+	0.560631i	0.817728	+	0.575605i	$0.195233\pi$
$164$	−21279.9			−0.0617818
$165$	−88842.4	+	66037.3i	−0.254045	+	0.188834i
$166$	406517.			1.14501
$167$	−19433.2	+	59809.3i	−0.0539205	+	0.165950i	−0.974390	−	0.224864i	$-0.927806\pi$
$167$	−19433.2	+	59809.3i	−0.0539205	+	0.165950i	0.920470	+	0.390814i	$0.127806\pi$
$168$	741.807	−	538.954i	0.00202777	−	0.00147326i
$169$	−408299.	−	296647.i	−1.09967	−	0.798955i
$170$	−14941.6	−	45985.4i	−0.0396528	−	0.122039i
$171$	53531.2	+	164752.i	0.139996	+	0.430864i
$172$	229464.	+	166716.i	0.591418	+	0.429690i
$173$	−485344.	+	352623.i	−1.23292	+	0.895767i	−0.997105	−	0.0760314i	$-0.975775\pi$
$173$	−485344.	+	352623.i	−1.23292	+	0.895767i	−0.235812	+	0.971799i	$0.575775\pi$
$174$	−11744.2	+	36144.9i	−0.0294070	+	0.0905053i
$175$	3479.30			0.00858810
$176$	−102730.	+	1118.41i	−0.249985	+	0.00272156i
$177$	−77229.0			−0.185288
$178$	−68973.1	+	212277.i	−0.163166	+	0.502173i
$179$	86352.3	−	62738.6i	0.201438	−	0.146353i	−0.482493	−	0.875900i	$-0.660269\pi$
$179$	86352.3	−	62738.6i	0.201438	−	0.146353i	0.683931	+	0.729546i	$0.260269\pi$
$180$	32134.8	+	23347.3i	0.0739255	+	0.0537100i
$181$	−56138.5	−	172777.i	−0.127369	−	0.392002i	0.866956	−	0.498385i	$-0.166073\pi$
$181$	−56138.5	−	172777.i	−0.127369	−	0.392002i	−0.994325	+	0.106382i	$0.966073\pi$
$182$	1841.62	+	5667.92i	0.00412118	+	0.0126837i
$183$	286494.	+	208150.i	0.632394	+	0.459461i
$184$	4688.90	−	3406.69i	0.0102100	−	0.00741801i
$185$	−109094.	+	335756.i	−0.234353	+	0.721265i
$186$	−150338.			−0.318630
$187$	−158269.	+	1723.06i	−0.330973	+	0.00360327i
$188$	−159765.			−0.329675
$189$	−358.609	+	1103.68i	−0.000730241	+	0.00224745i
$190$	212114.	−	154110.i	0.426271	−	0.309704i
$191$	299996.	+	217960.i	0.595021	+	0.432308i	0.844108	−	0.536173i	$-0.180131\pi$
$191$	299996.	+	217960.i	0.595021	+	0.432308i	−0.249087	+	0.968481i	$0.580131\pi$
$192$	11391.6	+	35059.7i	0.0223014	+	0.0686366i
$193$	62200.3	+	191433.i	0.120199	+	0.369933i	0.992996	−	0.118150i	$-0.0376963\pi$
$193$	62200.3	+	191433.i	0.120199	+	0.369933i	−0.872797	+	0.488083i	$0.837696\pi$
$194$	541528.	+	393443.i	1.03304	+	0.750546i
$195$	−208862.	+	151747.i	−0.393344	+	0.285782i
$196$	−83085.8	+	255712.i	−0.154485	+	0.475457i
$197$	329001.			0.603992			0.301996	−	0.953309i	$-0.402347\pi$
$197$	329001.			0.603992			0.301996	+	0.953309i	$0.402347\pi$
$198$	104354.	−	77567.4i	0.189168	−	0.140610i
$199$	729463.			1.30578			0.652891	−	0.757452i	$-0.273556\pi$
$199$	729463.			1.30578			0.652891	+	0.757452i	$0.273556\pi$
$200$	−43225.9	+	133036.i	−0.0764133	+	0.235176i
$201$	−48500.4	+	35237.6i	−0.0846750	+	0.0615200i
$202$	119755.	+	87007.0i	0.206497	+	0.150029i
$203$	519.316	+	1598.29i	0.000884487	+	0.00272217i
$204$	17550.4	+	54014.4i	0.0295264	+	0.0908729i
$205$	−32977.7	−	23959.7i	−0.0548070	−	0.0398196i
$206$	−255877.	+	185905.i	−0.420109	+	0.305227i
$207$	−2266.73	+	6976.29i	−0.00367684	+	0.0113162i
$208$	−239600.			−0.383997
$209$	−274089.	−	813323.i	−0.434036	−	1.28794i
$210$	1756.41			0.00274839
$211$	−182726.	+	562372.i	−0.282549	+	0.869595i	0.704574	+	0.709630i	$0.251138\pi$
$211$	−182726.	+	562372.i	−0.282549	+	0.869595i	−0.987123	+	0.159965i	$0.948862\pi$
$212$	328957.	−	239001.i	0.502689	−	0.365225i
$213$	−212686.	−	154525.i	−0.321210	−	0.233373i
$214$	−219690.	−	676137.i	−0.327926	−	1.00925i
$215$	167893.	+	516722.i	0.247706	+	0.762361i
$216$	−37745.5	−	27423.7i	−0.0550466	−	0.0399937i
$217$	−5378.18	+	3907.48i	−0.00775329	+	0.00563310i
$218$	24702.2	−	76025.7i	0.0352043	−	0.108348i
$219$	3463.51			0.00487985
$220$	−160460.	−	113933.i	−0.223517	−	0.158706i
$221$	−369137.			−0.508402
$222$	128141.	−	394379.i	0.174505	−	0.537071i
$223$	518643.	−	376816.i	0.698404	−	0.507420i	−0.181008	−	0.983482i	$-0.557936\pi$
$223$	518643.	−	376816.i	0.698404	−	0.507420i	0.879412	+	0.476062i	$0.157936\pi$
$224$	1318.77	+	958.141i	0.00175610	+	0.00127588i
$225$	−54707.7	−	168373.i	−0.0720431	−	0.221726i
$226$	−259098.	−	797421.i	−0.337437	−	1.03852i
$227$	325100.	+	236199.i	0.418748	+	0.304238i	0.777134	−	0.629335i	$-0.216673\pi$
$227$	325100.	+	236199.i	0.418748	+	0.304238i	−0.358386	+	0.933574i	$0.616673\pi$
$228$	−249149.	+	181018.i	−0.317412	+	0.230613i
$229$	104660.	−	322111.i	0.131884	−	0.405898i	−0.863208	−	0.504848i	$-0.831548\pi$
$229$	104660.	−	322111.i	0.131884	−	0.405898i	0.995092	+	0.0989502i	$0.0315484\pi$
$230$	11102.1			0.0138384
$231$	1717.08	−	5487.18i	0.00211719	−	0.00676580i
$232$	−67564.5			−0.0824135
$233$	359299.	−	1.10581e6i	0.433577	−	1.33441i	−0.460960	−	0.887421i	$-0.652495\pi$
$233$	359299.	−	1.10581e6i	0.433577	−	1.33441i	0.894537	−	0.446993i	$-0.147505\pi$
$234$	245329.	−	178242.i	0.292893	−	0.212800i
$235$	−247589.	−	179884.i	−0.292457	−	0.212482i
$236$	−42426.8	−	130576.i	−0.0495861	−	0.152610i
$237$	−71496.6	−	220044.i	−0.0826827	−	0.254471i
$238$	2031.75	+	1476.15i	0.00232502	+	0.00168923i
$239$	−868453.	+	630968.i	−0.983449	+	0.714517i	−0.958477	−	0.285171i	$-0.907950\pi$
$239$	−868453.	+	630968.i	−0.983449	+	0.714517i	−0.0249720	+	0.999688i	$0.507950\pi$
$240$	−21821.1	+	67158.6i	−0.0244540	+	0.0752616i
$241$	859568.			0.953318			0.476659	−	0.879088i	$-0.341848\pi$
$241$	859568.			0.953318			0.476659	+	0.879088i	$0.341848\pi$
$242$	−512805.	+	389910.i	−0.562877	+	0.427983i
$243$	59049.0			0.0641500
$244$	−194544.	+	598744.i	−0.209191	+	0.643824i
$245$	−416673.	+	302731.i	−0.443486	+	0.322211i
$246$	38735.6	+	28143.1i	0.0408106	+	0.0296506i
$247$	−618541.	−	1.90367e6i	−0.645099	−	1.98541i
$248$	−82590.4	−	254187.i	−0.0852708	−	0.262436i
$249$	−739978.	−	537625.i	−0.756345	−	0.549517i
$250$	−526718.	+	382683.i	−0.533001	+	0.387248i
$251$	−262893.	+	809101.i	−0.263387	+	0.810622i	0.728674	+	0.684861i	$0.240137\pi$
$251$	−262893.	+	809101.i	−0.263387	+	0.810622i	−0.992061	+	0.125761i	$0.959863\pi$
$252$	−2063.08			−0.00204651
$253$	10853.5	−	34684.0i	0.0106603	−	0.0340665i
$254$	453781.			0.441328
$255$	−33618.5	+	103467.i	−0.0323764	+	0.0996442i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	1.57308e6	+	1.14291e6i	1.48566	+	1.07939i	0.975678	+	0.219210i	$0.0703480\pi$
$257$	1.57308e6	+	1.14291e6i	1.48566	+	1.07939i	0.509982	+	0.860185i	$0.329652\pi$
$258$	−197207.	−	606941.i	−0.184448	−	0.567672i
$259$	−5666.28	−	17439.0i	−0.00524866	−	0.0161537i
$260$	−371310.	−	269773.i	−0.340646	−	0.247494i
$261$	69180.1	−	50262.3i	0.0628608	−	0.0456710i
$262$	38120.9	−	117324.i	0.0343091	−	0.105593i
$263$	2.00871e6			1.79072			0.895360	−	0.445342i	$-0.146918\pi$
$263$	2.00871e6			1.79072			0.895360	+	0.445342i	$0.146918\pi$
$264$	188477.	+	133826.i	0.166436	+	0.118176i
$265$	778887.			0.681333
$266$	−4208.17	+	12951.4i	−0.00364661	+	0.0112231i
$267$	406291.	−	295188.i	0.348786	−	0.253408i
$268$	−86222.9	−	62644.6i	−0.0733307	−	0.0532778i
$269$	−549282.	−	1.69052e6i	−0.462822	−	1.42442i	−0.861701	−	0.507417i	$-0.830600\pi$
$269$	−549282.	−	1.69052e6i	−0.462822	−	1.42442i	0.398878	−	0.917004i	$-0.369400\pi$
$270$	−27617.4	−	84997.6i	−0.0230554	−	0.0709573i
$271$	−149494.	−	108614.i	−0.123652	−	0.0898383i	0.524240	−	0.851570i	$-0.324349\pi$
$271$	−149494.	−	108614.i	−0.123652	−	0.0898383i	−0.647892	+	0.761732i	$0.724349\pi$
$272$	−81684.3	+	59347.1i	−0.0669447	+	0.0486382i
$273$	4143.64	−	12752.8i	0.00336493	−	0.0103562i
$274$	−1.12257e6			−0.903309
$275$	280113.	+	831198.i	0.223358	+	0.662786i
$276$	−13040.5			−0.0103044
$277$	−444058.	+	1.36667e6i	−0.347729	+	1.07020i	0.612378	+	0.790565i	$0.290213\pi$
$277$	−444058.	+	1.36667e6i	−0.347729	+	1.07020i	−0.960107	+	0.279634i	$0.909787\pi$
$278$	660261.	−	479707.i	0.512393	−	0.372275i
$279$	273659.	+	198825.i	0.210474	+	0.152919i
$280$	964.908	+	2969.68i	0.000735514	+	0.00226368i
$281$	−61549.6	−	189430.i	−0.0465007	−	0.143114i	0.925110	−	0.379698i	$-0.123972\pi$
$281$	−61549.6	−	189430.i	−0.0465007	−	0.143114i	−0.971611	+	0.236584i	$0.923972\pi$
$282$	290818.	+	211292.i	0.217770	+	0.158219i
$283$	−1.12417e6	+	816760.i	−0.834386	+	0.606217i	−0.920797	−	0.390043i	$-0.872460\pi$
$283$	−1.12417e6	+	816760.i	−0.834386	+	0.606217i	0.0864107	+	0.996260i	$0.472460\pi$
$284$	144424.	−	444492.i	0.106254	−	0.327016i
$285$	−589922.			−0.430212
$286$	−1.20579e6	+	896274.i	−0.871679	+	0.647926i
$287$	2117.20			0.00151725
$288$	25631.1	−	78884.4i	0.0182090	−	0.0560415i
$289$	1.02284e6	−	743138.i	0.720384	−	0.523390i
$290$	−104705.	−	76072.9i	−0.0731095	−	0.0531172i
$291$	−465402.	−	1.43236e6i	−0.322178	−	0.991561i
$292$	1902.73	+	5855.99i	0.00130593	+	0.00401923i
$293$	1.83865e6	+	1.33586e6i	1.25121	+	0.909057i	0.998291	−	0.0584304i	$-0.0186096\pi$
$293$	1.83865e6	+	1.33586e6i	1.25121	+	0.909057i	0.252918	+	0.967488i	$0.418610\pi$
$294$	489424.	−	355587.i	0.330230	−	0.239926i
$295$	81270.5	−	250125.i	0.0543723	−	0.167341i
$296$	737199.			0.489053
$297$	−292539.	+	3184.84i	−0.192439	+	0.00209506i
$298$	−959305.			−0.625772
$299$	26191.6	−	80609.5i	0.0169428	−	0.0521445i
$300$	254625.	−	184996.i	0.163342	−	0.118675i
$301$	−22830.0	−	16587.0i	−0.0145241	−	0.0105524i
$302$	592494.	+	1.82351e6i	0.373824	+	1.15051i
$303$	−102920.	−	316756.i	−0.0644012	−	0.198206i
$304$	−442932.	−	321809.i	−0.274886	−	0.199717i
$305$	−975631.	+	708837.i	−0.600532	+	0.436312i
$306$	39488.3	−	121532.i	0.0241082	−	0.0741974i
$307$	2.98610e6			1.80825			0.904125	−	0.427268i	$-0.140524\pi$
$307$	2.98610e6			1.80825			0.904125	+	0.427268i	$0.140524\pi$
$308$	10220.8	−	111.273i	0.00613917	−	6.68366e-5i
$309$	711632.			0.423993
$310$	158206.	−	486907.i	0.0935014	−	0.287768i
$311$	−706342.	+	513187.i	−0.414108	+	0.300867i	−0.775263	−	0.631639i	$-0.782383\pi$
$311$	−706342.	+	513187.i	−0.414108	+	0.300867i	0.361155	+	0.932506i	$0.382383\pi$
$312$	436141.	+	316875.i	0.253653	+	0.184290i
$313$	153869.	+	473561.i	0.0887750	+	0.273221i	0.985581	−	0.169202i	$-0.0541189\pi$
$313$	153869.	+	473561.i	0.0887750	+	0.273221i	−0.896806	+	0.442423i	$0.854119\pi$
$314$	−169757.	−	522459.i	−0.0971636	−	0.299039i
$315$	−3197.17	−	2322.88i	−0.00181547	−	0.00131902i
$316$	332765.	−	241768.i	0.187465	−	0.136201i
$317$	−847270.	+	2.60763e6i	−0.473559	+	1.45746i	0.374333	+	0.927294i	$0.377872\pi$
$317$	−847270.	+	2.60763e6i	−0.473559	+	1.45746i	−0.847892	+	0.530169i	$0.822128\pi$
$318$	−914880.			−0.507337
$319$	−340019.	+	252739.i	−0.187080	+	0.139058i
$320$	−125537.			−0.0685327
$321$	−494303.	+	1.52131e6i	−0.267751	+	0.824052i
$322$	−466.511	+	338.940i	−0.000250739	+	0.000182173i
$323$	−682399.	−	495792.i	−0.363942	−	0.264419i
$324$	32439.4	+	99838.1i	0.0171676	+	0.0528365i
$325$	632136.	+	1.94551e6i	0.331972	+	1.02171i
$326$	647079.	+	470130.i	0.337220	+	0.245005i
$327$	−145510.	+	105720.i	−0.0752532	+	0.0546746i
$328$	−26303.4	+	80953.7i	−0.0134998	+	0.0415482i
$329$	15895.4			0.00809622
$330$	141406.	+	419603.i	0.0714796	+	0.212106i
$331$	−3.59901e6			−1.80557			−0.902783	−	0.430097i	$-0.858479\pi$
$331$	−3.59901e6			−1.80557			−0.902783	+	0.430097i	$0.858479\pi$
$332$	502482.	−	1.54648e6i	0.250193	−	0.770016i
$333$	−754827.	+	548414.i	−0.373024	+	0.271018i
$334$	203507.	+	147857.i	0.0998192	+	0.0725229i
$335$	−63087.0	−	194162.i	−0.0307134	−	0.0945262i
$336$	−1133.38	−	3488.19i	−0.000547681	−	0.00168559i
$337$	1.12157e6	+	814866.i	0.537961	+	0.390851i	0.823327	−	0.567567i	$-0.192115\pi$
$337$	1.12157e6	+	814866.i	0.537961	+	0.390851i	−0.285366	+	0.958418i	$0.592115\pi$
$338$	−1.63320e6	+	1.18659e6i	−0.777583	+	0.564947i
$339$	−582970.	+	1.79420e6i	−0.275516	+	0.847951i
$340$	−193408.			−0.0907353
$341$	−1.36648e6	−	970253.i	−0.636380	−	0.451855i
$342$	692922.			0.320346
$343$	16534.1	−	50886.7i	0.00758832	−	0.0233544i
$344$	917858.	−	666863.i	0.418195	−	0.303837i
$345$	−20209.1	−	14682.7i	−0.00914110	−	0.00664140i
$346$	741539.	+	2.28222e6i	0.333000	+	1.02487i
$347$	−406747.	−	1.25184e6i	−0.181343	−	0.558116i	0.818523	−	0.574473i	$-0.194793\pi$
$347$	−406747.	−	1.25184e6i	−0.181343	−	0.558116i	−0.999866	+	0.0163575i	$0.994793\pi$
$348$	122987.	+	89355.1i	0.0544390	+	0.0395523i
$349$	1.62828e6	−	1.18301e6i	0.715592	−	0.519908i	−0.169381	−	0.985551i	$-0.554177\pi$
$349$	1.62828e6	−	1.18301e6i	0.715592	−	0.519908i	0.884973	+	0.465643i	$0.154177\pi$
$350$	4300.66	−	13236.1i	0.00187657	−	0.00577549i
$351$	−682298.			−0.295601
$352$	−122726.	+	392189.i	−0.0527935	+	0.168709i
$353$	−1.49229e6			−0.637407			−0.318703	−	0.947854i	$-0.603247\pi$
$353$	−1.49229e6			−0.637407			−0.318703	+	0.947854i	$0.603247\pi$
$354$	−95460.3	+	293797.i	−0.0404869	+	0.124606i
$355$	724283.	−	526222.i	0.305026	−	0.221615i
$356$	722296.	+	524778.i	0.302058	+	0.219458i
$357$	−1746.13	−	5374.04i	−0.000725114	−	0.00223167i
$358$	−131935.	−	406053.i	−0.0544065	−	0.167446i
$359$	−3.42308e6	−	2.48702e6i	−1.40178	−	1.01846i	−0.994454	−	0.105176i	$-0.966460\pi$
$359$	−3.42308e6	−	2.48702e6i	−1.40178	−	1.01846i	−0.407331	−	0.913281i	$-0.633540\pi$
$360$	128539.	−	93389.2i	0.0522732	−	0.0379787i
$361$	648232.	−	1.99505e6i	0.261796	−	0.805724i
$362$	−726672.			−0.291452
$363$	1.44912e6	−	31556.5i	0.577213	−	0.0125696i
$364$	23838.4			0.00943027
$365$	−3644.76	+	11217.4i	−0.00143198	+	0.00440718i
$366$	1.14598e6	−	832600.i	0.447170	−	0.324888i
$367$	−2.75186e6	−	1.99934e6i	−1.06650	−	0.774858i	−0.0912208	−	0.995831i	$-0.529077\pi$
$367$	−2.75186e6	−	1.99934e6i	−1.06650	−	0.774858i	−0.975280	+	0.220972i	$0.929077\pi$
$368$	−7164.00	−	22048.5i	−0.00275763	−	0.00848711i
$369$	−33290.3	−	102457.i	−0.0127278	−	0.0391720i
$370$	1.14245e6	+	830035.i	0.433841	+	0.315204i
$371$	−32728.8	+	23778.9i	−0.0123451	+	0.00896925i
$372$	−185828.	+	571921.i	−0.0696233	+	0.214278i
$373$	3.01172e6			1.12084			0.560418	−	0.828210i	$-0.310640\pi$
$373$	3.01172e6			1.12084			0.560418	+	0.828210i	$0.310640\pi$
$374$	−189077.	+	604222.i	−0.0698971	+	0.223366i
$375$	1.46488e6			0.537929
$376$	−197480.	+	607781.i	−0.0720367	+	0.221706i
$377$	−799361.	+	580769.i	−0.289661	+	0.210451i
$378$	3755.40	+	2728.46i	0.00135184	+	0.000982172i
$379$	−550858.	−	1.69537e6i	−0.196989	−	0.606270i	−0.999948	−	0.0102349i	$-0.996742\pi$
$379$	−550858.	−	1.69537e6i	−0.196989	−	0.606270i	0.802959	−	0.596035i	$-0.203258\pi$
$380$	−324082.	−	997422.i	−0.115132	−	0.354340i
$381$	−826012.	−	600133.i	−0.291524	−	0.211804i
$382$	1.19998e6	−	871840.i	0.420743	−	0.305688i
$383$	1.68093e6	−	5.17336e6i	0.585533	−	1.80209i	−0.0115841	−	0.999933i	$-0.503687\pi$
$383$	1.68093e6	−	5.17336e6i	0.585533	−	1.80209i	0.597118	−	0.802154i	$-0.296313\pi$
$384$	147456.			0.0510310
$385$	15964.6	+	11335.5i	0.00548918	+	0.00389753i
$386$	805138.			0.275044
$387$	−443716.	+	1.36562e6i	−0.150601	+	0.463502i
$388$	2.16611e6	−	1.57377e6i	0.730469	−	0.530716i
$389$	−2.90304e6	−	2.10918e6i	−0.972699	−	0.706707i	−0.0166339	−	0.999862i	$-0.505295\pi$
$389$	−2.90304e6	−	2.10918e6i	−0.972699	−	0.706707i	−0.956065	+	0.293154i	$0.905295\pi$
$390$	319113.	+	982128.i	0.106239	+	0.326969i
$391$	−11037.1	−	33968.8i	−0.00365102	−	0.0112367i
$392$	870086.	+	632155.i	0.285988	+	0.207782i
$393$	−224554.	+	163148.i	−0.0733398	+	0.0532845i
$394$	406667.	−	1.25159e6i	0.131977	−	0.406184i
$395$	787904.			0.254086
$396$	−166095.	−	492865.i	−0.0532254	−	0.157939i
$397$	5.21167e6			1.65959			0.829795	−	0.558069i	$-0.188457\pi$
$397$	5.21167e6			1.65959			0.829795	+	0.558069i	$0.188457\pi$
$398$	901666.	−	2.77504e6i	0.285324	−	0.878137i
$399$	24788.5	−	18009.9i	0.00779504	−	0.00566343i
$400$	452667.	+	328882.i	0.141459	+	0.102776i
$401$	−198319.	−	610364.i	−0.0615891	−	0.189552i	0.915528	−	0.402255i	$-0.131773\pi$
$401$	−198319.	−	610364.i	−0.0615891	−	0.189552i	−0.977117	+	0.212703i	$0.931773\pi$
$402$	74102.0	+	228062.i	0.0228699	+	0.0703864i
$403$	−3.16207e6	−	2.29738e6i	−0.969859	−	0.704644i
$404$	479019.	−	348028.i	0.146016	−	0.106087i
$405$	−62139.1	+	191245.i	−0.0188247	+	0.0579364i
$406$	6722.17			0.00202392
$407$	3.70996e6	−	2.75765e6i	1.11016	−	0.825188i
$408$	227177.			0.0675636
$409$	−1.57118e6	+	4.83560e6i	−0.464428	+	1.42936i	0.395273	+	0.918564i	$0.370650\pi$
$409$	−1.57118e6	+	4.83560e6i	−0.464428	+	1.42936i	−0.859701	+	0.510798i	$0.829350\pi$
$410$	−131911.	+	95838.9i	−0.0387544	+	0.0281567i
$411$	2.04340e6	+	1.48461e6i	0.596689	+	0.433520i
$412$	390945.	+	1.20320e6i	0.113468	+	0.349218i
$413$	4221.15	+	12991.4i	0.00121774	+	0.00374783i
$414$	23737.6	+	17246.3i	0.00680668	+	0.00494534i
$415$	2.51993e6	−	1.83084e6i	0.718238	−	0.521831i
$416$	−296162.	+	911492.i	−0.0839065	+	0.258238i
$417$	−1.83629e6			−0.517130
$418$	−3.43286e6	+	37373.1i	−0.960981	+	0.0104621i
$419$	−2.44419e6			−0.680143			−0.340072	−	0.940400i	$-0.610451\pi$
$419$	−2.44419e6			−0.680143			−0.340072	+	0.940400i	$0.610451\pi$
$420$	2171.04	−	6681.78i	0.000600545	−	0.00184829i
$421$	−4.33962e6	+	3.15292e6i	−1.19329	+	0.866977i	−0.993608	−	0.112884i	$-0.963991\pi$
$421$	−4.33962e6	+	3.15292e6i	−1.19329	+	0.866977i	−0.199683	+	0.979861i	$0.563991\pi$
$422$	1.91353e6	+	1.39026e6i	0.523062	+	0.380027i
$423$	−249936.	−	769223.i	−0.0679169	−	0.209027i
$424$	−502601.	−	1.54685e6i	−0.135772	−	0.417862i
$425$	697397.	+	506689.i	0.187287	+	0.136072i
$426$	−850742.	+	618100.i	−0.227130	+	0.165019i
$427$	19355.7	−	59570.6i	0.00513734	−	0.0158111i
$428$	−2.84373e6			−0.750376
$429$	3.38022e6	−	36800.1i	0.886751	−	0.00965397i
$430$	2.17325e6			0.566812
$431$	1.69723e6	−	5.22353e6i	0.440095	−	1.35447i	−0.447679	−	0.894194i	$-0.647749\pi$
$431$	1.69723e6	−	5.22353e6i	0.440095	−	1.35447i	0.887774	−	0.460280i	$-0.152251\pi$
$432$	−150982.	+	109695.i	−0.0389238	+	0.0282798i
$433$	85891.1	+	62403.5i	0.0220155	+	0.0159952i	0.598739	−	0.800945i	$-0.295669\pi$
$433$	85891.1	+	62403.5i	0.0220155	+	0.0159952i	−0.576723	+	0.816940i	$0.695669\pi$
$434$	8217.13	+	25289.7i	0.00209409	+	0.00644496i
$435$	89986.2	+	276949.i	0.0228009	+	0.0701741i
$436$	−258685.	−	187946.i	−0.0651712	−	0.0473496i
$437$	156686.	−	113839.i	0.0392489	−	0.0285160i
$438$	4281.13	−	13176.0i	0.00106629	−	0.00328169i
$439$	−4.59366e6			−1.13762			−0.568811	−	0.822469i	$-0.692596\pi$
$439$	−4.59366e6			−1.13762			−0.568811	+	0.822469i	$0.692596\pi$
$440$	−631768.	+	469599.i	−0.155570	+	0.115637i
$441$	−1.36116e6			−0.333283
$442$	−456279.	+	1.40428e6i	−0.111090	+	0.341899i
$443$	−4.03165e6	+	2.92917e6i	−0.976053	+	0.709144i	−0.956823	−	0.290671i	$-0.906122\pi$
$443$	−4.03165e6	+	2.92917e6i	−0.976053	+	0.709144i	−0.0192303	+	0.999815i	$0.506122\pi$
$444$	−1.34192e6	−	974958.i	−0.323048	−	0.234708i
$445$	528485.	+	1.62651e6i	0.126512	+	0.389365i
$446$	−792416.	−	2.43881e6i	−0.188632	−	0.580551i
$447$	1.74621e6	+	1.26870e6i	0.413360	+	0.300323i
$448$	5275.07	−	3832.56i	0.00124175	−	0.000902183i
$449$	−1.94826e6	+	5.99612e6i	−0.456069	+	1.40364i	0.413806	+	0.910365i	$0.364199\pi$
$449$	−1.94826e6	+	5.99612e6i	−0.456069	+	1.40364i	−0.869875	+	0.493271i	$0.835801\pi$
$450$	−708152.			−0.164852
$451$	170452.	+	505794.i	0.0394603	+	0.117093i
$452$	−3.35383e6			−0.772139
$453$	1.33311e6	−	4.10290e6i	0.305226	−	0.939388i
$454$	1.30040e6	−	944797.i	0.296099	−	0.215129i
$455$	36942.6	+	26840.4i	0.00836565	+	0.00607800i
$456$	380666.	+	1.17157e6i	0.0857299	+	0.263850i
$457$	2.48617e6	+	7.65166e6i	0.556854	+	1.71382i	0.690997	+	0.722857i	$0.257172\pi$
$457$	2.48617e6	+	7.65166e6i	0.556854	+	1.71382i	−0.134144	+	0.990962i	$0.542828\pi$
$458$	−1.09602e6	−	796302.i	−0.244148	−	0.177384i
$459$	−232609.	+	169000.i	−0.0515341	+	0.0374417i
$460$	13723.0	−	42235.0i	0.00302381	−	0.00930632i
$461$	1.76141e6			0.386018			0.193009	−	0.981197i	$-0.438175\pi$
$461$	1.76141e6			0.386018			0.193009	+	0.981197i	$0.438175\pi$
$462$	−18752.0	−	13314.7i	−0.00408737	−	0.00290219i
$463$	−2.64405e6			−0.573214			−0.286607	−	0.958048i	$-0.592527\pi$
$463$	−2.64405e6			−0.573214			−0.286607	+	0.958048i	$0.592527\pi$
$464$	−83514.3	+	257031.i	−0.0180080	+	0.0554230i
$465$	−931923.	+	677082.i	−0.199870	+	0.145214i
$466$	−3.76263e6	−	2.73371e6i	−0.802651	−	0.583160i
$467$	2.51159e6	+	7.72987e6i	0.532912	+	1.64014i	0.748117	+	0.663567i	$0.230958\pi$
$467$	2.51159e6	+	7.72987e6i	0.532912	+	1.64014i	−0.215205	+	0.976569i	$0.569042\pi$
$468$	−374830.	−	1.15361e6i	−0.0791078	−	0.243469i
$469$	8578.54	+	6232.67i	0.00180087	+	0.00130841i
$470$	−990356.	+	719536.i	−0.206798	+	0.150248i
$471$	−381953.	+	1.17553e6i	−0.0793338	+	0.244164i
$472$	−549184.			−0.113465
$473$	2.12459e6	−	6.78943e6i	0.436639	−	1.39534i
$474$	−925472.			−0.189198
$475$	−1.44445e6	+	4.44557e6i	−0.293744	+	0.904052i
$476$	8126.99	−	5904.60i	0.00164404	−	0.00119446i
$477$	1.66534e6	+	1.20994e6i	0.335126	+	0.243483i
$478$	1.32688e6	+	4.08371e6i	0.265620	+	0.817496i
$479$	1.73466e6	+	5.33873e6i	0.345442	+	1.06316i	0.961347	+	0.275340i	$0.0887905\pi$
$479$	1.73466e6	+	5.33873e6i	0.345442	+	1.06316i	−0.615905	+	0.787821i	$0.711209\pi$
$480$	228514.	+	166025.i	0.0452699	+	0.0328905i
$481$	8.72186e6	−	6.33680e6i	1.71888	−	1.24884i
$482$	1.06248e6	−	3.26999e6i	0.208308	−	0.641105i
$483$	1297.44			0.000253057
$484$	849446.	+	2.43278e6i	0.164825	+	0.472052i
$485$	5.12880e6			0.990060
$486$	72988.6	−	224636.i	0.0140173	−	0.0431408i
$487$	−3.89340e6	+	2.82872e6i	−0.743886	+	0.540465i	−0.893926	−	0.448215i	$-0.852060\pi$
$487$	−3.89340e6	+	2.82872e6i	−0.743886	+	0.540465i	0.150040	+	0.988680i	$0.452060\pi$
$488$	2.03729e6	+	1.48018e6i	0.387261	+	0.281361i
$489$	−556115.	−	1.71155e6i	−0.105170	−	0.323680i
$490$	636619.	+	1.95931e6i	0.119781	+	0.368649i
$491$	3.15250e6	+	2.29042e6i	0.590134	+	0.428758i	0.842363	−	0.538910i	$-0.181164\pi$
$491$	3.15250e6	+	2.29042e6i	0.590134	+	0.428758i	−0.252229	+	0.967668i	$0.581164\pi$
$492$	154942.	−	112572.i	0.0288574	−	0.0209661i
$493$	−128665.	+	395991.i	−0.0238421	+	0.0733784i
$494$	−8.00657e6			−1.47614
$495$	297533.	−	950810.i	0.0545786	−	0.174414i
$496$	−1.06907e6			−0.195120
$497$	−14369.2	+	44223.7i	−0.00260940	+	0.00803090i
$498$	−2.95991e6	+	2.15050e6i	−0.534817	+	0.388567i
$499$	−6.68808e6	−	4.85918e6i	−1.20240	−	0.873598i	−0.207885	−	0.978153i	$-0.566658\pi$
$499$	−6.68808e6	−	4.85918e6i	−1.20240	−	0.873598i	−0.994519	+	0.104556i	$0.966658\pi$
$500$	804754.	+	2.47678e6i	0.143959	+	0.443060i
$501$	−174899.	−	538284.i	−0.0311310	−	0.0958114i
$502$	2.75305e6	+	2.00021e6i	0.487590	+	0.354255i
$503$	4.38776e6	−	3.18790e6i	0.773256	−	0.561803i	−0.129691	−	0.991554i	$-0.541399\pi$
$503$	4.38776e6	−	3.18790e6i	0.773256	−	0.561803i	0.902947	+	0.429751i	$0.141399\pi$
$504$	−2550.11	+	7848.42i	−0.000447179	+	0.00137628i
$505$	1.13420e6			0.197906
$506$	−118530.	−	84161.0i	−0.0205803	−	0.0146128i
$507$	4.54217e6			0.784772
$508$	560904.	−	1.72628e6i	0.0964338	−	0.296793i
$509$	−3.34715e6	+	2.43185e6i	−0.572639	+	0.416047i	−0.836063	−	0.548634i	$-0.815148\pi$
$509$	−3.34715e6	+	2.43185e6i	−0.572639	+	0.416047i	0.263424	+	0.964680i	$0.415148\pi$
$510$	352058.	+	255785.i	0.0599361	+	0.0435461i
$511$	−189.307	−	582.628i	−3.20712e−5	−	9.87049e-5i
$512$	81007.0	+	249314.i	0.0136568	+	0.0420312i
$513$	−1.26132e6	−	916402.i	−0.211608	−	0.153742i
$514$	6.29234e6	−	4.57165e6i	1.05052	−	0.763248i
$515$	−748873.	+	2.30479e6i	−0.124420	+	0.382925i
$516$	−2.55270e6			−0.422062
$517$	1.27971e6	+	3.79738e6i	0.210565	+	0.624825i
$518$	−73345.9			−0.0120102
$519$	1.66846e6	−	5.13500e6i	0.271893	−	0.836801i
$520$	−1.48524e6	+	1.07909e6i	−0.240873	+	0.175005i
$521$	4.82766e6	+	3.50750e6i	0.779188	+	0.566113i	0.904735	−	0.425974i	$-0.140069\pi$
$521$	4.82766e6	+	3.50750e6i	0.779188	+	0.566113i	−0.125547	+	0.992088i	$0.540069\pi$
$522$	−105698.	−	325304.i	−0.0169781	−	0.0522533i
$523$	1.77441e6	+	5.46108e6i	0.283661	+	0.873020i	0.986797	+	0.161964i	$0.0517828\pi$
$523$	1.77441e6	+	5.46108e6i	0.283661	+	0.873020i	−0.703135	+	0.711056i	$0.748217\pi$
$524$	−399207.	−	290041.i	−0.0635141	−	0.0461457i
$525$	−25333.3	+	18405.7i	−0.00401138	+	0.00291444i
$526$	2.48290e6	−	7.64159e6i	0.391287	−	1.20426i
$527$	−1.64706e6			−0.258334
$528$	742074.	−	551590.i	0.115841	−	0.0861057i
$529$	−6.42814e6			−0.998726
$530$	962757.	−	2.96306e6i	0.148877	−	0.458196i
$531$	562316.	−	408547.i	0.0865454	−	0.0628789i
$532$	44068.5	+	32017.6i	0.00675070	+	0.00490467i
$533$	384662.	+	1.18387e6i	0.0586491	+	0.180503i
$534$	−620758.	−	1.91050e6i	−0.0942039	−	0.289930i
$535$	−4.40696e6	−	3.20184e6i	−0.665663	−	0.483632i
$536$	−344892.	+	250578.i	−0.0518526	+	0.0376731i
$537$	−296853.	+	913619.i	−0.0444227	+	0.136719i
$538$	−7.11005e6			−1.05905
$539$	6.74343e6	−	73415.0i	0.999790	−	0.0108846i
$540$	−357487.			−0.0527565
$541$	1.81565e6	−	5.58800e6i	0.266710	−	0.820849i	−0.724584	−	0.689186i	$-0.757968\pi$
$541$	1.81565e6	−	5.58800e6i	0.266710	−	0.820849i	0.991295	−	0.131663i	$-0.0420317\pi$
$542$	−597976.	+	434455.i	−0.0874350	+	0.0635253i
$543$	1.32275e6	+	961036.i	0.192522	+	0.139875i
$544$	124803.	+	384103.i	0.0180812	+	0.0556481i
$545$	−189273.	−	582523.i	−0.0272959	−	0.0840082i
$546$	−43392.8	−	31526.7i	−0.00622925	−	0.00452582i
$547$	−5.94812e6	+	4.32156e6i	−0.849985	+	0.617550i	−0.925142	−	0.379621i	$-0.876054\pi$
$547$	−5.94812e6	+	4.32156e6i	−0.849985	+	0.617550i	0.0751567	+	0.997172i	$0.476054\pi$
$548$	−1.38757e6	+	4.27050e6i	−0.197380	+	0.607474i
$549$	−3.18713e6			−0.451304
$550$	3.50831e6	−	38194.6i	0.494528	−	0.00538387i
$551$	−2.25776e6			−0.316810
$552$	−16119.0	+	49609.2i	−0.00225160	+	0.00692970i
$553$	−33107.7	+	24054.2i	−0.00460380	+	0.00334486i
$554$	4.65024e6	+	3.37860e6i	0.643726	+	0.467694i
$555$	−981844.	−	3.02181e6i	−0.135304	−	0.416422i
$556$	−1.00879e6	−	3.10473e6i	−0.138393	−	0.425929i
$557$	−6.64030e6	−	4.82446e6i	−0.906880	−	0.658887i	0.0333437	−	0.999444i	$-0.489384\pi$
$557$	−6.64030e6	−	4.82446e6i	−0.906880	−	0.658887i	−0.940224	+	0.340557i	$0.889384\pi$
$558$	1.09464e6	−	795300.i	0.148828	−	0.108130i
$559$	5.12704e6	−	1.57794e7i	0.693964	−	2.13580i
$560$	12490.0			0.00168304
$561$	1.14327e6	−	849802.i	0.153370	−	0.114001i
$562$	−796715.			−0.106405
$563$	216678.	−	666868.i	0.0288101	−	0.0886684i	−0.935618	−	0.353015i	$-0.885156\pi$
$563$	216678.	−	666868.i	0.0288101	−	0.0886684i	0.964428	+	0.264347i	$0.0851564\pi$
$564$	1.16327e6	−	845166.i	0.153987	−	0.111878i
$565$	−5.19747e6	−	3.77618e6i	−0.684969	−	0.497659i
$566$	1.71758e6	+	5.28618e6i	0.225360	+	0.693587i
$567$	−3227.48	−	9933.15i	−0.000421605	−	0.00129757i
$568$	−1.51243e6	−	1.09885e6i	−0.196700	−	0.142911i
$569$	6.22955e6	−	4.52603e6i	0.806633	−	0.586053i	−0.106219	−	0.994343i	$-0.533875\pi$
$569$	6.22955e6	−	4.52603e6i	0.806633	−	0.586053i	0.912852	+	0.408290i	$0.133875\pi$
$570$	−729184.	+	2.24420e6i	−0.0940048	+	0.289317i
$571$	9.38506e6			1.20461			0.602306	−	0.798266i	$-0.294249\pi$
$571$	9.38506e6			1.20461			0.602306	+	0.798266i	$0.294249\pi$
$572$	1.91919e6	+	5.69495e6i	0.245261	+	0.727780i
$573$	−3.33734e6			−0.424633
$574$	2617.00	−	8054.29i	0.000331531	−	0.00102035i
$575$	−160130.	+	116341.i	−0.0201977	+	0.0146745i
$576$	−268412.	−	195013.i	−0.0337090	−	0.0244911i
$577$	3.56102e6	+	1.09597e7i	0.445282	+	1.37044i	0.882174	+	0.470923i	$0.156079\pi$
$577$	3.56102e6	+	1.09597e7i	0.445282	+	1.37044i	−0.436892	+	0.899514i	$0.643921\pi$
$578$	−1.56276e6	−	4.80969e6i	−0.194569	−	0.598822i
$579$	−1.46558e6	−	1.06481e6i	−0.181683	−	0.132000i
$580$	−418821.	+	304292.i	−0.0516962	+	0.0375595i
$581$	−49993.3	+	153863.i	−0.00614428	+	0.0189102i
$582$	−6.02429e6			−0.737222
$583$	−8.31566e6	−	5.90445e6i	−1.01327	−	0.719462i
$584$	24629.4			0.00298828
$585$	718004.	−	2.20979e6i	0.0867435	−	0.266969i
$586$	7.35460e6	−	5.34343e6i	0.884739	−	0.642800i
$587$	1.05188e7	+	7.64233e6i	1.26000	+	0.915441i	0.998758	−	0.0498333i	$-0.0158690\pi$
$587$	1.05188e7	+	7.64233e6i	1.26000	+	0.915441i	0.261239	+	0.965274i	$0.415869\pi$
$588$	−747773.	−	2.30141e6i	−0.0891921	−	0.274505i
$589$	−2.75987e6	−	8.49402e6i	−0.327794	−	1.00885i
$590$	−851076.	−	618343.i	−0.100656	−	0.0731306i
$591$	−2.39550e6	+	1.74043e6i	−0.282116	+	0.204969i
$592$	911228.	−	2.80447e6i	0.106862	−	0.328887i
$593$	−5.36206e6			−0.626173			−0.313087	−	0.949725i	$-0.601363\pi$
$593$	−5.36206e6			−0.626173			−0.313087	+	0.949725i	$0.601363\pi$
$594$	−349482.	+	1.11682e6i	−0.0406405	+	0.129873i
$595$	19242.6			0.00222829
$596$	−1.18577e6	+	3.64941e6i	−0.136736	+	0.420831i
$597$	−5.31134e6	+	3.85891e6i	−0.609913	+	0.443128i
$598$	−274282.	−	199278.i	−0.0313650	−	0.0227880i
$599$	−2.27155e6	−	6.99110e6i	−0.258675	−	0.796120i	−0.993083	−	0.117412i	$-0.962540\pi$
$599$	−2.27155e6	−	6.99110e6i	−0.258675	−	0.796120i	0.734408	−	0.678708i	$-0.237460\pi$
$600$	−389033.	−	1.19732e6i	−0.0441172	−	0.135779i
$601$	−1.10155e7	−	8.00324e6i	−1.24400	−	0.903816i	−0.246138	−	0.969235i	$-0.579162\pi$
$601$	−1.10155e7	−	8.00324e6i	−1.24400	−	0.903816i	−0.997858	+	0.0654192i	$0.979162\pi$
$602$	−91320.1	+	66347.9i	−0.0102701	+	0.00746167i
$603$	166729.	−	513140.i	0.0186732	−	0.0574702i
$604$	7.66940e6			0.855400
$605$	−1.42275e6	+	4.72652e6i	−0.158030	+	0.524993i
$606$	−1.33223e6			−0.147366
$607$	−69336.6	+	213396.i	−0.00763820	+	0.0235080i	−0.954803	−	0.297239i	$-0.903934\pi$
$607$	−69336.6	+	213396.i	−0.00763820	+	0.0235080i	0.947165	+	0.320747i	$0.103934\pi$
$608$	−1.77173e6	+	1.28724e6i	−0.194374	+	0.141221i
$609$	−12236.3	−	8890.18i	−0.00133692	−	0.000971331i
$610$	1.49063e6	+	4.58769e6i	0.162198	+	0.499194i
$611$	2.88795e6	+	8.88821e6i	0.312959	+	0.963188i
$612$	−413527.	−	300445.i	−0.0446298	−	0.0324255i
$613$	8.41246e6	−	6.11201e6i	0.904216	−	0.656951i	−0.0353296	−	0.999376i	$-0.511248\pi$
$613$	8.41246e6	−	6.11201e6i	0.904216	−	0.656951i	0.939545	+	0.342424i	$0.111248\pi$
$614$	3.69102e6	−	1.13598e7i	0.395117	−	1.21605i
$615$	366864.			0.0391127
$616$	12210.4	−	39019.9i	0.00129651	−	0.00414319i
$617$	−5.76529e6			−0.609688			−0.304844	−	0.952402i	$-0.598604\pi$
$617$	−5.76529e6			−0.609688			−0.304844	+	0.952402i	$0.598604\pi$
$618$	879625.	−	2.70721e6i	0.0926460	−	0.285135i
$619$	−9.55842e6	+	6.94460e6i	−1.00267	+	0.728485i	−0.962660	−	0.270714i	$-0.912740\pi$
$619$	−9.55842e6	+	6.94460e6i	−1.00267	+	0.728485i	−0.0400135	+	0.999199i	$0.512740\pi$
$620$	−1.65675e6	−	1.20370e6i	−0.173093	−	0.125759i
$621$	−20400.6	−	62786.6i	−0.00212283	−	0.00653338i
$622$	1.07919e6	+	3.32142e6i	0.111847	+	0.344229i
$623$	−71863.1	−	52211.6i	−0.00741798	−	0.00538948i
$624$	1.74456e6	−	1.26750e6i	0.179360	−	0.130313i
$625$	569094.	−	1.75149e6i	0.0582752	−	0.179353i
$626$	1.99172e6			0.203139
$627$	6.29821e6	+	4.47198e6i	0.639806	+	0.454288i
$628$	−2.19738e6			−0.222334
$629$	1.40387e6	−	4.32068e6i	0.141482	−	0.435437i
$630$	−12788.7	+	9291.53i	−0.00128373	+	0.000932687i
$631$	−8.15428e6	−	5.92443e6i	−0.815290	−	0.592343i	0.100069	−	0.994980i	$-0.468094\pi$
$631$	−8.15428e6	−	5.92443e6i	−0.815290	−	0.592343i	−0.915360	+	0.402637i	$0.868094\pi$
$632$	−508420.	−	1.56476e6i	−0.0506326	−	0.155831i
$633$	−1.64453e6	−	5.06134e6i	−0.163130	−	0.502061i
$634$	8.87273e6	+	6.44641e6i	0.876666	+	0.636935i
$635$	2.81291e6	−	2.04370e6i	0.276836	−	0.201133i
$636$	−1.13085e6	+	3.48041e6i	−0.110857	+	0.341183i
$637$	1.57279e7			1.53576
$638$	541190.	+	1.60591e6i	0.0526379	+	0.156196i
$639$	2.36604e6			0.229230
$640$	−155173.	+	477572.i	−0.0149749	+	0.0460881i
$641$	−444511.	+	322956.i	−0.0427305	+	0.0310455i	−0.608945	−	0.793212i	$-0.708407\pi$
$641$	−444511.	+	322956.i	−0.0427305	+	0.0310455i	0.566215	+	0.824258i	$0.308407\pi$
$642$	5.17641e6	+	3.76088e6i	0.495668	+	0.360124i
$643$	4.96547e6	+	1.52821e7i	0.473623	+	1.45766i	0.847806	+	0.530307i	$0.177923\pi$
$643$	4.96547e6	+	1.52821e7i	0.473623	+	1.45766i	−0.374183	+	0.927355i	$0.622077\pi$
$644$	712.765	+	2193.67i	6.77223e−5	+	0.000208428i
$645$	−3.95595e6	−	2.87416e6i	−0.374413	−	0.272027i
$646$	−2.72960e6	+	1.98317e6i	−0.257346	+	0.186973i
$647$	−4.18779e6	+	1.28887e7i	−0.393300	+	1.21045i	0.536977	+	0.843597i	$0.319566\pi$
$647$	−4.18779e6	+	1.28887e7i	−0.393300	+	1.21045i	−0.930277	+	0.366857i	$0.880434\pi$
$648$	419904.			0.0392837
$649$	−2.76377e6	+	2.05434e6i	−0.257567	+	0.191452i
$650$	8.18254e6			0.759635
$651$	18488.5	−	56901.9i	0.00170982	−	0.00526228i
$652$	2.58832e6	−	1.88052e6i	0.238451	−	0.173244i
$653$	−3.23232e6	−	2.34842e6i	−0.296641	−	0.215522i	0.429502	−	0.903066i	$-0.358689\pi$
$653$	−3.23232e6	−	2.34842e6i	−0.296641	−	0.215522i	−0.726143	+	0.687543i	$0.758689\pi$
$654$	222320.	+	684231.i	0.0203252	+	0.0625545i
$655$	−292089.	−	898959.i	−0.0266019	−	0.0818722i
$656$	275453.	+	200128.i	0.0249913	+	0.0181572i
$657$	−25218.3	+	18322.2i	−0.00227931	+	0.00165601i
$658$	19647.8	−	60469.8i	0.00176909	−	0.00544469i
$659$	−2.14695e7			−1.92578			−0.962892	−	0.269889i	$-0.913013\pi$
$659$	−2.14695e7			−1.92578			−0.962892	+	0.269889i	$0.913013\pi$
$660$	1.77105e6	−	19281.3i	0.158260	−	0.00172296i
$661$	6.17516e6			0.549724			0.274862	−	0.961484i	$-0.411368\pi$
$661$	6.17516e6			0.549724			0.274862	+	0.961484i	$0.411368\pi$
$662$	−4.44862e6	+	1.36914e7i	−0.394530	+	1.21424i
$663$	2.68774e6	−	1.95276e6i	0.237467	−	0.172530i
$664$	−5.26206e6	−	3.82311e6i	−0.463165	−	0.336509i
$665$	32243.8	+	99236.1i	0.00282743	+	0.00870193i
$666$	1.15327e6	+	3.54941e6i	0.100750	+	0.310078i
$667$	−77344.5	−	56194.1i	−0.00673155	−	0.00489075i
$668$	814030.	−	591427.i	0.0705828	−	0.0512814i
$669$	−1.78294e6	+	5.48731e6i	−0.154018	+	0.474018i
$670$	−816616.			−0.0702798
$671$	1.57896e7	−	171900.i	1.35383	−	0.0147390i
$672$	−14670.8			−0.00125323
$673$	−7.18765e6	+	2.21213e7i	−0.611715	+	1.88267i	−0.170207	+	0.985408i	$0.554444\pi$
$673$	−7.18765e6	+	2.21213e7i	−0.611715	+	1.88267i	−0.441508	+	0.897257i	$0.645556\pi$
$674$	4.48627e6	−	3.25946e6i	0.380396	−	0.276374i
$675$	1.28904e6	+	936543.i	0.108895	+	0.0791167i
$676$	2.49530e6	+	7.67975e6i	0.210018	+	0.646369i
$677$	−548695.	−	1.68871e6i	−0.0460108	−	0.141607i	0.925412	−	0.378963i	$-0.123719\pi$
$677$	−548695.	−	1.68871e6i	−0.0460108	−	0.141607i	−0.971423	+	0.237356i	$0.923719\pi$
$678$	6.10494e6	+	4.43550e6i	0.510044	+	0.370568i
$679$	−215512.	+	156579.i	−0.0179390	+	0.0130334i
$680$	−239065.	+	735767.i	−0.0198264	+	0.0610194i
$681$	−3.61661e6			−0.298837
$682$	−5.38012e6	+	3.99909e6i	−0.442926	+	0.329231i
$683$	4.78941e6			0.392853			0.196426	−	0.980519i	$-0.437066\pi$
$683$	4.78941e6			0.392853			0.196426	+	0.980519i	$0.437066\pi$
$684$	856499.	−	2.63603e6i	0.0699982	−	0.215432i
$685$	−6.95862e6	+	5.05573e6i	−0.566626	+	0.411678i
$686$	−173147.	−	125799.i	−0.0140477	−	0.0102063i
$687$	941942.	+	2.89900e6i	0.0761434	+	0.234345i
$688$	−1.40236e6	−	4.31603e6i	−0.112951	−	0.347627i
$689$	−1.92427e7	−	1.39806e7i	−1.54425	−	1.12196i
$690$	−80836.3	+	58731.0i	−0.00646373	+	0.00469618i
$691$	1.54728e6	−	4.76203e6i	0.123274	−	0.379400i	−0.870308	−	0.492507i	$-0.836081\pi$
$691$	1.54728e6	−	4.76203e6i	0.123274	−	0.379400i	0.993583	+	0.113108i	$0.0360805\pi$
$692$	9.59868e6			0.761985
$693$	16525.2	+	49036.5i	0.00130712	+	0.00387870i
$694$	−5.26504e6			−0.414957
$695$	1.93238e6	−	5.94726e6i	0.151751	−	0.467041i
$696$	491947.	−	357421.i	0.0384942	−	0.0279677i
$697$	424374.	+	308326.i	0.0330877	+	0.0240396i
$698$	−2.48779e6	−	7.65663e6i	−0.193275	−	0.594839i
$699$	3.23369e6	+	9.95229e6i	0.250326	+	0.770424i
$700$	−45037.0	−	32721.3i	−0.00347396	−	0.00252398i
$701$	−3.05642e6	+	2.22062e6i	−0.234919	+	0.170679i	−0.699017	−	0.715105i	$-0.746379\pi$
$701$	−3.05642e6	+	2.22062e6i	−0.234919	+	0.170679i	0.464098	+	0.885784i	$0.346379\pi$
$702$	−843367.	+	2.59562e6i	−0.0645913	+	0.198791i
$703$	2.46345e7			1.87999
$704$	1.34028e6	+	951651.i	0.101921	+	0.0723679i
$705$	2.75433e6			0.208710
$706$	−1.84457e6	+	5.67701e6i	−0.139278	+	0.428655i
$707$	−47658.9	+	34626.2i	−0.00358588	+	0.00260529i
$708$	999673.	+	726305.i	0.0749505	+	0.0544548i
$709$	617866.	+	1.90160e6i	0.0461614	+	0.142070i	0.971481	−	0.237119i	$-0.0762030\pi$
$709$	617866.	+	1.90160e6i	0.0461614	+	0.142070i	−0.925319	+	0.379189i	$0.876203\pi$
$710$	−1.10661e6	−	3.40578e6i	−0.0823848	−	0.253554i
$711$	1.68463e6	+	1.22395e6i	0.124977	+	0.0908009i
$712$	2.88918e6	−	2.09911e6i	0.213587	−	0.155180i
$713$	116865.	−	359672.i	0.00860912	−	0.0264962i
$714$	−22602.4			−0.00165924
$715$	−3.43793e6	+	1.09864e7i	−0.251496	+	0.803693i
$716$	−1.70780e6			−0.124496
$717$	2.98548e6	−	9.18835e6i	0.216878	−	0.667482i
$718$	−1.36923e7	+	9.94806e6i	−0.991212	+	0.720157i
$719$	−7.86754e6	−	5.71610e6i	−0.567566	−	0.412361i	0.266654	−	0.963792i	$-0.414082\pi$
$719$	−7.86754e6	−	5.71610e6i	−0.567566	−	0.412361i	−0.834220	+	0.551431i	$0.814082\pi$
$720$	−196390.	−	604427.i	−0.0141185	−	0.0434523i
$721$	−38896.1	−	119710.i	−0.00278656	−	0.00857614i
$722$	−6.78838e6	−	4.93204e6i	−0.484644	−	0.352114i
$723$	−6.25865e6	+	4.54717e6i	−0.445282	+	0.323516i
$724$	−898216.	+	2.76443e6i	−0.0636846	+	0.196001i
$725$	2.30738e6			0.163033
$726$	1.67116e6	−	5.55177e6i	0.117673	−	0.390922i
$727$	−4.16302e6			−0.292127			−0.146064	−	0.989275i	$-0.546660\pi$
$727$	−4.16302e6			−0.292127			−0.146064	+	0.989275i	$0.546660\pi$
$728$	29465.9	−	90686.7i	0.00206059	−	0.00634184i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	38168.4	+	27731.0i	0.00265092	+	0.00192601i
$731$	−2.16053e6	−	6.64944e6i	−0.149544	−	0.460248i
$732$	−1.75089e6	−	5.38870e6i	−0.120776	−	0.371712i
$733$	−7.37146e6	−	5.35568e6i	−0.506749	−	0.368175i	0.304840	−	0.952404i	$-0.401397\pi$
$733$	−7.37146e6	−	5.35568e6i	−0.506749	−	0.368175i	−0.811589	+	0.584229i	$0.801397\pi$
$734$	−1.10074e7	+	7.99737e6i	−0.754130	+	0.547908i
$735$	1.43239e6	−	4.40845e6i	0.0978012	−	0.301001i
$736$	−92732.8			−0.00631014
$737$	−798330.	+	2.55118e6i	−0.0541394	+	0.173010i
$738$	−430919.			−0.0291242
$739$	−3.50280e6	+	1.07805e7i	−0.235942	+	0.726154i	0.761053	+	0.648689i	$0.224683\pi$
$739$	−3.50280e6	+	1.07805e7i	−0.235942	+	0.726154i	−0.996995	+	0.0774647i	$0.975317\pi$
$740$	4.56978e6	−	3.32014e6i	0.306772	−	0.222883i
$741$	1.45743e7	+	1.05888e7i	0.975082	+	0.708438i
$742$	50005.1	+	153900.i	0.00333430	+	0.0102619i
$743$	−3.77186e6	−	1.16086e7i	−0.250659	−	0.771449i	−0.994654	−	0.103264i	$-0.967071\pi$
$743$	−3.77186e6	−	1.16086e7i	−0.250659	−	0.771449i	0.743995	−	0.668185i	$-0.232929\pi$
$744$	1.94602e6	+	1.41387e6i	0.128889	+	0.0936431i
$745$	−5.94658e6	+	4.32044e6i	−0.392533	+	0.285192i
$746$	3.72269e6	−	1.14573e7i	0.244912	−	0.753761i
$747$	8.23196e6			0.539762
$748$	2.06489e6	+	1.46615e6i	0.134940	+	0.0958131i
$749$	282930.			0.0184278
$750$	1.81070e6	−	5.57275e6i	0.117542	−	0.361757i
$751$	1.67934e7	−	1.22011e7i	1.08652	−	0.789404i	0.107713	−	0.994182i	$-0.465647\pi$
$751$	1.67934e7	−	1.22011e7i	1.08652	−	0.789404i	0.978808	+	0.204778i	$0.0656473\pi$
$752$	2.06804e6	+	1.50252e6i	0.133356	+	0.0968891i
$753$	−2.36603e6	−	7.28191e6i	−0.152067	−	0.468013i
$754$	1.22131e6	+	3.75882e6i	0.0782346	+	0.240781i
$755$	1.18854e7	+	8.63521e6i	0.758830	+	0.551323i
$756$	15021.6	−	10913.8i	0.000955898	−	0.000694500i
$757$	5.56063e6	−	1.71139e7i	0.352683	−	1.08545i	−0.604658	−	0.796485i	$-0.706690\pi$
$757$	5.56063e6	−	1.71139e7i	0.352683	−	1.08545i	0.957341	−	0.288961i	$-0.0933097\pi$
$758$	−7.13046e6			−0.450759
$759$	104455.	+	309955.i	0.00658147	+	0.0195297i
$760$	−4.19500e6			−0.263450
$761$	5.15403e6	−	1.58625e7i	0.322616	−	0.992909i	−0.649890	−	0.760029i	$-0.725185\pi$
$761$	5.15403e6	−	1.58625e7i	0.322616	−	0.992909i	0.972505	−	0.232881i	$-0.0748151\pi$
$762$	−3.30405e6	+	2.40053e6i	−0.206138	+	0.149768i
$763$	25737.3	+	18699.2i	0.00160048	+	0.00116282i
$764$	−1.83341e6	−	5.64267e6i	−0.113639	−	0.349745i
$765$	−302567.	−	931205.i	−0.0186925	−	0.0575296i
$766$	−1.76029e7	−	1.27892e7i	−1.08396	−	0.787541i
$767$	−6.49744e6	+	4.72066e6i	−0.398799	+	0.289744i
$768$	182266.	−	560956.i	0.0111507	−	0.0343183i
$769$	1.10319e7			0.672718			0.336359	−	0.941734i	$-0.390804\pi$
$769$	1.10319e7			0.672718			0.336359	+	0.941734i	$0.390804\pi$
$770$	62856.2	−	46721.6i	0.00382051	−	0.00283982i
$771$	−1.75000e7			−1.06023
$772$	995205.	−	3.06293e6i	0.0600993	−	0.184967i
$773$	2.77975e6	−	2.01961e6i	0.167324	−	0.121568i	−0.500972	−	0.865463i	$-0.667024\pi$
$773$	2.77975e6	−	2.01961e6i	0.167324	−	0.121568i	0.668296	+	0.743896i	$0.267024\pi$
$774$	4.64665e6	+	3.37599e6i	0.278797	+	0.202558i
$775$	2.82053e6	+	8.68070e6i	0.168685	+	0.519159i
$776$	−3.30952e6	−	1.01857e7i	−0.197293	−	0.607205i
$777$	133511.	+	97001.2i	0.00793347	+	0.00576401i
$778$	−1.16121e7	+	8.43672e6i	−0.687802	+	0.499717i
$779$	−878966.	+	2.70518e6i	−0.0518954	+	0.159718i
$780$	4.13068e6			0.243100
$781$	−1.17218e7	+	127614.i	−0.687648	+	0.00748635i
$782$	−142868.			−0.00835444
$783$	−237820.	+	731935.i	−0.0138626	+	0.0426646i
$784$	3.48035e6	−	2.52862e6i	0.202224	−	0.146924i
$785$	−3.40530e6	−	2.47410e6i	−0.197234	−	0.143299i
$786$	343088.	+	1.05592e6i	0.0198084	+	0.0609640i
$787$	3.53686e6	+	1.08853e7i	0.203555	+	0.626477i	0.999770	+	0.0214632i	$0.00683247\pi$
$787$	3.53686e6	+	1.08853e7i	0.203555	+	0.626477i	−0.796215	+	0.605014i	$0.793168\pi$
$788$	−4.25867e6	−	3.09411e6i	−0.244320	−	0.177509i
$789$	−1.46257e7	+	1.06262e7i	−0.836421	+	0.607695i
$790$	973903.	−	2.99737e6i	0.0555198	−	0.170872i
$791$	333682.			0.0189623
$792$	−2.08028e6	+	22647.7i	−0.117844	+	0.00128296i
$793$	3.68266e7			2.07960
$794$	6.44198e6	−	1.98264e7i	0.362634	−	1.11607i
$795$	−5.67119e6	+	4.12036e6i	−0.318241	+	0.231216i
$796$	−9.44237e6	−	6.86029e6i	−0.528200	−	0.383760i
$797$	−9.75593e6	−	3.00257e7i	−0.544030	−	1.67435i	−0.723285	−	0.690550i	$-0.757369\pi$
$797$	−9.75593e6	−	3.00257e7i	−0.544030	−	1.67435i	0.179254	−	0.983803i	$-0.442631\pi$
$798$	−37873.5	−	116563.i	−0.00210537	−	0.00647966i
$799$	3.18610e6	+	2.31484e6i	0.176560	+	0.128278i
$800$	1.81067e6	−	1.31553e6i	0.100026	−	0.0726733i
$801$	−1.39671e6	+	4.29862e6i	−0.0769172	+	0.236727i
$802$	−2.56710e6			−0.140931
$803$	123948.	−	92131.5i	0.00678344	−	0.00504219i
$804$	959196.			0.0523320
$805$	−1365.34	+	4202.07i	−7.42591e−5	+	0.000228546i
$806$	−1.26483e7	+	9.18951e6i	−0.685794	+	0.498259i
$807$	1.29423e7	+	9.40316e6i	0.699567	+	0.508265i
$808$	−731876.	−	2.25248e6i	−0.0394375	−	0.121376i
$809$	−1.02411e6	−	3.15188e6i	−0.0550142	−	0.169316i	0.919774	−	0.392448i	$-0.128372\pi$
$809$	−1.02411e6	−	3.15188e6i	−0.0550142	−	0.169316i	−0.974788	+	0.223132i	$0.928372\pi$
$810$	650729.	+	472783.i	0.0348488	+	0.0253191i
$811$	6.16149e6	−	4.47659e6i	0.328953	−	0.238998i	−0.411033	−	0.911620i	$-0.634832\pi$
$811$	6.16149e6	−	4.47659e6i	0.328953	−	0.238998i	0.739986	+	0.672622i	$0.234832\pi$
$812$	8309.05	−	25572.6i	0.000442244	−	0.00136109i
$813$	1.66306e6			0.0882434
$814$	−5.90495e6	−	1.75222e7i	−0.312360	−	0.926888i
$815$	6.12848e6			0.323190
$816$	280806.	−	864231.i	0.0147632	−	0.0454365i
$817$	3.06715e7	−	2.22841e7i	1.60761	−	1.16799i
$818$	1.64536e7	+	1.19543e7i	0.859763	+	0.624654i
$819$	37292.8	+	114775.i	0.00194274	+	0.00597915i
$820$	201542.	+	620282.i	0.0104672	+	0.0322147i
$821$	2.52833e7	+	1.83694e7i	1.30911	+	0.951122i	1.00000		9.54010e-5i	$3.03671e-5\pi$
$821$	2.52833e7	+	1.83694e7i	1.30911	+	0.951122i	0.309108	+	0.951027i	$0.399970\pi$
$822$	8.17359e6	−	5.93846e6i	0.421923	−	0.306545i
$823$	3.84034e6	−	1.18194e7i	0.197638	−	0.608267i	−0.802298	−	0.596924i	$-0.796389\pi$
$823$	3.84034e6	−	1.18194e7i	0.197638	−	0.608267i	0.999936	−	0.0113430i	$-0.00361067\pi$
$824$	5.06049e6			0.259642
$825$	−6.43664e6	−	4.57027e6i	−0.329249	−	0.233780i
$826$	54639.7			0.00278650
$827$	−8.60743e6	+	2.64909e7i	−0.437632	+	1.34689i	0.452732	+	0.891646i	$0.350449\pi$
$827$	−8.60743e6	+	2.64909e7i	−0.437632	+	1.34689i	−0.890365	+	0.455248i	$0.849551\pi$
$828$	94950.2	−	68985.4i	0.00481305	−	0.00349688i
$829$	−588896.	−	427858.i	−0.0297613	−	0.0216229i	0.572805	−	0.819692i	$-0.305855\pi$
$829$	−588896.	−	427858.i	−0.0297613	−	0.0216229i	−0.602566	+	0.798069i	$0.705855\pi$
$830$	−3.85011e6	−	1.18494e7i	−0.193990	−	0.597038i
$831$	−3.99652e6	−	1.23000e7i	−0.200761	−	0.617880i
$832$	3.10145e6	+	2.25333e6i	0.155330	+	0.112854i
$833$	5.36196e6	−	3.89569e6i	0.267739	−	0.194523i
$834$	−2.26977e6	+	6.98565e6i	−0.112997	+	0.347769i
$835$	1.92742e6			0.0956664
$836$	−4.10107e6	+	1.31056e7i	−0.202946	+	0.648545i
$837$	−3.04435e6			−0.150204
$838$	−3.02119e6	+	9.29826e6i	−0.148617	+	0.457395i
$839$	1.01777e7	−	7.39450e6i	0.499164	−	0.362664i	−0.309534	−	0.950888i	$-0.600173\pi$
$839$	1.01777e7	−	7.39450e6i	0.499164	−	0.362664i	0.808697	+	0.588225i	$0.200173\pi$
$840$	−22735.5	−	16518.3i	−0.00111175	−	0.000807731i
$841$	−5.99390e6	−	1.84473e7i	−0.292226	−	0.899380i
$842$	6.63035e6	+	2.04061e7i	0.322297	+	0.991928i
$843$	1.45025e6	+	1.05367e6i	0.0702868	+	0.0510664i
$844$	7.65411e6	−	5.56104e6i	0.369861	−	0.268720i
$845$	−4.77987e6	+	1.47109e7i	−0.230289	+	0.708758i
$846$	−3.23524e6			−0.155410
$847$	−84513.6	−	242044.i	−0.00404779	−	0.0115927i
$848$	−6.50581e6			−0.310679
$849$	3.86456e6	−	1.18939e7i	0.184006	−	0.566311i
$850$	2.78959e6	−	2.02675e6i	0.132432	−	0.0962174i
$851$	843910.	+	613136.i	0.0399459	+	0.0290224i
$852$	1.29982e6	+	4.00043e6i	0.0613456	+	0.188802i
$853$	764502.	+	2.35289e6i	0.0359754	+	0.110721i	0.967432	−	0.253133i	$-0.0814609\pi$
$853$	764502.	+	2.35289e6i	0.0359754	+	0.110721i	−0.931456	+	0.363854i	$0.881461\pi$
$854$	−202695.	−	147267.i	−0.00951040	−	0.00690971i
$855$	4.29532e6	−	3.12073e6i	0.200946	−	0.145996i
$856$	−3.51504e6	+	1.08182e7i	−0.163963	+	0.504627i
$857$	−3.29116e7			−1.53072			−0.765362	−	0.643600i	$-0.777440\pi$
$857$	−3.29116e7			−1.53072			−0.765362	+	0.643600i	$0.777440\pi$
$858$	4.03819e6	−	1.29046e7i	0.187270	−	0.598449i
$859$	−1.12463e7			−0.520028			−0.260014	−	0.965605i	$-0.583727\pi$
$859$	−1.12463e7			−0.520028			−0.260014	+	0.965605i	$0.583727\pi$
$860$	2.68629e6	−	8.26755e6i	0.123853	−	0.381180i
$861$	−15415.6	+	11200.1i	−0.000708685	+	0.000514890i
$862$	−1.77736e7	−	1.29133e7i	−0.814717	−	0.591927i
$863$	−6.23301e6	−	1.91832e7i	−0.284886	−	0.876788i	−0.986433	−	0.164165i	$-0.947507\pi$
$863$	−6.23301e6	−	1.91832e7i	−0.284886	−	0.876788i	0.701547	−	0.712623i	$-0.252493\pi$
$864$	230680.	+	709960.i	0.0105130	+	0.0323556i
$865$	1.48752e7	+	1.08074e7i	0.675961	+	0.491115i
$866$	343564.	−	249614.i	0.0155673	−	0.0113103i
$867$	−3.51622e6	+	1.08218e7i	−0.158865	+	0.488936i
$868$	106365.			0.00479180
$869$	−8.41194e6	−	5.97281e6i	−0.377874	−	0.268305i
$870$	1.16481e6			0.0521742
$871$	−1.92652e6	+	5.92923e6i	−0.0860456	+	0.264821i
$872$	−1.03474e6	+	751783.i	−0.0460830	+	0.0334812i
$873$	1.09659e7	+	7.96722e6i	0.486979	+	0.353811i
$874$	−239395.	−	736782.i	−0.0106008	−	0.0326258i
$875$	−80067.1	−	246421.i	−0.00353536	−	0.0108807i
$876$	−44832.6	−	32572.8i	−0.00197394	−	0.00143415i
$877$	−1.65220e7	+	1.20039e7i	−0.725375	+	0.527016i	−0.888097	−	0.459656i	$-0.847973\pi$
$877$	−1.65220e7	+	1.20039e7i	−0.725375	+	0.527016i	0.162722	+	0.986672i	$0.447973\pi$
$878$	−5.67808e6	+	1.74753e7i	−0.248579	+	0.765049i
$879$	−2.04543e7			−0.892919
$880$	1.00555e6	+	2.98384e6i	0.0437721	+	0.129888i
$881$	4.49818e6			0.195253			0.0976263	−	0.995223i	$-0.468875\pi$
$881$	4.49818e6			0.195253			0.0976263	+	0.995223i	$0.468875\pi$
$882$	−1.68249e6	+	5.17817e6i	−0.0728250	+	0.224132i
$883$	−3.08903e6	+	2.24431e6i	−0.133327	+	0.0968681i	−0.652450	−	0.757832i	$-0.726259\pi$
$883$	−3.08903e6	+	2.24431e6i	−0.133327	+	0.0968681i	0.519123	+	0.854700i	$0.326259\pi$
$884$	4.77821e6	+	3.47157e6i	0.205653	+	0.149416i
$885$	731435.	+	2.25112e6i	0.0313919	+	0.0966143i
$886$	6.15981e6	+	1.89580e7i	0.263623	+	0.811348i
$887$	1.74286e7	+	1.26626e7i	0.743794	+	0.540398i	0.893897	−	0.448273i	$-0.147961\pi$
$887$	1.74286e7	+	1.26626e7i	0.743794	+	0.540398i	−0.150103	+	0.988670i	$0.547961\pi$
$888$	−5.36766e6	+	3.89983e6i	−0.228430	+	0.165964i
$889$	−55805.8	+	171753.i	−0.00236824	+	0.00728868i
$890$	6.84085e6			0.289491
$891$	2.11317e6	−	1.57074e6i	0.0891745	−	0.0662842i
$892$	−1.02573e7			−0.431637
$893$	−6.59908e6	+	2.03099e7i	−0.276920	+	0.852272i
$894$	6.98485e6	−	5.07479e6i	0.292289	−	0.212361i
$895$	−2.64659e6	−	1.92286e6i	−0.110441	−	0.0802399i
$896$	−8059.59	−	24804.9i	−0.000335385	−	0.00103221i
$897$	235725.	+	725486.i	0.00978191	+	0.0301056i
$898$	2.04024e7	+	1.48232e7i	0.844289	+	0.613412i
$899$	−3.56667e6	+	2.59134e6i	−0.147185	+	0.106936i
$900$	−875324.	+	2.69397e6i	−0.0360216	+	0.110863i
$901$	−1.00231e7			−0.411330
$902$	2.13484e6	−	23241.8i	0.0873675	−	0.000951161i
$903$	253975.			0.0103651
$904$	−4.14556e6	+	1.27587e7i	−0.168718	+	0.519262i
$905$	−4.50453e6	+	3.27273e6i	−0.182822	+	0.132828i
$906$	−1.39605e7	−	1.01429e7i	−0.565043	−	0.410528i
$907$	−2.04718e6	−	6.30057e6i	−0.0826300	−	0.254309i	0.901203	−	0.433397i	$-0.142685\pi$
$907$	−2.04718e6	−	6.30057e6i	−0.0826300	−	0.254309i	−0.983833	+	0.179088i	$0.942685\pi$
$908$	−1.98684e6	−	6.11485e6i	−0.0799737	−	0.246134i
$909$	2.42504e6	+	1.76189e6i	0.0973438	+	0.0707244i
$910$	147771.	−	107362.i	0.00591540	−	0.00429779i
$911$	−9.43049e6	+	2.90241e7i	−0.376477	+	1.15868i	0.566000	+	0.824405i	$0.308490\pi$
$911$	−9.43049e6	+	2.90241e7i	−0.376477	+	1.15868i	−0.942477	+	0.334271i	$0.891510\pi$
$912$	4.92745e6			0.196171
$913$	−4.07825e7	+	443995.i	−1.61919	+	0.0176279i
$914$	3.21817e7			1.27422
$915$	3.35392e6	−	1.03223e7i	0.132434	−	0.407590i
$916$	−4.38407e6	+	3.18521e6i	−0.172639	+	0.125429i
$917$	39718.2	+	28856.9i	0.00155979	+	0.00113325i
$918$	355395.	+	1.09379e6i	0.0139189	+	0.0428379i
$919$	−4.79890e6	−	1.47695e7i	−0.187436	−	0.576869i	0.812546	−	0.582897i	$-0.198081\pi$
$919$	−4.79890e6	−	1.47695e7i	−0.187436	−	0.576869i	−0.999982	+	0.00602850i	$0.998081\pi$
$920$	−143709.	−	104411.i	−0.00559776	−	0.00406701i
$921$	−2.17423e7	+	1.57967e7i	−0.844608	+	0.613644i
$922$	2.17722e6	−	6.70080e6i	0.0843481	−	0.259597i
$923$	−2.73391e7			−1.05628
$924$	−73830.9	+	54879.2i	−0.00284484	+	0.00211460i
$925$	−2.51760e7			−0.967458
$926$	−3.26823e6	+	1.00586e7i	−0.125252	+	0.385486i
$927$	−5.18150e6	+	3.76458e6i	−0.198041	+	0.143886i
$928$	874573.	+	635414.i	0.0333370	+	0.0242207i
$929$	1.47381e7	+	4.53592e7i	0.560276	+	1.72435i	0.681587	+	0.731738i	$0.261290\pi$
$929$	1.47381e7	+	4.53592e7i	0.560276	+	1.72435i	−0.121311	+	0.992615i	$0.538710\pi$
$930$	1.42385e6	+	4.38216e6i	0.0539830	+	0.166143i
$931$	2.90752e7	+	2.11243e7i	1.09938	+	0.798746i
$932$	−1.50505e7	+	1.09348e7i	−0.567560	+	0.412357i
$933$	2.42819e6	−	7.47319e6i	0.0913225	−	0.281062i
$934$	3.25106e7			1.21943
$935$	1.54919e6	+	4.59703e6i	0.0579530	+	0.171968i
$936$	−4.85190e6			−0.181018
$937$	4.43316e6	−	1.36439e7i	0.164955	−	0.507678i	−0.834078	−	0.551646i	$-0.814000\pi$
$937$	4.43316e6	−	1.36439e7i	0.164955	−	0.507678i	0.999033	+	0.0439678i	$0.0139999\pi$
$938$	34314.2	−	24930.7i	0.00127340	−	0.000925182i
$939$	−3.62551e6	−	2.63409e6i	−0.134185	−	0.0974914i
$940$	1.51313e6	+	4.65694e6i	0.0558543	+	0.171902i
$941$	9.12708e6	+	2.80903e7i	0.336014	+	1.03415i	0.966220	+	0.257718i	$0.0829706\pi$
$941$	9.12708e6	+	2.80903e7i	0.336014	+	1.03415i	−0.630206	+	0.776428i	$0.717029\pi$
$942$	3.99987e6	+	2.90607e6i	0.146865	+	0.106704i
$943$	−97440.9	+	70794.9i	−0.00356831	+	0.00259253i
$944$	−678829.	+	2.08922e6i	−0.0247931	+	0.0763052i
$945$	35567.3			0.00129560
$946$	−2.32024e7	−	1.64746e7i	−0.842956	−	0.598532i
$947$	1.69481e7			0.614109			0.307054	−	0.951692i	$-0.400657\pi$
$947$	1.69481e7			0.614109			0.307054	+	0.951692i	$0.400657\pi$
$948$	−1.14395e6	+	3.52070e6i	−0.0413414	+	0.127236i
$949$	291392.	−	211709.i	0.0105030	−	0.00763087i
$950$	1.51265e7	+	1.09901e7i	0.543788	+	0.395085i
$951$	−7.62543e6	−	2.34687e7i	−0.273409	−	0.841467i
$952$	−12416.9	−	38215.4i	−0.000444040	−	0.00136661i
$953$	2.82219e7	+	2.05044e7i	1.00659	+	0.731333i	0.963492	−	0.267737i	$-0.0862760\pi$
$953$	2.82219e7	+	2.05044e7i	1.00659	+	0.731333i	0.0431019	+	0.999071i	$0.486276\pi$
$954$	6.66138e6	−	4.83977e6i	0.236970	−	0.172169i
$955$	3.51199e6	−	1.08088e7i	0.124608	−	0.383503i
$956$	1.71755e7			0.607805
$957$	1.13872e6	−	3.63896e6i	0.0401919	−	0.128439i
$958$	2.24539e7			0.790456
$959$	138053.	−	424883.i	0.00484729	−	0.0149184i
$960$	914056.	−	664101.i	0.0320107	−	0.0232571i
$961$	9.05261e6	+	6.57711e6i	0.316203	+	0.229735i
$962$	−1.33258e7	−	4.10127e7i	−0.464255	−	1.42883i
$963$	−4.44873e6	−	1.36918e7i	−0.154586	−	0.475767i
$964$	−1.11265e7	−	8.08386e6i	−0.385625	−	0.280173i
$965$	4.99092e6	−	3.62612e6i	0.172529	−	0.125350i
$966$	1603.72	−	4935.75i	5.52950e−5	−	0.000170181i
$967$	4.59896e6			0.158159			0.0790794	−	0.996868i	$-0.474802\pi$
$967$	4.59896e6			0.158159			0.0790794	+	0.996868i	$0.474802\pi$
$968$	1.03048e7	−	224402.i	0.353470	−	0.00769729i
$969$	7.59142e6			0.259725
$970$	6.33955e6	−	1.95111e7i	0.216336	−	0.665814i
$971$	1.96705e7	−	1.42914e7i	0.669525	−	0.486438i	−0.200341	−	0.979726i	$-0.564205\pi$
$971$	1.96705e7	−	1.42914e7i	0.669525	−	0.486438i	0.869866	+	0.493288i	$0.164205\pi$
$972$	−764346.	−	555330.i	−0.0259492	−	0.0188532i
$973$	100367.	+	308898.i	0.00339867	+	0.0104600i
$974$	5.94858e6	+	1.83079e7i	0.200917	+	0.618358i
$975$	−1.48946e7	−	1.08215e7i	−0.501784	−	0.364567i
$976$	8.14916e6	−	5.92071e6i	0.273835	−	0.198952i
$977$	1.29140e6	−	3.97452e6i	0.0432836	−	0.133213i	−0.927079	−	0.374865i	$-0.877689\pi$
$977$	1.29140e6	−	3.97452e6i	0.0432836	−	0.133213i	0.970363	+	0.241652i	$0.0776891\pi$
$978$	−7.19850e6			−0.240655
$979$	6.68767e6	−	2.13714e7i	0.223007	−	0.712650i
$980$	8.24057e6			0.274089
$981$	500220.	−	1.53952e6i	0.0165954	−	0.0510755i
$982$	1.26100e7	−	9.16169e6i	0.417288	−	0.303177i
$983$	−3.02818e7	−	2.20010e7i	−0.999534	−	0.726204i	−0.0375461	−	0.999295i	$-0.511954\pi$
$983$	−3.02818e7	−	2.20010e7i	−0.999534	−	0.726204i	−0.961988	+	0.273091i	$0.911954\pi$
$984$	−236731.	−	728583.i	−0.00779412	−	0.0239878i
$985$	−3.11596e6	−	9.58994e6i	−0.102330	−	0.314938i
$986$	1.34740e6	+	978944.i	0.0441372	+	0.0320675i
$987$	−115737.	+	84087.8i	−0.00378163	+	0.00274752i
$988$	−9.89666e6	+	3.04588e7i	−0.322549	+	0.992705i
$989$	1.60535e6			0.0521892
$990$	−3.24932e6	−	2.30715e6i	−0.105367	−	0.0748148i
$991$	−4.60166e7			−1.48844			−0.744218	−	0.667937i	$-0.767178\pi$
$991$	−4.60166e7			−1.48844			−0.744218	+	0.667937i	$0.767178\pi$
$992$	−1.32145e6	+	4.06699e6i	−0.0426354	+	0.131218i
$993$	2.62049e7	−	1.90390e7i	0.843354	−	0.612733i
$994$	150476.	+	109327.i	0.00483059	+	0.00350963i
$995$	−6.90874e6	−	2.12629e7i	−0.221228	−	0.680871i
$996$	4.52234e6	+	1.39183e7i	0.144449	+	0.444569i
$997$	−2.01777e7	−	1.46600e7i	−0.642887	−	0.467085i	0.217954	−	0.975959i	$-0.430062\pi$
$997$	−2.01777e7	−	1.46600e7i	−0.642887	−	0.467085i	−0.860841	+	0.508874i	$0.830062\pi$
$998$	−2.67523e7	+	1.94367e7i	−0.850228	+	0.617727i
$999$	2.59487e6	−	7.98617e6i	0.0822623	−	0.253177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.6.e.a.31.1	✓	8
3.2	odd	2		198.6.f.c.163.2		8
11.4	even	5		726.6.a.be.1.2		4
11.5	even	5	inner	66.6.e.a.49.1	yes	8
11.7	odd	10		726.6.a.bb.1.2		4
33.5	odd	10		198.6.f.c.181.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.6.e.a.31.1	✓	8	1.1	even	1	trivial
66.6.e.a.49.1	yes	8	11.5	even	5	inner
198.6.f.c.163.2		8	3.2	odd	2
198.6.f.c.181.2		8	33.5	odd	10
726.6.a.bb.1.2		4	11.7	odd	10
726.6.a.be.1.2		4	11.4	even	5

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	66.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-9.47098 - 29.1487i) q^{5} +(11.1246 + 34.2380i) q^{6} +(1.28786 + 0.935685i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-9.47098 - 29.1487i) q^{5} +(11.1246 + 34.2380i) q^{6} +(1.28786 + 0.935685i) q^{7} +(-51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} -122.595 q^{10} +(-119.850 + 382.997i) q^{11} +144.000 q^{12} +(-289.220 + 890.129i) q^{13} +(5.15144 - 3.74274i) q^{14} +(223.158 + 162.134i) q^{15} +(79.1084 + 243.470i) q^{16} +(121.877 + 375.100i) q^{17} +(-262.122 - 190.442i) q^{18} +(-1730.20 + 1257.07i) q^{19} +(-151.536 + 466.379i) q^{20} -14.3269 q^{21} +(1308.87 + 929.347i) q^{22} -90.5594 q^{23} +(177.994 - 547.809i) q^{24} +(1768.23 - 1284.70i) q^{25} +(3028.76 + 2200.52i) q^{26} +(225.273 + 693.320i) q^{27} +(-7.87070 - 24.2235i) q^{28} +(854.075 + 620.522i) q^{29} +(892.633 - 648.536i) q^{30} +(-1290.47 + 3971.67i) q^{31} +1024.00 q^{32} +(-1153.44 - 3422.68i) q^{33} +1577.61 q^{34} +(15.0767 - 46.4013i) q^{35} +(-1048.49 + 761.770i) q^{36} +(-9318.86 - 6770.54i) q^{37} +(2643.52 + 8135.91i) q^{38} +(-2602.98 - 8011.16i) q^{39} +(1586.90 + 1152.95i) q^{40} +(1075.99 - 781.752i) q^{41} +(-17.7091 + 54.5029i) q^{42} -17727.1 q^{43} +(5153.29 - 3830.49i) q^{44} -2482.55 q^{45} +(-111.938 + 344.508i) q^{46} +(8078.28 - 5869.21i) q^{47} +(-1863.98 - 1354.26i) q^{48} +(-5192.87 - 15982.0i) q^{49} +(-2701.62 - 8314.72i) q^{50} +(-2871.71 - 2086.42i) q^{51} +(12115.0 - 8802.08i) q^{52} +(-7853.15 + 24169.5i) q^{53} +2916.00 q^{54} +(12299.0 - 133.898i) q^{55} -101.880 q^{56} +(5947.91 - 18305.8i) q^{57} +(3416.30 - 2482.09i) q^{58} +(6942.17 + 5043.78i) q^{59} +(-1363.82 - 4197.41i) q^{60} +(-12159.0 - 37421.5i) q^{61} +(13514.0 + 9818.51i) q^{62} +(104.317 - 75.7905i) q^{63} +(1265.73 - 3895.53i) q^{64} +28685.3 q^{65} +(-14446.4 + 157.276i) q^{66} +6661.08 q^{67} +(1950.04 - 6001.60i) q^{68} +(659.377 - 479.065i) q^{69} +(-157.885 - 114.710i) q^{70} +(9026.52 + 27780.8i) q^{71} +(1601.94 + 4930.28i) q^{72} +(-311.338 - 226.200i) q^{73} +(-37275.4 + 27082.2i) q^{74} +(-6078.64 + 18708.1i) q^{75} +34218.4 q^{76} +(-512.715 + 381.105i) q^{77} -33693.7 q^{78} +(-7944.07 + 24449.3i) q^{79} +(6347.61 - 4611.81i) q^{80} +(-5307.96 - 3856.46i) q^{81} +(-1643.97 - 5059.60i) q^{82} +(31405.1 + 96655.1i) q^{83} +(185.452 + 134.739i) q^{84} +(9779.38 - 7105.14i) q^{85} +(-21911.9 + 67437.9i) q^{86} -9501.25 q^{87} +(-8202.22 - 24339.0i) q^{88} -55800.4 q^{89} +(-3068.60 + 9444.18i) q^{90} +(-1205.36 + 875.742i) q^{91} +(1172.22 + 851.671i) q^{92} +(-11614.3 - 35745.1i) q^{93} +(-12342.5 - 37986.3i) q^{94} +(53028.6 + 38527.5i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(-51711.3 + 159151. i) q^{97} -67217.9 q^{98} +(26504.5 + 18819.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 150 q^{5} - 72 q^{6} + 474 q^{7} - 128 q^{8} - 162 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 150 * q^5 - 72 * q^6 + 474 * q^7 - 128 * q^8 - 162 * q^9	\( 8 q - 8 q^{2} - 18 q^{3} - 32 q^{4} + 150 q^{5} - 72 q^{6} + 474 q^{7} - 128 q^{8} - 162 q^{9} - 1200 q^{10} - 582 q^{11} + 1152 q^{12} + 510 q^{13} + 1896 q^{14} - 512 q^{16} + 2004 q^{17} - 648 q^{18} - 540 q^{19} + 2400 q^{20} - 1224 q^{21} + 672 q^{22} - 9944 q^{23} - 1152 q^{24} + 12228 q^{25} - 600 q^{26} - 1458 q^{27} - 6496 q^{28} - 11964 q^{29} - 9160 q^{31} + 8192 q^{32} + 4302 q^{33} + 2896 q^{34} + 42634 q^{35} - 2592 q^{36} - 718 q^{37} + 7560 q^{38} + 4590 q^{39} - 1666 q^{41} - 14616 q^{42} - 70528 q^{43} - 32 q^{44} - 24300 q^{45} + 56664 q^{46} + 51914 q^{47} - 4608 q^{48} - 23052 q^{49} - 52888 q^{50} - 21294 q^{51} - 2400 q^{52} - 53636 q^{53} + 23328 q^{54} + 104980 q^{55} - 8704 q^{56} + 17010 q^{57} - 47856 q^{58} - 17600 q^{59} + 21600 q^{60} - 10618 q^{61} + 77640 q^{62} + 38394 q^{63} - 8192 q^{64} + 116324 q^{65} - 2232 q^{66} - 182364 q^{67} + 32064 q^{68} - 82746 q^{69} - 79104 q^{70} + 29954 q^{71} - 10368 q^{72} + 127228 q^{73} - 2872 q^{74} - 118998 q^{75} - 43200 q^{76} - 33046 q^{77} - 25920 q^{78} + 39938 q^{79} - 13122 q^{81} - 51624 q^{82} + 208842 q^{83} + 68256 q^{84} + 125910 q^{85} + 51528 q^{86} + 36864 q^{87} + 30592 q^{88} - 344008 q^{89} + 48600 q^{90} + 282622 q^{91} - 147104 q^{92} - 82440 q^{93} - 106544 q^{94} + 31306 q^{95} - 18432 q^{96} - 26202 q^{97} + 323072 q^{98} + 13608 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 18 * q^3 - 32 * q^4 + 150 * q^5 - 72 * q^6 + 474 * q^7 - 128 * q^8 - 162 * q^9 - 1200 * q^10 - 582 * q^11 + 1152 * q^12 + 510 * q^13 + 1896 * q^14 - 512 * q^16 + 2004 * q^17 - 648 * q^18 - 540 * q^19 + 2400 * q^20 - 1224 * q^21 + 672 * q^22 - 9944 * q^23 - 1152 * q^24 + 12228 * q^25 - 600 * q^26 - 1458 * q^27 - 6496 * q^28 - 11964 * q^29 - 9160 * q^31 + 8192 * q^32 + 4302 * q^33 + 2896 * q^34 + 42634 * q^35 - 2592 * q^36 - 718 * q^37 + 7560 * q^38 + 4590 * q^39 - 1666 * q^41 - 14616 * q^42 - 70528 * q^43 - 32 * q^44 - 24300 * q^45 + 56664 * q^46 + 51914 * q^47 - 4608 * q^48 - 23052 * q^49 - 52888 * q^50 - 21294 * q^51 - 2400 * q^52 - 53636 * q^53 + 23328 * q^54 + 104980 * q^55 - 8704 * q^56 + 17010 * q^57 - 47856 * q^58 - 17600 * q^59 + 21600 * q^60 - 10618 * q^61 + 77640 * q^62 + 38394 * q^63 - 8192 * q^64 + 116324 * q^65 - 2232 * q^66 - 182364 * q^67 + 32064 * q^68 - 82746 * q^69 - 79104 * q^70 + 29954 * q^71 - 10368 * q^72 + 127228 * q^73 - 2872 * q^74 - 118998 * q^75 - 43200 * q^76 - 33046 * q^77 - 25920 * q^78 + 39938 * q^79 - 13122 * q^81 - 51624 * q^82 + 208842 * q^83 + 68256 * q^84 + 125910 * q^85 + 51528 * q^86 + 36864 * q^87 + 30592 * q^88 - 344008 * q^89 + 48600 * q^90 + 282622 * q^91 - 147104 * q^92 - 82440 * q^93 - 106544 * q^94 + 31306 * q^95 - 18432 * q^96 - 26202 * q^97 + 323072 * q^98 + 13608 * q^99

Introduction

L-functions

Modular forms

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